ring_theory.power_series.basic ⟷ Mathlib.RingTheory.PowerSeries.Order

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

@@ -4,9 +4,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
 -/
 import Data.Finsupp.Interval
-import Data.MvPolynomial.Basic
-import Data.Polynomial.AlgebraMap
-import Data.Polynomial.Coeff
+import Algebra.MvPolynomial.Basic
+import Algebra.Polynomial.AlgebraMap
+import Algebra.Polynomial.Coeff
 import LinearAlgebra.StdBasis
 import RingTheory.Ideal.LocalRing
 import RingTheory.Multiplicity

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

@@ -486,7 +486,7 @@ theorem X_pow_eq (s : σ) (n : ℕ) : (X s : MvPowerSeries σ R) ^ n = monomial
   by
   induction' n with n ih
   · rw [pow_zero, Finsupp.single_zero, monomial_zero_one]
-  · rw [pow_succ', ih, Nat.succ_eq_add_one, Finsupp.single_add, X, monomial_mul_monomial, one_mul]
+  · rw [pow_succ, ih, Nat.succ_eq_add_one, Finsupp.single_add, X, monomial_mul_monomial, one_mul]
 #align mv_power_series.X_pow_eq MvPowerSeries.X_pow_eq
 -/
 

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

@@ -302,7 +302,7 @@ theorem commute_monomial {a : R} {n} : Commute φ (monomial R n a) ↔ ∀ m, Co
   by
   refine' ext_iff.trans ⟨fun h m => _, fun h m => _⟩
   · have := h (m + n)
-    rwa [coeff_add_mul_monomial, add_comm, coeff_add_monomial_mul] at this 
+    rwa [coeff_add_mul_monomial, add_comm, coeff_add_monomial_mul] at this
   · rw [coeff_mul_monomial, coeff_monomial_mul]
     split_ifs <;> [apply h; rfl]
 #align mv_power_series.commute_monomial MvPowerSeries.commute_monomial
@@ -388,10 +388,10 @@ theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
   ext k
   simp only [coeff_mul_monomial, coeff_monomial]
   split_ifs with h₁ h₂ h₃ h₃ h₂ <;> try rfl
-  · rw [← h₂, tsub_add_cancel_of_le h₁] at h₃ ; exact (h₃ rfl).elim
-  · rw [h₃, add_tsub_cancel_right] at h₂ ; exact (h₂ rfl).elim
+  · rw [← h₂, tsub_add_cancel_of_le h₁] at h₃; exact (h₃ rfl).elim
+  · rw [h₃, add_tsub_cancel_right] at h₂; exact (h₂ rfl).elim
   · exact MulZeroClass.zero_mul b
-  · rw [h₂] at h₁ ; exact (h₁ <| le_add_left le_rfl).elim
+  · rw [h₂] at h₁; exact (h₁ <| le_add_left le_rfl).elim
 #align mv_power_series.monomial_mul_monomial MvPowerSeries.monomial_mul_monomial
 -/
 
@@ -613,10 +613,9 @@ theorem smul_eq_C_mul (f : MvPowerSeries σ R) (a : R) : a • f = C σ R a * f
 #print MvPowerSeries.X_inj /-
 theorem X_inj [Nontrivial R] {s t : σ} : (X s : MvPowerSeries σ R) = X t ↔ s = t :=
   ⟨by
-    intro h; replace h := congr_arg (coeff R (single s 1)) h;
-    rw [coeff_X, if_pos rfl, coeff_X] at h 
-    split_ifs at h  with H
-    · rw [Finsupp.single_eq_single_iff] at H 
+    intro h; replace h := congr_arg (coeff R (single s 1)) h; rw [coeff_X, if_pos rfl, coeff_X] at h
+    split_ifs at h with H
+    · rw [Finsupp.single_eq_single_iff] at H
       cases H; · exact H.1; · exfalso; exact one_ne_zero H.1
     · exfalso; exact one_ne_zero h, congr_arg X⟩
 #align mv_power_series.X_inj MvPowerSeries.X_inj
@@ -821,21 +820,21 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
   · rintro ⟨φ, rfl⟩ m h
     rw [coeff_mul, Finset.sum_eq_zero]
     rintro ⟨i, j⟩ hij; rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
-    contrapose! h; subst i; rw [Finsupp.mem_antidiagonal] at hij 
+    contrapose! h; subst i; rw [Finsupp.mem_antidiagonal] at hij
     rw [← hij, Finsupp.add_apply, Finsupp.single_eq_same]; exact Nat.le_add_right n _
   · intro h; refine' ⟨fun m => coeff R (m + single s n) φ, _⟩
     ext m; by_cases H : m - single s n + single s n = m
     · rw [coeff_mul, Finset.sum_eq_single (single s n, m - single s n)]
       · rw [coeff_X_pow, if_pos rfl, one_mul]
         simpa using congr_arg (fun m : σ →₀ ℕ => coeff R m φ) H.symm
-      · rintro ⟨i, j⟩ hij hne; rw [Finsupp.mem_antidiagonal] at hij 
+      · rintro ⟨i, j⟩ hij hne; rw [Finsupp.mem_antidiagonal] at hij
         rw [coeff_X_pow]; split_ifs with hi
         · exfalso; apply hne; rw [← hij, ← hi, Prod.mk.inj_iff]; refine' ⟨rfl, _⟩
           ext t; simp only [add_tsub_cancel_left, Finsupp.add_apply, Finsupp.tsub_apply]
         · exact MulZeroClass.zero_mul _
       · intro hni; exfalso; apply hni; rwa [Finsupp.mem_antidiagonal, add_comm]
     · rw [h, coeff_mul, Finset.sum_eq_zero]
-      · rintro ⟨i, j⟩ hij; rw [Finsupp.mem_antidiagonal] at hij 
+      · rintro ⟨i, j⟩ hij; rw [Finsupp.mem_antidiagonal] at hij
         rw [coeff_X_pow]; split_ifs with hi
         · exfalso; apply H; rw [← hij, hi]; ext
           rw [coe_add, coe_add, Pi.add_apply, Pi.add_apply, add_tsub_cancel_left, add_comm]
@@ -940,7 +939,7 @@ theorem mul_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) (h : constantCoeff σ
         Finset.insert_erase this, Finset.sum_insert (Finset.not_mem_erase _ _),
         Finset.insert_erase this, if_neg (not_lt_of_ge <| le_rfl), zero_add, add_comm, ←
         sub_eq_add_neg, sub_eq_zero, Finset.sum_congr rfl]
-      rintro ⟨i, j⟩ hij; rw [Finset.mem_erase, Finsupp.mem_antidiagonal] at hij 
+      rintro ⟨i, j⟩ hij; rw [Finset.mem_erase, Finsupp.mem_antidiagonal] at hij
       cases' hij with h₁ h₂
       subst n; rw [if_pos]
       suffices (0 : _) + j < i + j by simpa
@@ -984,9 +983,9 @@ instance map.isLocalRingHom : IsLocalRingHom (map σ f) :=
   ⟨by
     rintro φ ⟨ψ, h⟩
     replace h := congr_arg (constant_coeff σ S) h
-    rw [constant_coeff_map] at h 
+    rw [constant_coeff_map] at h
     have : IsUnit (constant_coeff σ S ↑ψ) := @is_unit_constant_coeff σ S _ (↑ψ) ψ.is_unit
-    rw [h] at this 
+    rw [h] at this
     rcases isUnit_of_map_unit f _ this with ⟨c, hc⟩
     exact isUnit_of_mul_eq_one φ (inv_of_unit φ c) (mul_inv_of_unit φ c hc.symm)⟩
 #align mv_power_series.map.is_local_ring_hom MvPowerSeries.map.isLocalRingHom
@@ -1099,12 +1098,12 @@ protected theorem mul_inv_rev (φ ψ : MvPowerSeries σ k) : (φ * ψ)⁻¹ = ψ
   by
   by_cases h : constant_coeff σ k (φ * ψ) = 0
   · rw [inv_eq_zero.mpr h]
-    simp only [map_mul, mul_eq_zero] at h 
+    simp only [map_mul, mul_eq_zero] at h
     -- we don't have `no_zero_divisors (mw_power_series σ k)` yet,
       cases h <;>
       simp [inv_eq_zero.mpr h]
   · rw [MvPowerSeries.inv_eq_iff_mul_eq_one h]
-    simp only [not_or, map_mul, mul_eq_zero] at h 
+    simp only [not_or, map_mul, mul_eq_zero] at h
     rw [← mul_assoc, mul_assoc _⁻¹, MvPowerSeries.inv_mul_cancel _ h.left, mul_one,
       MvPowerSeries.inv_mul_cancel _ h.right]
 #align mv_power_series.mul_inv_rev MvPowerSeries.mul_inv_rev
@@ -1631,14 +1630,14 @@ theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
   by
   symm
   apply Finset.sum_bij fun (p : ℕ × ℕ) h => (single () p.1, single () p.2)
-  · rintro ⟨i, j⟩ hij; rw [Finset.Nat.mem_antidiagonal] at hij 
+  · rintro ⟨i, j⟩ hij; rw [Finset.Nat.mem_antidiagonal] at hij
     rw [Finsupp.mem_antidiagonal, ← Finsupp.single_add, hij]
   · rintro ⟨i, j⟩ hij; rfl
   · rintro ⟨i, j⟩ ⟨k, l⟩ hij hkl
     simpa only [Prod.mk.inj_iff, Finsupp.unique_single_eq_iff] using id
   · rintro ⟨f, g⟩ hfg
     refine' ⟨(f (), g ()), _, _⟩
-    · rw [Finsupp.mem_antidiagonal] at hfg 
+    · rw [Finsupp.mem_antidiagonal] at hfg
       rw [Finset.Nat.mem_antidiagonal, ← Finsupp.add_apply, hfg, Finsupp.single_eq_same]
     · rw [Prod.mk.inj_iff]; dsimp
       exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
@@ -1754,7 +1753,7 @@ theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * X
   by
   rw [coeff_mul, Finset.sum_eq_single (d, n), coeff_X_pow, if_pos rfl, mul_one]
   · rintro ⟨i, j⟩ h1 h2; rw [coeff_X_pow, if_neg, MulZeroClass.mul_zero]; rintro rfl; apply h2
-    rw [Finset.Nat.mem_antidiagonal, add_right_cancel_iff] at h1 ; subst h1
+    rw [Finset.Nat.mem_antidiagonal, add_right_cancel_iff] at h1; subst h1
   · exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
 #align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_X_pow
 -/
@@ -1765,7 +1764,7 @@ theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (X ^ n
   by
   rw [coeff_mul, Finset.sum_eq_single (n, d), coeff_X_pow, if_pos rfl, one_mul]
   · rintro ⟨i, j⟩ h1 h2; rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]; rintro rfl; apply h2
-    rw [Finset.Nat.mem_antidiagonal, add_comm, add_right_cancel_iff] at h1 ; subst h1
+    rw [Finset.Nat.mem_antidiagonal, add_comm, add_right_cancel_iff] at h1; subst h1
   · rw [add_comm]
     exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
 #align power_series.coeff_X_pow_mul PowerSeries.coeff_X_pow_mul
@@ -1792,7 +1791,7 @@ theorem coeff_X_pow_mul' (p : PowerSeries R) (n d : ℕ) :
   · refine' (coeff_mul _ _ _).trans (Finset.sum_eq_zero fun x hx => _)
     rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
     have := finset.nat.mem_antidiagonal.mp hx
-    rw [add_comm] at this 
+    rw [add_comm] at this
     exact ((le_of_add_le_right this.le).trans_lt <| not_le.mp h).Ne
 #align power_series.coeff_X_pow_mul' PowerSeries.coeff_X_pow_mul'
 -/
@@ -2079,14 +2078,14 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
   congr 1
   symm
   apply Finset.sum_bij fun (p : ℕ × ℕ) h => (single () p.1, single () p.2)
-  · rintro ⟨i, j⟩ hij; rw [Finset.Nat.mem_antidiagonal] at hij 
+  · rintro ⟨i, j⟩ hij; rw [Finset.Nat.mem_antidiagonal] at hij
     rw [Finsupp.mem_antidiagonal, ← Finsupp.single_add, hij]
   · rintro ⟨i, j⟩ hij
     by_cases H : j < n
     · rw [if_pos H, if_pos]; · rfl
       constructor
       · rintro ⟨⟩; simpa [Finsupp.single_eq_same] using le_of_lt H
-      · intro hh; rw [lt_iff_not_ge] at H ; apply H
+      · intro hh; rw [lt_iff_not_ge] at H; apply H
         simpa [Finsupp.single_eq_same] using hh ()
     · rw [if_neg H, if_neg]; rintro ⟨h₁, h₂⟩; apply h₂; rintro ⟨⟩
       simpa [Finsupp.single_eq_same] using not_lt.1 H
@@ -2094,7 +2093,7 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
     simpa only [Prod.mk.inj_iff, Finsupp.unique_single_eq_iff] using id
   · rintro ⟨f, g⟩ hfg
     refine' ⟨(f (), g ()), _, _⟩
-    · rw [Finsupp.mem_antidiagonal] at hfg 
+    · rw [Finsupp.mem_antidiagonal] at hfg
       rw [Finset.Nat.mem_antidiagonal, ← Finsupp.add_apply, hfg, Finsupp.single_eq_same]
     · rw [Prod.mk.inj_iff]; dsimp
       exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
@@ -2203,15 +2202,15 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSerie
   ext n; rw [(coeff R n).map_zero]; apply Nat.strong_induction_on n
   clear n; intro n ih
   replace h := congr_arg (coeff R (m + n)) h
-  rw [LinearMap.map_zero, coeff_mul, Finset.sum_eq_single (m, n)] at h 
+  rw [LinearMap.map_zero, coeff_mul, Finset.sum_eq_single (m, n)] at h
   · replace h := eq_zero_or_eq_zero_of_mul_eq_zero h
-    rw [Classical.or_iff_not_imp_left] at h ; exact h hm₁
+    rw [Classical.or_iff_not_imp_left] at h; exact h hm₁
   · rintro ⟨i, j⟩ hij hne
     by_cases hj : j < n; · rw [ih j hj, MulZeroClass.mul_zero]
     by_cases hi : i < m
-    · specialize hm₂ _ hi; push_neg at hm₂ ; rw [hm₂, MulZeroClass.zero_mul]
-    rw [Finset.Nat.mem_antidiagonal] at hij 
-    push_neg at hi hj 
+    · specialize hm₂ _ hi; push_neg at hm₂; rw [hm₂, MulZeroClass.zero_mul]
+    rw [Finset.Nat.mem_antidiagonal] at hij
+    push_neg at hi hj
     suffices m < i by
       have : m + n < i + j := add_lt_add_of_lt_of_le this hj
       exfalso; exact ne_of_lt this hij.symm
@@ -2263,7 +2262,7 @@ theorem rescale_injective {a : R} (ha : a ≠ 0) : Function.Injective (rescale a
   rw [PowerSeries.ext_iff] at *
   intro n
   specialize h n
-  rw [coeff_rescale, coeff_rescale, mul_eq_mul_left_iff] at h 
+  rw [coeff_rescale, coeff_rescale, mul_eq_mul_left_iff] at h
   apply h.resolve_right
   intro h'
   exact ha (pow_eq_zero h')
@@ -2549,9 +2548,9 @@ theorem order_eq_top {φ : PowerSeries R} : φ.order = ⊤ ↔ φ = 0 :=
 the `i`th coefficient is `0` for all `i < n`.-/
 theorem nat_le_order (φ : PowerSeries R) (n : ℕ) (h : ∀ i < n, coeff R i φ = 0) : ↑n ≤ order φ :=
   by
-  by_contra H; rw [not_le] at H 
+  by_contra H; rw [not_le] at H
   have : (order φ).Dom := PartENat.dom_of_le_natCast H.le
-  rw [← PartENat.natCast_get this, PartENat.coe_lt_coe] at H 
+  rw [← PartENat.natCast_get this, PartENat.coe_lt_coe] at H
   exact coeff_order this (h _ H)
 #align power_series.nat_le_order PowerSeries.nat_le_order
 -/
@@ -2611,7 +2610,7 @@ private theorem order_add_of_order_eq.aux (φ ψ : PowerSeries R) (h : order φ
   by
   suffices order (φ + ψ) = order φ by rw [le_inf_iff, this]; exact ⟨le_rfl, le_of_lt H⟩
   · rw [order_eq]; constructor
-    · intro i hi; rw [← hi] at H ; rw [(coeff _ _).map_add, coeff_of_lt_order i H, add_zero]
+    · intro i hi; rw [← hi] at H; rw [(coeff _ _).map_add, coeff_of_lt_order i H, add_zero]
       exact (order_eq_nat.1 hi.symm).1
     · intro i hi
       rw [(coeff _ _).map_add, coeff_of_lt_order i hi, coeff_of_lt_order i (lt_trans hi H),
@@ -2644,7 +2643,7 @@ theorem order_mul_ge (φ ψ : PowerSeries R) : order φ + order ψ ≤ order (φ
   · rw [coeff_of_lt_order i hi, MulZeroClass.zero_mul]
   by_cases hj : ↑j < order ψ
   · rw [coeff_of_lt_order j hj, MulZeroClass.mul_zero]
-  rw [not_lt] at hi hj ; rw [Finset.Nat.mem_antidiagonal] at hij 
+  rw [not_lt] at hi hj; rw [Finset.Nat.mem_antidiagonal] at hij
   exfalso
   apply ne_of_lt (lt_of_lt_of_le hn <| add_le_add hi hj)
   rw [← Nat.cast_add, hij]
@@ -2659,8 +2658,8 @@ theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
   split_ifs with h
   · rw [h, order_eq_top, LinearMap.map_zero]
   · rw [order_eq]; constructor <;> intro i hi
-    · rw [PartENat.natCast_inj] at hi ; rwa [hi, coeff_monomial_same]
-    · rw [PartENat.coe_lt_coe] at hi ; rw [coeff_monomial, if_neg]; exact ne_of_lt hi
+    · rw [PartENat.natCast_inj] at hi; rwa [hi, coeff_monomial_same]
+    · rw [PartENat.coe_lt_coe] at hi; rw [coeff_monomial, if_neg]; exact ne_of_lt hi
 #align power_series.order_monomial PowerSeries.order_monomial
 -/
 
@@ -2682,7 +2681,7 @@ theorem coeff_mul_of_lt_order {φ ψ : PowerSeries R} {n : ℕ} (h : ↑n < ψ.o
   rw [coeff_mul]
   apply Finset.sum_congr rfl fun x hx => _
   refine' mul_eq_zero_of_right (coeff R x.fst φ) (coeff_of_lt_order x.snd (lt_of_le_of_lt _ h))
-  rw [Finset.Nat.mem_antidiagonal] at hx 
+  rw [Finset.Nat.mem_antidiagonal] at hx
   norm_cast
   linarith
 #align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_order
@@ -2703,7 +2702,7 @@ theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type _} [CommRing R] (k : ℕ
   apply Finset.induction_on s
   · simp
   · intro a s ha ih t
-    simp only [Finset.mem_insert, forall_eq_or_imp] at t 
+    simp only [Finset.mem_insert, forall_eq_or_imp] at t
     rw [Finset.prod_insert ha, ← mul_assoc, mul_right_comm, coeff_mul_one_sub_of_lt_order _ t.1]
     exact ih t.2
 #align power_series.coeff_mul_prod_one_sub_of_lt_order PowerSeries.coeff_mul_prod_one_sub_of_lt_order
@@ -2740,7 +2739,7 @@ theorem order_eq_multiplicity_X {R : Type _} [Semiring R] (φ : PowerSeries R) :
       (PartENat.find_le _ _ _)
   rintro ⟨ψ, H⟩
   have := congr_arg (coeff R n) H
-  rw [← (ψ.commute_X.pow_right _).Eq, coeff_mul_of_lt_order, ← hn] at this 
+  rw [← (ψ.commute_X.pow_right _).Eq, coeff_mul_of_lt_order, ← hn] at this
   · exact coeff_order _ this
   · rw [X_pow_eq, order_monomial]
     split_ifs
@@ -2847,7 +2846,7 @@ theorem coe_zero : ((0 : R[X]) : PowerSeries R) = 0 :=
 theorem coe_one : ((1 : R[X]) : PowerSeries R) = 1 :=
   by
   have := coe_monomial 0 (1 : R)
-  rwa [PowerSeries.monomial_zero_eq_C_apply] at this 
+  rwa [PowerSeries.monomial_zero_eq_C_apply] at this
 #align polynomial.coe_one Polynomial.coe_one
 -/
 
@@ -2869,7 +2868,7 @@ theorem coe_mul : ((φ * ψ : R[X]) : PowerSeries R) = φ * ψ :=
 theorem coe_C (a : R) : ((C a : R[X]) : PowerSeries R) = PowerSeries.C R a :=
   by
   have := coe_monomial 0 a
-  rwa [PowerSeries.monomial_zero_eq_C_apply] at this 
+  rwa [PowerSeries.monomial_zero_eq_C_apply] at this
 #align polynomial.coe_C Polynomial.coe_C
 -/
 

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

@@ -867,7 +867,7 @@ section Ring
 
 variable [Ring R]
 
-/- ./././Mathport/Syntax/Translate/Command.lean:298:8: warning: using_well_founded used, estimated equivalent -/
+/- ./././Mathport/Syntax/Translate/Command.lean:299:8: warning: using_well_founded used, estimated equivalent -/
 #print MvPowerSeries.inv.aux /-
 /-
 The inverse of a multivariate formal power series is defined by
@@ -881,8 +881,7 @@ protected noncomputable def inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerS
   | n =>
     if n = 0 then a
     else -a * ∑ x in n.antidiagonal, if h : x.2 < n then coeff R x.1 φ * inv.aux x.2 else 0
-termination_by
-  _ x => WellFounded.wrap (Finsupp.lt_wf σ) x
+termination_by x => WellFounded.wrap (Finsupp.lt_wf σ) x
 #align mv_power_series.inv.aux MvPowerSeries.inv.aux
 -/
 

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

@@ -1951,7 +1951,7 @@ theorem rescale_zero : rescale 0 = (C R).comp (constantCoeff R) :=
     PowerSeries.coeff_mk _ _, coeff_C]
   split_ifs
   · simp only [h, one_mul, coeff_zero_eq_constant_coeff, pow_zero]
-  · rw [zero_pow' n h, MulZeroClass.zero_mul]
+  · rw [zero_pow n h, MulZeroClass.zero_mul]
 #align power_series.rescale_zero PowerSeries.rescale_zero
 -/
 

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

@@ -840,7 +840,13 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
         · exfalso; apply H; rw [← hij, hi]; ext
           rw [coe_add, coe_add, Pi.add_apply, Pi.add_apply, add_tsub_cancel_left, add_comm]
         · exact MulZeroClass.zero_mul _
-      · classical
+      ·
+        classical
+        contrapose! H
+        ext t
+        by_cases hst : s = t
+        · subst t; simpa using tsub_add_cancel_of_le H
+        · simp [Finsupp.single_apply, hst]
 #align mv_power_series.X_pow_dvd_iff MvPowerSeries.X_pow_dvd_iff
 -/
 
@@ -1884,6 +1890,9 @@ theorem X_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
   by
   convert @MvPowerSeries.X_pow_dvd_iff Unit R _ () n φ; apply propext
   classical
+  constructor <;> intro h m hm
+  · rw [Finsupp.unique_single m]; convert h _ hm
+  · apply h; simpa only [Finsupp.single_eq_same] using hm
 #align power_series.X_pow_dvd_iff PowerSeries.X_pow_dvd_iff
 -/
 

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

@@ -840,13 +840,7 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
         · exfalso; apply H; rw [← hij, hi]; ext
           rw [coe_add, coe_add, Pi.add_apply, Pi.add_apply, add_tsub_cancel_left, add_comm]
         · exact MulZeroClass.zero_mul _
-      ·
-        classical
-        contrapose! H
-        ext t
-        by_cases hst : s = t
-        · subst t; simpa using tsub_add_cancel_of_le H
-        · simp [Finsupp.single_apply, hst]
+      · classical
 #align mv_power_series.X_pow_dvd_iff MvPowerSeries.X_pow_dvd_iff
 -/
 
@@ -1890,9 +1884,6 @@ theorem X_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
   by
   convert @MvPowerSeries.X_pow_dvd_iff Unit R _ () n φ; apply propext
   classical
-  constructor <;> intro h m hm
-  · rw [Finsupp.unique_single m]; convert h _ hm
-  · apply h; simpa only [Finsupp.single_eq_same] using hm
 #align power_series.X_pow_dvd_iff PowerSeries.X_pow_dvd_iff
 -/
 

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

@@ -867,6 +867,7 @@ section Ring
 
 variable [Ring R]
 
+/- ./././Mathport/Syntax/Translate/Command.lean:298:8: warning: using_well_founded used, estimated equivalent -/
 #print MvPowerSeries.inv.aux /-
 /-
 The inverse of a multivariate formal power series is defined by
@@ -880,7 +881,8 @@ protected noncomputable def inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerS
   | n =>
     if n = 0 then a
     else -a * ∑ x in n.antidiagonal, if h : x.2 < n then coeff R x.1 φ * inv.aux x.2 else 0
-termination_by' ⟨_, Finsupp.lt_wf σ⟩
+termination_by
+  _ x => WellFounded.wrap (Finsupp.lt_wf σ) x
 #align mv_power_series.inv.aux MvPowerSeries.inv.aux
 -/
 

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

@@ -2194,7 +2194,7 @@ variable [Ring R]
 #print PowerSeries.eq_zero_or_eq_zero_of_mul_eq_zero /-
 theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSeries R) (h : φ * ψ = 0) :
     φ = 0 ∨ ψ = 0 := by
-  rw [or_iff_not_imp_left]; intro H
+  rw [Classical.or_iff_not_imp_left]; intro H
   have ex : ∃ m, coeff R m φ ≠ 0 := by contrapose! H; exact ext H
   let m := Nat.find ex
   have hm₁ : coeff R m φ ≠ 0 := Nat.find_spec ex
@@ -2204,7 +2204,7 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSerie
   replace h := congr_arg (coeff R (m + n)) h
   rw [LinearMap.map_zero, coeff_mul, Finset.sum_eq_single (m, n)] at h 
   · replace h := eq_zero_or_eq_zero_of_mul_eq_zero h
-    rw [or_iff_not_imp_left] at h ; exact h hm₁
+    rw [Classical.or_iff_not_imp_left] at h ; exact h hm₁
   · rintro ⟨i, j⟩ hij hne
     by_cases hj : j < n; · rw [ih j hj, MulZeroClass.mul_zero]
     by_cases hi : i < m

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

@@ -2715,7 +2715,7 @@ theorem X_pow_order_dvd (h : (order φ).Dom) : X ^ (order φ).get h ∣ φ :=
   refine' ⟨PowerSeries.mk fun n => coeff R (n + (order φ).get h) φ, _⟩
   ext n
   simp only [coeff_mul, coeff_X_pow, coeff_mk, boole_mul, Finset.sum_ite,
-    Finset.Nat.filter_fst_eq_antidiagonal, Finset.sum_const_zero, add_zero]
+    Finset.filter_fst_eq_antidiagonal, Finset.sum_const_zero, add_zero]
   split_ifs with hn hn
   · simp [tsub_add_cancel_of_le hn]
   · simp only [Finset.sum_empty]

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

@@ -731,12 +731,12 @@ theorem algebraMap_apply {r : R} : algebraMap R (MvPowerSeries σ A) r = C σ A
 
 instance [Nonempty σ] [Nontrivial R] : Nontrivial (Subalgebra R (MvPowerSeries σ R)) :=
   ⟨⟨⊥, ⊤, by
-      rw [Ne.def, SetLike.ext_iff, not_forall]
+      rw [Ne.def, SetLike.ext_iff, Classical.not_forall]
       inhabit σ
       refine' ⟨X default, _⟩
       simp only [Algebra.mem_bot, not_exists, Set.mem_range, iff_true_iff, Algebra.mem_top]
       intro x
-      rw [ext_iff, not_forall]
+      rw [ext_iff, Classical.not_forall]
       refine' ⟨Finsupp.single default 1, _⟩
       simp [algebraMap_apply, coeff_C]⟩⟩
 

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

@@ -3,13 +3,13 @@ Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
 -/
-import Mathbin.Data.Finsupp.Interval
-import Mathbin.Data.MvPolynomial.Basic
-import Mathbin.Data.Polynomial.AlgebraMap
-import Mathbin.Data.Polynomial.Coeff
-import Mathbin.LinearAlgebra.StdBasis
-import Mathbin.RingTheory.Ideal.LocalRing
-import Mathbin.RingTheory.Multiplicity
+import Data.Finsupp.Interval
+import Data.MvPolynomial.Basic
+import Data.Polynomial.AlgebraMap
+import Data.Polynomial.Coeff
+import LinearAlgebra.StdBasis
+import RingTheory.Ideal.LocalRing
+import RingTheory.Multiplicity
 import Mathbin.Tactic.Linarith.Default
 
 #align_import ring_theory.power_series.basic from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"

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

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
-
-! This file was ported from Lean 3 source module ring_theory.power_series.basic
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Finsupp.Interval
 import Mathbin.Data.MvPolynomial.Basic
@@ -17,6 +12,8 @@ import Mathbin.RingTheory.Ideal.LocalRing
 import Mathbin.RingTheory.Multiplicity
 import Mathbin.Tactic.Linarith.Default
 
+#align_import ring_theory.power_series.basic from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 # Formal power series
 

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

@@ -140,69 +140,93 @@ def coeff (n : σ →₀ ℕ) : MvPowerSeries σ R →ₗ[R] R :=
 
 variable {R}
 
+#print MvPowerSeries.ext /-
 /-- Two multivariate formal power series are equal if all their coefficients are equal.-/
 @[ext]
 theorem ext {φ ψ} (h : ∀ n : σ →₀ ℕ, coeff R n φ = coeff R n ψ) : φ = ψ :=
   funext h
 #align mv_power_series.ext MvPowerSeries.ext
+-/
 
+#print MvPowerSeries.ext_iff /-
 /-- Two multivariate formal power series are equal
  if and only if all their coefficients are equal.-/
 theorem ext_iff {φ ψ : MvPowerSeries σ R} : φ = ψ ↔ ∀ n : σ →₀ ℕ, coeff R n φ = coeff R n ψ :=
   Function.funext_iff
 #align mv_power_series.ext_iff MvPowerSeries.ext_iff
+-/
 
+#print MvPowerSeries.monomial_def /-
 theorem monomial_def [DecidableEq σ] (n : σ →₀ ℕ) : monomial R n = LinearMap.stdBasis R _ n := by
   convert rfl
 #align mv_power_series.monomial_def MvPowerSeries.monomial_def
+-/
 
+#print MvPowerSeries.coeff_monomial /-
 -- unify the `decidable` arguments
 theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
     coeff R m (monomial R n a) = if m = n then a else 0 := by
   rw [coeff, monomial_def, LinearMap.proj_apply, LinearMap.stdBasis_apply, Function.update_apply,
     Pi.zero_apply]
 #align mv_power_series.coeff_monomial MvPowerSeries.coeff_monomial
+-/
 
+#print MvPowerSeries.coeff_monomial_same /-
 @[simp]
 theorem coeff_monomial_same (n : σ →₀ ℕ) (a : R) : coeff R n (monomial R n a) = a :=
   LinearMap.stdBasis_same R _ n a
 #align mv_power_series.coeff_monomial_same MvPowerSeries.coeff_monomial_same
+-/
 
+#print MvPowerSeries.coeff_monomial_ne /-
 theorem coeff_monomial_ne {m n : σ →₀ ℕ} (h : m ≠ n) (a : R) : coeff R m (monomial R n a) = 0 :=
   LinearMap.stdBasis_ne R _ _ _ h a
 #align mv_power_series.coeff_monomial_ne MvPowerSeries.coeff_monomial_ne
+-/
 
+#print MvPowerSeries.eq_of_coeff_monomial_ne_zero /-
 theorem eq_of_coeff_monomial_ne_zero {m n : σ →₀ ℕ} {a : R} (h : coeff R m (monomial R n a) ≠ 0) :
     m = n :=
   by_contra fun h' => h <| coeff_monomial_ne h' a
 #align mv_power_series.eq_of_coeff_monomial_ne_zero MvPowerSeries.eq_of_coeff_monomial_ne_zero
+-/
 
+#print MvPowerSeries.coeff_comp_monomial /-
 @[simp]
 theorem coeff_comp_monomial (n : σ →₀ ℕ) : (coeff R n).comp (monomial R n) = LinearMap.id :=
   LinearMap.ext <| coeff_monomial_same n
 #align mv_power_series.coeff_comp_monomial MvPowerSeries.coeff_comp_monomial
+-/
 
+#print MvPowerSeries.coeff_zero /-
 @[simp]
 theorem coeff_zero (n : σ →₀ ℕ) : coeff R n (0 : MvPowerSeries σ R) = 0 :=
   rfl
 #align mv_power_series.coeff_zero MvPowerSeries.coeff_zero
+-/
 
 variable (m n : σ →₀ ℕ) (φ ψ : MvPowerSeries σ R)
 
 instance : One (MvPowerSeries σ R) :=
   ⟨monomial R (0 : σ →₀ ℕ) 1⟩
 
+#print MvPowerSeries.coeff_one /-
 theorem coeff_one [DecidableEq σ] : coeff R n (1 : MvPowerSeries σ R) = if n = 0 then 1 else 0 :=
   coeff_monomial _ _ _
 #align mv_power_series.coeff_one MvPowerSeries.coeff_one
+-/
 
+#print MvPowerSeries.coeff_zero_one /-
 theorem coeff_zero_one : coeff R (0 : σ →₀ ℕ) 1 = 1 :=
   coeff_monomial_same 0 1
 #align mv_power_series.coeff_zero_one MvPowerSeries.coeff_zero_one
+-/
 
+#print MvPowerSeries.monomial_zero_one /-
 theorem monomial_zero_one : monomial R (0 : σ →₀ ℕ) 1 = 1 :=
   rfl
 #align mv_power_series.monomial_zero_one MvPowerSeries.monomial_zero_one
+-/
 
 instance : AddMonoidWithOne (MvPowerSeries σ R) :=
   { MvPowerSeries.addMonoid with
@@ -214,19 +238,26 @@ instance : AddMonoidWithOne (MvPowerSeries σ R) :=
 instance : Mul (MvPowerSeries σ R) :=
   ⟨fun φ ψ n => ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ⟩
 
+#print MvPowerSeries.coeff_mul /-
 theorem coeff_mul :
     coeff R n (φ * ψ) = ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ :=
   rfl
 #align mv_power_series.coeff_mul MvPowerSeries.coeff_mul
+-/
 
+#print MvPowerSeries.zero_mul /-
 protected theorem zero_mul : (0 : MvPowerSeries σ R) * φ = 0 :=
   ext fun n => by simp [coeff_mul]
 #align mv_power_series.zero_mul MvPowerSeries.zero_mul
+-/
 
+#print MvPowerSeries.mul_zero /-
 protected theorem mul_zero : φ * 0 = 0 :=
   ext fun n => by simp [coeff_mul]
 #align mv_power_series.mul_zero MvPowerSeries.mul_zero
+-/
 
+#print MvPowerSeries.coeff_monomial_mul /-
 theorem coeff_monomial_mul (a : R) :
     coeff R m (monomial R n a * φ) = if n ≤ m then a * coeff R (m - n) φ else 0 :=
   by
@@ -237,7 +268,9 @@ theorem coeff_monomial_mul (a : R) :
   rw [coeff_mul, ← Finset.sum_filter_of_ne this, antidiagonal_filter_fst_eq, Finset.sum_ite_index]
   simp only [Finset.sum_singleton, coeff_monomial_same, Finset.sum_empty]
 #align mv_power_series.coeff_monomial_mul MvPowerSeries.coeff_monomial_mul
+-/
 
+#print MvPowerSeries.coeff_mul_monomial /-
 theorem coeff_mul_monomial (a : R) :
     coeff R m (φ * monomial R n a) = if n ≤ m then coeff R (m - n) φ * a else 0 :=
   by
@@ -248,19 +281,25 @@ theorem coeff_mul_monomial (a : R) :
   rw [coeff_mul, ← Finset.sum_filter_of_ne this, antidiagonal_filter_snd_eq, Finset.sum_ite_index]
   simp only [Finset.sum_singleton, coeff_monomial_same, Finset.sum_empty]
 #align mv_power_series.coeff_mul_monomial MvPowerSeries.coeff_mul_monomial
+-/
 
+#print MvPowerSeries.coeff_add_monomial_mul /-
 theorem coeff_add_monomial_mul (a : R) : coeff R (m + n) (monomial R m a * φ) = a * coeff R n φ :=
   by
   rw [coeff_monomial_mul, if_pos, add_tsub_cancel_left]
   exact le_add_right le_rfl
 #align mv_power_series.coeff_add_monomial_mul MvPowerSeries.coeff_add_monomial_mul
+-/
 
+#print MvPowerSeries.coeff_add_mul_monomial /-
 theorem coeff_add_mul_monomial (a : R) : coeff R (m + n) (φ * monomial R n a) = coeff R m φ * a :=
   by
   rw [coeff_mul_monomial, if_pos, add_tsub_cancel_right]
   exact le_add_left le_rfl
 #align mv_power_series.coeff_add_mul_monomial MvPowerSeries.coeff_add_mul_monomial
+-/
 
+#print MvPowerSeries.commute_monomial /-
 @[simp]
 theorem commute_monomial {a : R} {n} : Commute φ (monomial R n a) ↔ ∀ m, Commute (coeff R m φ) a :=
   by
@@ -270,23 +309,33 @@ theorem commute_monomial {a : R} {n} : Commute φ (monomial R n a) ↔ ∀ m, Co
   · rw [coeff_mul_monomial, coeff_monomial_mul]
     split_ifs <;> [apply h; rfl]
 #align mv_power_series.commute_monomial MvPowerSeries.commute_monomial
+-/
 
+#print MvPowerSeries.one_mul /-
 protected theorem one_mul : (1 : MvPowerSeries σ R) * φ = φ :=
   ext fun n => by simpa using coeff_add_monomial_mul 0 n φ 1
 #align mv_power_series.one_mul MvPowerSeries.one_mul
+-/
 
+#print MvPowerSeries.mul_one /-
 protected theorem mul_one : φ * 1 = φ :=
   ext fun n => by simpa using coeff_add_mul_monomial n 0 φ 1
 #align mv_power_series.mul_one MvPowerSeries.mul_one
+-/
 
+#print MvPowerSeries.mul_add /-
 protected theorem mul_add (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : φ₁ * (φ₂ + φ₃) = φ₁ * φ₂ + φ₁ * φ₃ :=
   ext fun n => by simp only [coeff_mul, mul_add, Finset.sum_add_distrib, LinearMap.map_add]
 #align mv_power_series.mul_add MvPowerSeries.mul_add
+-/
 
+#print MvPowerSeries.add_mul /-
 protected theorem add_mul (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : (φ₁ + φ₂) * φ₃ = φ₁ * φ₃ + φ₂ * φ₃ :=
   ext fun n => by simp only [coeff_mul, add_mul, Finset.sum_add_distrib, LinearMap.map_add]
 #align mv_power_series.add_mul MvPowerSeries.add_mul
+-/
 
+#print MvPowerSeries.mul_assoc /-
 protected theorem mul_assoc (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : φ₁ * φ₂ * φ₃ = φ₁ * (φ₂ * φ₃) :=
   by
   ext1 n
@@ -303,6 +352,7 @@ protected theorem mul_assoc (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : φ₁ * 
   · rintro ⟨⟨i, j⟩, ⟨k, l⟩⟩; dsimp only; rintro rfl rfl
     refine' ⟨⟨(i + k, l), (i, k)⟩, _, _⟩ <;> simp [add_assoc]
 #align mv_power_series.mul_assoc MvPowerSeries.mul_assoc
+-/
 
 instance : Semiring (MvPowerSeries σ R) :=
   { MvPowerSeries.addMonoidWithOne, MvPowerSeries.hasMul,
@@ -334,6 +384,7 @@ section Semiring
 
 variable [Semiring R]
 
+#print MvPowerSeries.monomial_mul_monomial /-
 theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
     monomial R m a * monomial R n b = monomial R (m + n) (a * b) :=
   by
@@ -345,9 +396,11 @@ theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
   · exact MulZeroClass.zero_mul b
   · rw [h₂] at h₁ ; exact (h₁ <| le_add_left le_rfl).elim
 #align mv_power_series.monomial_mul_monomial MvPowerSeries.monomial_mul_monomial
+-/
 
 variable (σ) (R)
 
+#print MvPowerSeries.C /-
 /-- The constant multivariate formal power series.-/
 def C : R →+* MvPowerSeries σ R :=
   { monomial R (0 : σ →₀ ℕ) with
@@ -355,26 +408,35 @@ def C : R →+* MvPowerSeries σ R :=
     map_mul' := fun a b => (monomial_mul_monomial 0 0 a b).symm
     map_zero' := (monomial R (0 : _)).map_zero }
 #align mv_power_series.C MvPowerSeries.C
+-/
 
 variable {σ} {R}
 
+#print MvPowerSeries.monomial_zero_eq_C /-
 @[simp]
 theorem monomial_zero_eq_C : ⇑(monomial R (0 : σ →₀ ℕ)) = C σ R :=
   rfl
 #align mv_power_series.monomial_zero_eq_C MvPowerSeries.monomial_zero_eq_C
+-/
 
+#print MvPowerSeries.monomial_zero_eq_C_apply /-
 theorem monomial_zero_eq_C_apply (a : R) : monomial R (0 : σ →₀ ℕ) a = C σ R a :=
   rfl
 #align mv_power_series.monomial_zero_eq_C_apply MvPowerSeries.monomial_zero_eq_C_apply
+-/
 
+#print MvPowerSeries.coeff_C /-
 theorem coeff_C [DecidableEq σ] (n : σ →₀ ℕ) (a : R) :
     coeff R n (C σ R a) = if n = 0 then a else 0 :=
   coeff_monomial _ _ _
 #align mv_power_series.coeff_C MvPowerSeries.coeff_C
+-/
 
+#print MvPowerSeries.coeff_zero_C /-
 theorem coeff_zero_C (a : R) : coeff R (0 : σ →₀ ℕ) (C σ R a) = a :=
   coeff_monomial_same 0 a
 #align mv_power_series.coeff_zero_C MvPowerSeries.coeff_zero_C
+-/
 
 #print MvPowerSeries.X /-
 /-- The variables of the multivariate formal power series ring.-/
@@ -383,67 +445,92 @@ def X (s : σ) : MvPowerSeries σ R :=
 #align mv_power_series.X MvPowerSeries.X
 -/
 
+#print MvPowerSeries.coeff_X /-
 theorem coeff_X [DecidableEq σ] (n : σ →₀ ℕ) (s : σ) :
     coeff R n (X s : MvPowerSeries σ R) = if n = single s 1 then 1 else 0 :=
   coeff_monomial _ _ _
 #align mv_power_series.coeff_X MvPowerSeries.coeff_X
+-/
 
+#print MvPowerSeries.coeff_index_single_X /-
 theorem coeff_index_single_X [DecidableEq σ] (s t : σ) :
     coeff R (single t 1) (X s : MvPowerSeries σ R) = if t = s then 1 else 0 := by
   simp only [coeff_X, single_left_inj one_ne_zero]
 #align mv_power_series.coeff_index_single_X MvPowerSeries.coeff_index_single_X
+-/
 
+#print MvPowerSeries.coeff_index_single_self_X /-
 @[simp]
 theorem coeff_index_single_self_X (s : σ) : coeff R (single s 1) (X s : MvPowerSeries σ R) = 1 :=
   coeff_monomial_same _ _
 #align mv_power_series.coeff_index_single_self_X MvPowerSeries.coeff_index_single_self_X
+-/
 
+#print MvPowerSeries.coeff_zero_X /-
 theorem coeff_zero_X (s : σ) : coeff R (0 : σ →₀ ℕ) (X s : MvPowerSeries σ R) = 0 := by
   rw [coeff_X, if_neg]; intro h; exact one_ne_zero (single_eq_zero.mp h.symm)
 #align mv_power_series.coeff_zero_X MvPowerSeries.coeff_zero_X
+-/
 
+#print MvPowerSeries.commute_X /-
 theorem commute_X (φ : MvPowerSeries σ R) (s : σ) : Commute φ (X s) :=
   φ.commute_monomial.mpr fun m => Commute.one_right _
 #align mv_power_series.commute_X MvPowerSeries.commute_X
+-/
 
+#print MvPowerSeries.X_def /-
 theorem X_def (s : σ) : X s = monomial R (single s 1) 1 :=
   rfl
 #align mv_power_series.X_def MvPowerSeries.X_def
+-/
 
+#print MvPowerSeries.X_pow_eq /-
 theorem X_pow_eq (s : σ) (n : ℕ) : (X s : MvPowerSeries σ R) ^ n = monomial R (single s n) 1 :=
   by
   induction' n with n ih
   · rw [pow_zero, Finsupp.single_zero, monomial_zero_one]
   · rw [pow_succ', ih, Nat.succ_eq_add_one, Finsupp.single_add, X, monomial_mul_monomial, one_mul]
 #align mv_power_series.X_pow_eq MvPowerSeries.X_pow_eq
+-/
 
+#print MvPowerSeries.coeff_X_pow /-
 theorem coeff_X_pow [DecidableEq σ] (m : σ →₀ ℕ) (s : σ) (n : ℕ) :
     coeff R m ((X s : MvPowerSeries σ R) ^ n) = if m = single s n then 1 else 0 := by
   rw [X_pow_eq s n, coeff_monomial]
 #align mv_power_series.coeff_X_pow MvPowerSeries.coeff_X_pow
+-/
 
+#print MvPowerSeries.coeff_mul_C /-
 @[simp]
 theorem coeff_mul_C (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
     coeff R n (φ * C σ R a) = coeff R n φ * a := by simpa using coeff_add_mul_monomial n 0 φ a
 #align mv_power_series.coeff_mul_C MvPowerSeries.coeff_mul_C
+-/
 
+#print MvPowerSeries.coeff_C_mul /-
 @[simp]
 theorem coeff_C_mul (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
     coeff R n (C σ R a * φ) = a * coeff R n φ := by simpa using coeff_add_monomial_mul 0 n φ a
 #align mv_power_series.coeff_C_mul MvPowerSeries.coeff_C_mul
+-/
 
+#print MvPowerSeries.coeff_zero_mul_X /-
 theorem coeff_zero_mul_X (φ : MvPowerSeries σ R) (s : σ) : coeff R (0 : σ →₀ ℕ) (φ * X s) = 0 :=
   by
   have : ¬single s 1 ≤ 0 := fun h => by simpa using h s
   simp only [X, coeff_mul_monomial, if_neg this]
 #align mv_power_series.coeff_zero_mul_X MvPowerSeries.coeff_zero_mul_X
+-/
 
+#print MvPowerSeries.coeff_zero_X_mul /-
 theorem coeff_zero_X_mul (φ : MvPowerSeries σ R) (s : σ) : coeff R (0 : σ →₀ ℕ) (X s * φ) = 0 := by
   rw [← (φ.commute_X s).Eq, coeff_zero_mul_X]
 #align mv_power_series.coeff_zero_X_mul MvPowerSeries.coeff_zero_X_mul
+-/
 
 variable (σ) (R)
 
+#print MvPowerSeries.constantCoeff /-
 /-- The constant coefficient of a formal power series.-/
 def constantCoeff : MvPowerSeries σ R →+* R :=
   { coeff R (0 : σ →₀ ℕ) with
@@ -452,23 +539,30 @@ def constantCoeff : MvPowerSeries σ R →+* R :=
     map_mul' := fun φ ψ => by simp [coeff_mul, support_single_ne_zero]
     map_zero' := LinearMap.map_zero _ }
 #align mv_power_series.constant_coeff MvPowerSeries.constantCoeff
+-/
 
 variable {σ} {R}
 
+#print MvPowerSeries.coeff_zero_eq_constantCoeff /-
 @[simp]
 theorem coeff_zero_eq_constantCoeff : ⇑(coeff R (0 : σ →₀ ℕ)) = constantCoeff σ R :=
   rfl
 #align mv_power_series.coeff_zero_eq_constant_coeff MvPowerSeries.coeff_zero_eq_constantCoeff
+-/
 
+#print MvPowerSeries.coeff_zero_eq_constantCoeff_apply /-
 theorem coeff_zero_eq_constantCoeff_apply (φ : MvPowerSeries σ R) :
     coeff R (0 : σ →₀ ℕ) φ = constantCoeff σ R φ :=
   rfl
 #align mv_power_series.coeff_zero_eq_constant_coeff_apply MvPowerSeries.coeff_zero_eq_constantCoeff_apply
+-/
 
+#print MvPowerSeries.constantCoeff_C /-
 @[simp]
 theorem constantCoeff_C (a : R) : constantCoeff σ R (C σ R a) = a :=
   rfl
 #align mv_power_series.constant_coeff_C MvPowerSeries.constantCoeff_C
+-/
 
 #print MvPowerSeries.constantCoeff_comp_C /-
 @[simp]
@@ -477,35 +571,47 @@ theorem constantCoeff_comp_C : (constantCoeff σ R).comp (C σ R) = RingHom.id R
 #align mv_power_series.constant_coeff_comp_C MvPowerSeries.constantCoeff_comp_C
 -/
 
+#print MvPowerSeries.constantCoeff_zero /-
 @[simp]
 theorem constantCoeff_zero : constantCoeff σ R 0 = 0 :=
   rfl
 #align mv_power_series.constant_coeff_zero MvPowerSeries.constantCoeff_zero
+-/
 
+#print MvPowerSeries.constantCoeff_one /-
 @[simp]
 theorem constantCoeff_one : constantCoeff σ R 1 = 1 :=
   rfl
 #align mv_power_series.constant_coeff_one MvPowerSeries.constantCoeff_one
+-/
 
+#print MvPowerSeries.constantCoeff_X /-
 @[simp]
 theorem constantCoeff_X (s : σ) : constantCoeff σ R (X s) = 0 :=
   coeff_zero_X s
 #align mv_power_series.constant_coeff_X MvPowerSeries.constantCoeff_X
+-/
 
+#print MvPowerSeries.isUnit_constantCoeff /-
 /-- If a multivariate formal power series is invertible,
  then so is its constant coefficient.-/
 theorem isUnit_constantCoeff (φ : MvPowerSeries σ R) (h : IsUnit φ) :
     IsUnit (constantCoeff σ R φ) :=
   h.map _
 #align mv_power_series.is_unit_constant_coeff MvPowerSeries.isUnit_constantCoeff
+-/
 
+#print MvPowerSeries.coeff_smul /-
 @[simp]
 theorem coeff_smul (f : MvPowerSeries σ R) (n) (a : R) : coeff _ n (a • f) = a * coeff _ n f :=
   rfl
 #align mv_power_series.coeff_smul MvPowerSeries.coeff_smul
+-/
 
+#print MvPowerSeries.smul_eq_C_mul /-
 theorem smul_eq_C_mul (f : MvPowerSeries σ R) (a : R) : a • f = C σ R a * f := by ext; simp
 #align mv_power_series.smul_eq_C_mul MvPowerSeries.smul_eq_C_mul
+-/
 
 #print MvPowerSeries.X_inj /-
 theorem X_inj [Nontrivial R] {s t : σ} : (X s : MvPowerSeries σ R) = X t ↔ s = t :=
@@ -529,6 +635,7 @@ variable (f : R →+* S) (g : S →+* T)
 
 variable (σ)
 
+#print MvPowerSeries.map /-
 /-- The map between multivariate formal power series induced by a map on the coefficients.-/
 def map : MvPowerSeries σ R →+* MvPowerSeries σ S
     where
@@ -546,42 +653,57 @@ def map : MvPowerSeries σ R →+* MvPowerSeries σ S
         rw [coeff_mul, f.map_sum, coeff_mul, Finset.sum_congr rfl]
         rintro ⟨i, j⟩ hij; rw [f.map_mul]; rfl
 #align mv_power_series.map MvPowerSeries.map
+-/
 
 variable {σ}
 
+#print MvPowerSeries.map_id /-
 @[simp]
 theorem map_id : map σ (RingHom.id R) = RingHom.id _ :=
   rfl
 #align mv_power_series.map_id MvPowerSeries.map_id
+-/
 
+#print MvPowerSeries.map_comp /-
 theorem map_comp : map σ (g.comp f) = (map σ g).comp (map σ f) :=
   rfl
 #align mv_power_series.map_comp MvPowerSeries.map_comp
+-/
 
+#print MvPowerSeries.coeff_map /-
 @[simp]
 theorem coeff_map (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) : coeff S n (map σ f φ) = f (coeff R n φ) :=
   rfl
 #align mv_power_series.coeff_map MvPowerSeries.coeff_map
+-/
 
+#print MvPowerSeries.constantCoeff_map /-
 @[simp]
 theorem constantCoeff_map (φ : MvPowerSeries σ R) :
     constantCoeff σ S (map σ f φ) = f (constantCoeff σ R φ) :=
   rfl
 #align mv_power_series.constant_coeff_map MvPowerSeries.constantCoeff_map
+-/
 
+#print MvPowerSeries.map_monomial /-
 @[simp]
 theorem map_monomial (n : σ →₀ ℕ) (a : R) : map σ f (monomial R n a) = monomial S n (f a) := by
   ext m; simp [coeff_monomial, apply_ite f]
 #align mv_power_series.map_monomial MvPowerSeries.map_monomial
+-/
 
+#print MvPowerSeries.map_C /-
 @[simp]
 theorem map_C (a : R) : map σ f (C σ R a) = C σ S (f a) :=
   map_monomial _ _ _
 #align mv_power_series.map_C MvPowerSeries.map_C
+-/
 
+#print MvPowerSeries.map_X /-
 @[simp]
 theorem map_X (s : σ) : map σ f (X s) = X s := by simp [MvPowerSeries.X]
 #align mv_power_series.map_X MvPowerSeries.map_X
+-/
 
 end Map
 
@@ -596,15 +718,19 @@ instance : Algebra R (MvPowerSeries σ A) :=
     smul_def' := fun a σ => by ext n; simp [(coeff A n).map_smul_of_tower a, Algebra.smul_def]
     toRingHom := (MvPowerSeries.map σ (algebraMap R A)).comp (C σ R) }
 
+#print MvPowerSeries.c_eq_algebraMap /-
 theorem c_eq_algebraMap : C σ R = algebraMap R (MvPowerSeries σ R) :=
   rfl
 #align mv_power_series.C_eq_algebra_map MvPowerSeries.c_eq_algebraMap
+-/
 
+#print MvPowerSeries.algebraMap_apply /-
 theorem algebraMap_apply {r : R} : algebraMap R (MvPowerSeries σ A) r = C σ A (algebraMap R A r) :=
   by
   change (MvPowerSeries.map σ (algebraMap R A)).comp (C σ R) r = _
   simp
 #align mv_power_series.algebra_map_apply MvPowerSeries.algebraMap_apply
+-/
 
 instance [Nonempty σ] [Nontrivial R] : Nontrivial (Subalgebra R (MvPowerSeries σ R)) :=
   ⟨⟨⊥, ⊤, by
@@ -630,10 +756,12 @@ def truncFun (φ : MvPowerSeries σ R) : MvPolynomial σ R :=
 #align mv_power_series.trunc_fun MvPowerSeries.truncFun
 -/
 
+#print MvPowerSeries.coeff_truncFun /-
 theorem coeff_truncFun (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
     (truncFun n φ).coeff m = if m < n then coeff R m φ else 0 := by
   simp [trunc_fun, MvPolynomial.coeff_sum]
 #align mv_power_series.coeff_trunc_fun MvPowerSeries.coeff_truncFun
+-/
 
 variable (R)
 
@@ -649,10 +777,13 @@ def trunc : MvPowerSeries σ R →+ MvPolynomial σ R
 
 variable {R}
 
+#print MvPowerSeries.coeff_trunc /-
 theorem coeff_trunc (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
     (trunc R n φ).coeff m = if m < n then coeff R m φ else 0 := by simp [Trunc, coeff_trunc_fun]
 #align mv_power_series.coeff_trunc MvPowerSeries.coeff_trunc
+-/
 
+#print MvPowerSeries.trunc_one /-
 @[simp]
 theorem trunc_one (hnn : n ≠ 0) : trunc R n 1 = 1 :=
   MvPolynomial.ext _ _ fun m => by
@@ -663,7 +794,9 @@ theorem trunc_one (hnn : n ≠ 0) : trunc R n 1 = 1 :=
     · symm; rw [MvPolynomial.coeff_one]; refine' if_neg _
       rintro rfl; apply H; exact Ne.bot_lt hnn
 #align mv_power_series.trunc_one MvPowerSeries.trunc_one
+-/
 
+#print MvPowerSeries.trunc_c /-
 @[simp]
 theorem trunc_c (hnn : n ≠ 0) (a : R) : trunc R n (C σ R a) = MvPolynomial.C a :=
   MvPolynomial.ext _ _ fun m =>
@@ -675,6 +808,7 @@ theorem trunc_c (hnn : n ≠ 0) (a : R) : trunc R n (C σ R a) = MvPolynomial.C
       | try simp_all
     exfalso; apply H; subst m; exact Ne.bot_lt hnn
 #align mv_power_series.trunc_C MvPowerSeries.trunc_c
+-/
 
 end Trunc
 
@@ -682,6 +816,7 @@ section Semiring
 
 variable [Semiring R]
 
+#print MvPowerSeries.X_pow_dvd_iff /-
 theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
     (X s : MvPowerSeries σ R) ^ n ∣ φ ↔ ∀ m : σ →₀ ℕ, m s < n → coeff R m φ = 0 :=
   by
@@ -716,7 +851,9 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
         · subst t; simpa using tsub_add_cancel_of_le H
         · simp [Finsupp.single_apply, hst]
 #align mv_power_series.X_pow_dvd_iff MvPowerSeries.X_pow_dvd_iff
+-/
 
+#print MvPowerSeries.X_dvd_iff /-
 theorem X_dvd_iff {s : σ} {φ : MvPowerSeries σ R} :
     (X s : MvPowerSeries σ R) ∣ φ ↔ ∀ m : σ →₀ ℕ, m s = 0 → coeff R m φ = 0 :=
   by
@@ -725,6 +862,7 @@ theorem X_dvd_iff {s : σ} {φ : MvPowerSeries σ R} :
   · exact h m (hm.symm ▸ zero_lt_one)
   · exact h m (Nat.eq_zero_of_le_zero <| Nat.le_of_succ_le_succ hm)
 #align mv_power_series.X_dvd_iff MvPowerSeries.X_dvd_iff
+-/
 
 end Semiring
 
@@ -749,6 +887,7 @@ termination_by' ⟨_, Finsupp.lt_wf σ⟩
 #align mv_power_series.inv.aux MvPowerSeries.inv.aux
 -/
 
+#print MvPowerSeries.coeff_inv_aux /-
 theorem coeff_inv_aux [DecidableEq σ] (n : σ →₀ ℕ) (a : R) (φ : MvPowerSeries σ R) :
     coeff R n (inv.aux a φ) =
       if n = 0 then a
@@ -759,13 +898,17 @@ theorem coeff_inv_aux [DecidableEq σ] (n : σ →₀ ℕ) (a : R) (φ : MvPower
     rw [inv.aux]
     convert rfl
 #align mv_power_series.coeff_inv_aux MvPowerSeries.coeff_inv_aux
+-/
 
+#print MvPowerSeries.invOfUnit /-
 -- unify `decidable` instances
 /-- A multivariate formal power series is invertible if the constant coefficient is invertible.-/
 def invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) : MvPowerSeries σ R :=
   inv.aux (↑u⁻¹) φ
 #align mv_power_series.inv_of_unit MvPowerSeries.invOfUnit
+-/
 
+#print MvPowerSeries.coeff_invOfUnit /-
 theorem coeff_invOfUnit [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (u : Rˣ) :
     coeff R n (invOfUnit φ u) =
       if n = 0 then ↑u⁻¹
@@ -775,13 +918,17 @@ theorem coeff_invOfUnit [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries
             if x.2 < n then coeff R x.1 φ * coeff R x.2 (invOfUnit φ u) else 0 :=
   coeff_inv_aux n (↑u⁻¹) φ
 #align mv_power_series.coeff_inv_of_unit MvPowerSeries.coeff_invOfUnit
+-/
 
+#print MvPowerSeries.constantCoeff_invOfUnit /-
 @[simp]
 theorem constantCoeff_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) :
     constantCoeff σ R (invOfUnit φ u) = ↑u⁻¹ := by
   rw [← coeff_zero_eq_constant_coeff_apply, coeff_inv_of_unit, if_pos rfl]
 #align mv_power_series.constant_coeff_inv_of_unit MvPowerSeries.constantCoeff_invOfUnit
+-/
 
+#print MvPowerSeries.mul_invOfUnit /-
 theorem mul_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) (h : constantCoeff σ R φ = u) :
     φ * invOfUnit φ u = 1 :=
   ext fun n =>
@@ -806,6 +953,7 @@ theorem mul_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) (h : constantCoeff σ
         suffices i = 0 by simp [this]
         ext1 s; exact Nat.eq_zero_of_le_zero (H s)
 #align mv_power_series.mul_inv_of_unit MvPowerSeries.mul_invOfUnit
+-/
 
 end Ring
 
@@ -830,6 +978,7 @@ section LocalRing
 
 variable {S : Type _} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalRingHom f]
 
+#print MvPowerSeries.map.isLocalRingHom /-
 -- Thanks to the linter for informing us that  this instance does
 -- not actually need R and S to be local rings!
 /-- The map `A[[X]] → B[[X]]` induced by a local ring hom `A → B` is local -/
@@ -843,6 +992,7 @@ instance map.isLocalRingHom : IsLocalRingHom (map σ f) :=
     rcases isUnit_of_map_unit f _ this with ⟨c, hc⟩
     exact isUnit_of_mul_eq_one φ (inv_of_unit φ c) (mul_inv_of_unit φ c hc.symm)⟩
 #align mv_power_series.map.is_local_ring_hom MvPowerSeries.map.isLocalRingHom
+-/
 
 end LocalRing
 
@@ -860,6 +1010,7 @@ protected def inv (φ : MvPowerSeries σ k) : MvPowerSeries σ k :=
 instance : Inv (MvPowerSeries σ k) :=
   ⟨MvPowerSeries.inv⟩
 
+#print MvPowerSeries.coeff_inv /-
 theorem coeff_inv [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ k) :
     coeff k n φ⁻¹ =
       if n = 0 then (constantCoeff σ k φ)⁻¹
@@ -868,61 +1019,83 @@ theorem coeff_inv [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ k)
           ∑ x in n.antidiagonal, if x.2 < n then coeff k x.1 φ * coeff k x.2 φ⁻¹ else 0 :=
   coeff_inv_aux n _ φ
 #align mv_power_series.coeff_inv MvPowerSeries.coeff_inv
+-/
 
+#print MvPowerSeries.constantCoeff_inv /-
 @[simp]
 theorem constantCoeff_inv (φ : MvPowerSeries σ k) :
     constantCoeff σ k φ⁻¹ = (constantCoeff σ k φ)⁻¹ := by
   rw [← coeff_zero_eq_constant_coeff_apply, coeff_inv, if_pos rfl]
 #align mv_power_series.constant_coeff_inv MvPowerSeries.constantCoeff_inv
+-/
 
+#print MvPowerSeries.inv_eq_zero /-
 theorem inv_eq_zero {φ : MvPowerSeries σ k} : φ⁻¹ = 0 ↔ constantCoeff σ k φ = 0 :=
   ⟨fun h => by simpa using congr_arg (constant_coeff σ k) h, fun h =>
     ext fun n => by rw [coeff_inv];
       split_ifs <;>
         simp only [h, MvPowerSeries.coeff_zero, MulZeroClass.zero_mul, inv_zero, neg_zero]⟩
 #align mv_power_series.inv_eq_zero MvPowerSeries.inv_eq_zero
+-/
 
+#print MvPowerSeries.zero_inv /-
 @[simp]
 theorem zero_inv : (0 : MvPowerSeries σ k)⁻¹ = 0 := by rw [inv_eq_zero, constant_coeff_zero]
 #align mv_power_series.zero_inv MvPowerSeries.zero_inv
+-/
 
+#print MvPowerSeries.invOfUnit_eq /-
 @[simp]
 theorem invOfUnit_eq (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
     invOfUnit φ (Units.mk0 _ h) = φ⁻¹ :=
   rfl
 #align mv_power_series.inv_of_unit_eq MvPowerSeries.invOfUnit_eq
+-/
 
+#print MvPowerSeries.invOfUnit_eq' /-
 @[simp]
 theorem invOfUnit_eq' (φ : MvPowerSeries σ k) (u : Units k) (h : constantCoeff σ k φ = u) :
     invOfUnit φ u = φ⁻¹ := by
   rw [← inv_of_unit_eq φ (h.symm ▸ u.ne_zero)]
   congr 1; rw [Units.ext_iff]; exact h.symm
 #align mv_power_series.inv_of_unit_eq' MvPowerSeries.invOfUnit_eq'
+-/
 
+#print MvPowerSeries.mul_inv_cancel /-
 @[simp]
 protected theorem mul_inv_cancel (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
     φ * φ⁻¹ = 1 := by rw [← inv_of_unit_eq φ h, mul_inv_of_unit φ (Units.mk0 _ h) rfl]
 #align mv_power_series.mul_inv_cancel MvPowerSeries.mul_inv_cancel
+-/
 
+#print MvPowerSeries.inv_mul_cancel /-
 @[simp]
 protected theorem inv_mul_cancel (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
     φ⁻¹ * φ = 1 := by rw [mul_comm, φ.mul_inv_cancel h]
 #align mv_power_series.inv_mul_cancel MvPowerSeries.inv_mul_cancel
+-/
 
+#print MvPowerSeries.eq_mul_inv_iff_mul_eq /-
 protected theorem eq_mul_inv_iff_mul_eq {φ₁ φ₂ φ₃ : MvPowerSeries σ k}
     (h : constantCoeff σ k φ₃ ≠ 0) : φ₁ = φ₂ * φ₃⁻¹ ↔ φ₁ * φ₃ = φ₂ :=
   ⟨fun k => by simp [k, mul_assoc, MvPowerSeries.inv_mul_cancel _ h], fun k => by
     simp [← k, mul_assoc, MvPowerSeries.mul_inv_cancel _ h]⟩
 #align mv_power_series.eq_mul_inv_iff_mul_eq MvPowerSeries.eq_mul_inv_iff_mul_eq
+-/
 
+#print MvPowerSeries.eq_inv_iff_mul_eq_one /-
 protected theorem eq_inv_iff_mul_eq_one {φ ψ : MvPowerSeries σ k} (h : constantCoeff σ k ψ ≠ 0) :
     φ = ψ⁻¹ ↔ φ * ψ = 1 := by rw [← MvPowerSeries.eq_mul_inv_iff_mul_eq h, one_mul]
 #align mv_power_series.eq_inv_iff_mul_eq_one MvPowerSeries.eq_inv_iff_mul_eq_one
+-/
 
+#print MvPowerSeries.inv_eq_iff_mul_eq_one /-
 protected theorem inv_eq_iff_mul_eq_one {φ ψ : MvPowerSeries σ k} (h : constantCoeff σ k ψ ≠ 0) :
     ψ⁻¹ = φ ↔ φ * ψ = 1 := by rw [eq_comm, MvPowerSeries.eq_inv_iff_mul_eq_one h]
 #align mv_power_series.inv_eq_iff_mul_eq_one MvPowerSeries.inv_eq_iff_mul_eq_one
+-/
 
+#print MvPowerSeries.mul_inv_rev /-
 @[simp]
 protected theorem mul_inv_rev (φ ψ : MvPowerSeries σ k) : (φ * ψ)⁻¹ = ψ⁻¹ * φ⁻¹ :=
   by
@@ -937,11 +1110,13 @@ protected theorem mul_inv_rev (φ ψ : MvPowerSeries σ k) : (φ * ψ)⁻¹ = ψ
     rw [← mul_assoc, mul_assoc _⁻¹, MvPowerSeries.inv_mul_cancel _ h.left, mul_one,
       MvPowerSeries.inv_mul_cancel _ h.right]
 #align mv_power_series.mul_inv_rev MvPowerSeries.mul_inv_rev
+-/
 
 instance : InvOneClass (MvPowerSeries σ k) :=
   { MvPowerSeries.hasOne, MvPowerSeries.hasInv with
     inv_one := by rw [MvPowerSeries.inv_eq_iff_mul_eq_one, mul_one]; simp }
 
+#print MvPowerSeries.C_inv /-
 @[simp]
 theorem C_inv (r : k) : (C σ k r)⁻¹ = C σ k r⁻¹ :=
   by
@@ -950,15 +1125,20 @@ theorem C_inv (r : k) : (C σ k r)⁻¹ = C σ k r⁻¹ :=
   rw [MvPowerSeries.inv_eq_iff_mul_eq_one, ← map_mul, inv_mul_cancel hr, map_one]
   simpa using hr
 #align mv_power_series.C_inv MvPowerSeries.C_inv
+-/
 
+#print MvPowerSeries.X_inv /-
 @[simp]
 theorem X_inv (s : σ) : (X s : MvPowerSeries σ k)⁻¹ = 0 := by rw [inv_eq_zero, constant_coeff_X]
 #align mv_power_series.X_inv MvPowerSeries.X_inv
+-/
 
+#print MvPowerSeries.smul_inv /-
 @[simp]
 theorem smul_inv (r : k) (φ : MvPowerSeries σ k) : (r • φ)⁻¹ = r⁻¹ • φ⁻¹ := by
   simp [smul_eq_C_mul, mul_comm]
 #align mv_power_series.smul_inv MvPowerSeries.smul_inv
+-/
 
 end Field
 
@@ -977,15 +1157,20 @@ instance coeToMvPowerSeries : Coe (MvPolynomial σ R) (MvPowerSeries σ R) :=
 #align mv_polynomial.coe_to_mv_power_series MvPolynomial.coeToMvPowerSeries
 -/
 
+#print MvPolynomial.coe_def /-
 theorem coe_def : (φ : MvPowerSeries σ R) = fun n => coeff n φ :=
   rfl
 #align mv_polynomial.coe_def MvPolynomial.coe_def
+-/
 
+#print MvPolynomial.coeff_coe /-
 @[simp, norm_cast]
 theorem coeff_coe (n : σ →₀ ℕ) : MvPowerSeries.coeff R n ↑φ = coeff n φ :=
   rfl
 #align mv_polynomial.coeff_coe MvPolynomial.coeff_coe
+-/
 
+#print MvPolynomial.coe_monomial /-
 @[simp, norm_cast]
 theorem coe_monomial (n : σ →₀ ℕ) (a : R) :
     (monomial n a : MvPowerSeries σ R) = MvPowerSeries.monomial R n a :=
@@ -998,70 +1183,96 @@ theorem coe_monomial (n : σ →₀ ℕ) (a : R) :
         | subst m <;>
       contradiction
 #align mv_polynomial.coe_monomial MvPolynomial.coe_monomial
+-/
 
+#print MvPolynomial.coe_zero /-
 @[simp, norm_cast]
 theorem coe_zero : ((0 : MvPolynomial σ R) : MvPowerSeries σ R) = 0 :=
   rfl
 #align mv_polynomial.coe_zero MvPolynomial.coe_zero
+-/
 
+#print MvPolynomial.coe_one /-
 @[simp, norm_cast]
 theorem coe_one : ((1 : MvPolynomial σ R) : MvPowerSeries σ R) = 1 :=
   coe_monomial _ _
 #align mv_polynomial.coe_one MvPolynomial.coe_one
+-/
 
+#print MvPolynomial.coe_add /-
 @[simp, norm_cast]
 theorem coe_add : ((φ + ψ : MvPolynomial σ R) : MvPowerSeries σ R) = φ + ψ :=
   rfl
 #align mv_polynomial.coe_add MvPolynomial.coe_add
+-/
 
+#print MvPolynomial.coe_mul /-
 @[simp, norm_cast]
 theorem coe_mul : ((φ * ψ : MvPolynomial σ R) : MvPowerSeries σ R) = φ * ψ :=
   MvPowerSeries.ext fun n => by simp only [coeff_coe, MvPowerSeries.coeff_mul, coeff_mul]
 #align mv_polynomial.coe_mul MvPolynomial.coe_mul
+-/
 
+#print MvPolynomial.coe_C /-
 @[simp, norm_cast]
 theorem coe_C (a : R) : ((C a : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.C σ R a :=
   coe_monomial _ _
 #align mv_polynomial.coe_C MvPolynomial.coe_C
+-/
 
+#print MvPolynomial.coe_bit0 /-
 @[simp, norm_cast]
 theorem coe_bit0 :
     ((bit0 φ : MvPolynomial σ R) : MvPowerSeries σ R) = bit0 (φ : MvPowerSeries σ R) :=
   coe_add _ _
 #align mv_polynomial.coe_bit0 MvPolynomial.coe_bit0
+-/
 
+#print MvPolynomial.coe_bit1 /-
 @[simp, norm_cast]
 theorem coe_bit1 :
     ((bit1 φ : MvPolynomial σ R) : MvPowerSeries σ R) = bit1 (φ : MvPowerSeries σ R) := by
   rw [bit1, bit1, coe_add, coe_one, coe_bit0]
 #align mv_polynomial.coe_bit1 MvPolynomial.coe_bit1
+-/
 
+#print MvPolynomial.coe_X /-
 @[simp, norm_cast]
 theorem coe_X (s : σ) : ((X s : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.X s :=
   coe_monomial _ _
 #align mv_polynomial.coe_X MvPolynomial.coe_X
+-/
 
 variable (σ R)
 
+#print MvPolynomial.coe_injective /-
 theorem coe_injective : Function.Injective (coe : MvPolynomial σ R → MvPowerSeries σ R) :=
   fun x y h => by ext; simp_rw [← coeff_coe, h]
 #align mv_polynomial.coe_injective MvPolynomial.coe_injective
+-/
 
 variable {σ R φ ψ}
 
+#print MvPolynomial.coe_inj /-
 @[simp, norm_cast]
 theorem coe_inj : (φ : MvPowerSeries σ R) = ψ ↔ φ = ψ :=
   (coe_injective σ R).eq_iff
 #align mv_polynomial.coe_inj MvPolynomial.coe_inj
+-/
 
+#print MvPolynomial.coe_eq_zero_iff /-
 @[simp]
 theorem coe_eq_zero_iff : (φ : MvPowerSeries σ R) = 0 ↔ φ = 0 := by rw [← coe_zero, coe_inj]
 #align mv_polynomial.coe_eq_zero_iff MvPolynomial.coe_eq_zero_iff
+-/
 
+#print MvPolynomial.coe_eq_one_iff /-
 @[simp]
 theorem coe_eq_one_iff : (φ : MvPowerSeries σ R) = 1 ↔ φ = 1 := by rw [← coe_one, coe_inj]
 #align mv_polynomial.coe_eq_one_iff MvPolynomial.coe_eq_one_iff
+-/
 
+#print MvPolynomial.coeToMvPowerSeries.ringHom /-
 /-- The coercion from multivariable polynomials to multivariable power series
 as a ring homomorphism.
 -/
@@ -1073,24 +1284,30 @@ def coeToMvPowerSeries.ringHom : MvPolynomial σ R →+* MvPowerSeries σ R
   map_add' := coe_add
   map_mul' := coe_mul
 #align mv_polynomial.coe_to_mv_power_series.ring_hom MvPolynomial.coeToMvPowerSeries.ringHom
+-/
 
+#print MvPolynomial.coe_pow /-
 @[simp, norm_cast]
 theorem coe_pow (n : ℕ) :
     ((φ ^ n : MvPolynomial σ R) : MvPowerSeries σ R) = (φ : MvPowerSeries σ R) ^ n :=
   coeToMvPowerSeries.ringHom.map_pow _ _
 #align mv_polynomial.coe_pow MvPolynomial.coe_pow
+-/
 
 variable (φ ψ)
 
+#print MvPolynomial.coeToMvPowerSeries.ringHom_apply /-
 @[simp]
 theorem coeToMvPowerSeries.ringHom_apply : coeToMvPowerSeries.ringHom φ = φ :=
   rfl
 #align mv_polynomial.coe_to_mv_power_series.ring_hom_apply MvPolynomial.coeToMvPowerSeries.ringHom_apply
+-/
 
 section Algebra
 
 variable (A : Type _) [CommSemiring A] [Algebra R A]
 
+#print MvPolynomial.coeToMvPowerSeries.algHom /-
 /-- The coercion from multivariable polynomials to multivariable power series
 as an algebra homomorphism.
 -/
@@ -1098,12 +1315,15 @@ def coeToMvPowerSeries.algHom : MvPolynomial σ R →ₐ[R] MvPowerSeries σ A :
   { (MvPowerSeries.map σ (algebraMap R A)).comp coeToMvPowerSeries.ringHom with
     commutes' := fun r => by simp [algebraMap_apply, MvPowerSeries.algebraMap_apply] }
 #align mv_polynomial.coe_to_mv_power_series.alg_hom MvPolynomial.coeToMvPowerSeries.algHom
+-/
 
+#print MvPolynomial.coeToMvPowerSeries.algHom_apply /-
 @[simp]
 theorem coeToMvPowerSeries.algHom_apply :
     coeToMvPowerSeries.algHom A φ = MvPowerSeries.map σ (algebraMap R A) ↑φ :=
   rfl
 #align mv_polynomial.coe_to_mv_power_series.alg_hom_apply MvPolynomial.coeToMvPowerSeries.algHom_apply
+-/
 
 end Algebra
 
@@ -1113,25 +1333,33 @@ namespace MvPowerSeries
 
 variable {σ R A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : MvPowerSeries σ R)
 
+#print MvPowerSeries.algebraMvPolynomial /-
 instance algebraMvPolynomial : Algebra (MvPolynomial σ R) (MvPowerSeries σ A) :=
   RingHom.toAlgebra (MvPolynomial.coeToMvPowerSeries.algHom A).toRingHom
 #align mv_power_series.algebra_mv_polynomial MvPowerSeries.algebraMvPolynomial
+-/
 
+#print MvPowerSeries.algebraMvPowerSeries /-
 instance algebraMvPowerSeries : Algebra (MvPowerSeries σ R) (MvPowerSeries σ A) :=
   (map σ (algebraMap R A)).toAlgebra
 #align mv_power_series.algebra_mv_power_series MvPowerSeries.algebraMvPowerSeries
+-/
 
 variable (A)
 
+#print MvPowerSeries.algebraMap_apply' /-
 theorem algebraMap_apply' (p : MvPolynomial σ R) :
     algebraMap (MvPolynomial σ R) (MvPowerSeries σ A) p = map σ (algebraMap R A) p :=
   rfl
 #align mv_power_series.algebra_map_apply' MvPowerSeries.algebraMap_apply'
+-/
 
+#print MvPowerSeries.algebraMap_apply'' /-
 theorem algebraMap_apply'' :
     algebraMap (MvPowerSeries σ R) (MvPowerSeries σ A) f = map σ (algebraMap R A) f :=
   rfl
 #align mv_power_series.algebra_map_apply'' MvPowerSeries.algebraMap_apply''
+-/
 
 end MvPowerSeries
 
@@ -1210,16 +1438,20 @@ theorem coeff_def {s : Unit →₀ ℕ} {n : ℕ} (h : s () = n) : coeff R n = M
 #align power_series.coeff_def PowerSeries.coeff_def
 -/
 
+#print PowerSeries.ext /-
 /-- Two formal power series are equal if all their coefficients are equal.-/
 @[ext]
 theorem ext {φ ψ : PowerSeries R} (h : ∀ n, coeff R n φ = coeff R n ψ) : φ = ψ :=
   MvPowerSeries.ext fun n => by rw [← coeff_def]; · apply h; rfl
 #align power_series.ext PowerSeries.ext
+-/
 
+#print PowerSeries.ext_iff /-
 /-- Two formal power series are equal if all their coefficients are equal.-/
 theorem ext_iff {φ ψ : PowerSeries R} : φ = ψ ↔ ∀ n, coeff R n φ = coeff R n ψ :=
   ⟨fun h n => congr_arg (coeff R n) h, ext⟩
 #align power_series.ext_iff PowerSeries.ext_iff
+-/
 
 #print PowerSeries.mk /-
 /-- Constructor for formal power series.-/
@@ -1227,25 +1459,33 @@ def mk {R} (f : ℕ → R) : PowerSeries R := fun s => f (s ())
 #align power_series.mk PowerSeries.mk
 -/
 
+#print PowerSeries.coeff_mk /-
 @[simp]
 theorem coeff_mk (n : ℕ) (f : ℕ → R) : coeff R n (mk f) = f n :=
   congr_arg f Finsupp.single_eq_same
 #align power_series.coeff_mk PowerSeries.coeff_mk
+-/
 
+#print PowerSeries.coeff_monomial /-
 theorem coeff_monomial (m n : ℕ) (a : R) : coeff R m (monomial R n a) = if m = n then a else 0 :=
   calc
     coeff R m (monomial R n a) = _ := MvPowerSeries.coeff_monomial _ _ _
     _ = if m = n then a else 0 := by simp only [Finsupp.unique_single_eq_iff]
 #align power_series.coeff_monomial PowerSeries.coeff_monomial
+-/
 
+#print PowerSeries.monomial_eq_mk /-
 theorem monomial_eq_mk (n : ℕ) (a : R) : monomial R n a = mk fun m => if m = n then a else 0 :=
   ext fun m => by rw [coeff_monomial, coeff_mk]
 #align power_series.monomial_eq_mk PowerSeries.monomial_eq_mk
+-/
 
+#print PowerSeries.coeff_monomial_same /-
 @[simp]
 theorem coeff_monomial_same (n : ℕ) (a : R) : coeff R n (monomial R n a) = a :=
   MvPowerSeries.coeff_monomial_same _ _
 #align power_series.coeff_monomial_same PowerSeries.coeff_monomial_same
+-/
 
 #print PowerSeries.coeff_comp_monomial /-
 @[simp]
@@ -1256,15 +1496,19 @@ theorem coeff_comp_monomial (n : ℕ) : (coeff R n).comp (monomial R n) = Linear
 
 variable (R)
 
+#print PowerSeries.constantCoeff /-
 /-- The constant coefficient of a formal power series. -/
 def constantCoeff : PowerSeries R →+* R :=
   MvPowerSeries.constantCoeff Unit R
 #align power_series.constant_coeff PowerSeries.constantCoeff
+-/
 
+#print PowerSeries.C /-
 /-- The constant formal power series.-/
 def C : R →+* PowerSeries R :=
   MvPowerSeries.C Unit R
 #align power_series.C PowerSeries.C
+-/
 
 variable {R}
 
@@ -1275,80 +1519,115 @@ def X : PowerSeries R :=
 #align power_series.X PowerSeries.X
 -/
 
+#print PowerSeries.commute_X /-
 theorem commute_X (φ : PowerSeries R) : Commute φ X :=
   φ.commute_X _
 #align power_series.commute_X PowerSeries.commute_X
+-/
 
+#print PowerSeries.coeff_zero_eq_constantCoeff /-
 @[simp]
 theorem coeff_zero_eq_constantCoeff : ⇑(coeff R 0) = constantCoeff R := by
   rw [coeff, Finsupp.single_zero]; rfl
 #align power_series.coeff_zero_eq_constant_coeff PowerSeries.coeff_zero_eq_constantCoeff
+-/
 
+#print PowerSeries.coeff_zero_eq_constantCoeff_apply /-
 theorem coeff_zero_eq_constantCoeff_apply (φ : PowerSeries R) : coeff R 0 φ = constantCoeff R φ :=
   by rw [coeff_zero_eq_constant_coeff] <;> rfl
 #align power_series.coeff_zero_eq_constant_coeff_apply PowerSeries.coeff_zero_eq_constantCoeff_apply
+-/
 
+#print PowerSeries.monomial_zero_eq_C /-
 @[simp]
 theorem monomial_zero_eq_C : ⇑(monomial R 0) = C R := by
   rw [monomial, Finsupp.single_zero, MvPowerSeries.monomial_zero_eq_C, C]
 #align power_series.monomial_zero_eq_C PowerSeries.monomial_zero_eq_C
+-/
 
+#print PowerSeries.monomial_zero_eq_C_apply /-
 theorem monomial_zero_eq_C_apply (a : R) : monomial R 0 a = C R a := by simp
 #align power_series.monomial_zero_eq_C_apply PowerSeries.monomial_zero_eq_C_apply
+-/
 
+#print PowerSeries.coeff_C /-
 theorem coeff_C (n : ℕ) (a : R) : coeff R n (C R a : PowerSeries R) = if n = 0 then a else 0 := by
   rw [← monomial_zero_eq_C_apply, coeff_monomial]
 #align power_series.coeff_C PowerSeries.coeff_C
+-/
 
+#print PowerSeries.coeff_zero_C /-
 @[simp]
 theorem coeff_zero_C (a : R) : coeff R 0 (C R a) = a := by
   rw [← monomial_zero_eq_C_apply, coeff_monomial_same 0 a]
 #align power_series.coeff_zero_C PowerSeries.coeff_zero_C
+-/
 
+#print PowerSeries.X_eq /-
 theorem X_eq : (X : PowerSeries R) = monomial R 1 1 :=
   rfl
 #align power_series.X_eq PowerSeries.X_eq
+-/
 
+#print PowerSeries.coeff_X /-
 theorem coeff_X (n : ℕ) : coeff R n (X : PowerSeries R) = if n = 1 then 1 else 0 := by
   rw [X_eq, coeff_monomial]
 #align power_series.coeff_X PowerSeries.coeff_X
+-/
 
+#print PowerSeries.coeff_zero_X /-
 @[simp]
 theorem coeff_zero_X : coeff R 0 (X : PowerSeries R) = 0 := by
   rw [coeff, Finsupp.single_zero, X, MvPowerSeries.coeff_zero_X]
 #align power_series.coeff_zero_X PowerSeries.coeff_zero_X
+-/
 
+#print PowerSeries.coeff_one_X /-
 @[simp]
 theorem coeff_one_X : coeff R 1 (X : PowerSeries R) = 1 := by rw [coeff_X, if_pos rfl]
 #align power_series.coeff_one_X PowerSeries.coeff_one_X
+-/
 
+#print PowerSeries.X_ne_zero /-
 @[simp]
 theorem X_ne_zero [Nontrivial R] : (X : PowerSeries R) ≠ 0 := fun H => by
   simpa only [coeff_one_X, one_ne_zero, map_zero] using congr_arg (coeff R 1) H
 #align power_series.X_ne_zero PowerSeries.X_ne_zero
+-/
 
+#print PowerSeries.X_pow_eq /-
 theorem X_pow_eq (n : ℕ) : (X : PowerSeries R) ^ n = monomial R n 1 :=
   MvPowerSeries.X_pow_eq _ n
 #align power_series.X_pow_eq PowerSeries.X_pow_eq
+-/
 
+#print PowerSeries.coeff_X_pow /-
 theorem coeff_X_pow (m n : ℕ) : coeff R m ((X : PowerSeries R) ^ n) = if m = n then 1 else 0 := by
   rw [X_pow_eq, coeff_monomial]
 #align power_series.coeff_X_pow PowerSeries.coeff_X_pow
+-/
 
+#print PowerSeries.coeff_X_pow_self /-
 @[simp]
 theorem coeff_X_pow_self (n : ℕ) : coeff R n ((X : PowerSeries R) ^ n) = 1 := by
   rw [coeff_X_pow, if_pos rfl]
 #align power_series.coeff_X_pow_self PowerSeries.coeff_X_pow_self
+-/
 
+#print PowerSeries.coeff_one /-
 @[simp]
 theorem coeff_one (n : ℕ) : coeff R n (1 : PowerSeries R) = if n = 0 then 1 else 0 :=
   coeff_C n 1
 #align power_series.coeff_one PowerSeries.coeff_one
+-/
 
+#print PowerSeries.coeff_zero_one /-
 theorem coeff_zero_one : coeff R 0 (1 : PowerSeries R) = 1 :=
   coeff_zero_C 1
 #align power_series.coeff_zero_one PowerSeries.coeff_zero_one
+-/
 
+#print PowerSeries.coeff_mul /-
 theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
     coeff R n (φ * ψ) = ∑ p in Finset.Nat.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ :=
   by
@@ -1366,26 +1645,36 @@ theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
     · rw [Prod.mk.inj_iff]; dsimp
       exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
 #align power_series.coeff_mul PowerSeries.coeff_mul
+-/
 
+#print PowerSeries.coeff_mul_C /-
 @[simp]
 theorem coeff_mul_C (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (φ * C R a) = coeff R n φ * a :=
   MvPowerSeries.coeff_mul_C _ φ a
 #align power_series.coeff_mul_C PowerSeries.coeff_mul_C
+-/
 
+#print PowerSeries.coeff_C_mul /-
 @[simp]
 theorem coeff_C_mul (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (C R a * φ) = a * coeff R n φ :=
   MvPowerSeries.coeff_C_mul _ φ a
 #align power_series.coeff_C_mul PowerSeries.coeff_C_mul
+-/
 
+#print PowerSeries.coeff_smul /-
 @[simp]
 theorem coeff_smul {S : Type _} [Semiring S] [Module R S] (n : ℕ) (φ : PowerSeries S) (a : R) :
     coeff S n (a • φ) = a • coeff S n φ :=
   rfl
 #align power_series.coeff_smul PowerSeries.coeff_smul
+-/
 
+#print PowerSeries.smul_eq_C_mul /-
 theorem smul_eq_C_mul (f : PowerSeries R) (a : R) : a • f = C R a * f := by ext; simp
 #align power_series.smul_eq_C_mul PowerSeries.smul_eq_C_mul
+-/
 
+#print PowerSeries.coeff_succ_mul_X /-
 @[simp]
 theorem coeff_succ_mul_X (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (φ * X) = coeff R n φ :=
   by
@@ -1393,7 +1682,9 @@ theorem coeff_succ_mul_X (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (φ *
   convert φ.coeff_add_mul_monomial (single () n) (single () 1) _
   rw [mul_one]
 #align power_series.coeff_succ_mul_X PowerSeries.coeff_succ_mul_X
+-/
 
+#print PowerSeries.coeff_succ_X_mul /-
 @[simp]
 theorem coeff_succ_X_mul (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (X * φ) = coeff R n φ :=
   by
@@ -1401,11 +1692,14 @@ theorem coeff_succ_X_mul (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (X * 
   convert φ.coeff_add_monomial_mul (single () 1) (single () n) _
   rw [one_mul]
 #align power_series.coeff_succ_X_mul PowerSeries.coeff_succ_X_mul
+-/
 
+#print PowerSeries.constantCoeff_C /-
 @[simp]
 theorem constantCoeff_C (a : R) : constantCoeff R (C R a) = a :=
   rfl
 #align power_series.constant_coeff_C PowerSeries.constantCoeff_C
+-/
 
 #print PowerSeries.constantCoeff_comp_C /-
 @[simp]
@@ -1414,36 +1708,49 @@ theorem constantCoeff_comp_C : (constantCoeff R).comp (C R) = RingHom.id R :=
 #align power_series.constant_coeff_comp_C PowerSeries.constantCoeff_comp_C
 -/
 
+#print PowerSeries.constantCoeff_zero /-
 @[simp]
 theorem constantCoeff_zero : constantCoeff R 0 = 0 :=
   rfl
 #align power_series.constant_coeff_zero PowerSeries.constantCoeff_zero
+-/
 
+#print PowerSeries.constantCoeff_one /-
 @[simp]
 theorem constantCoeff_one : constantCoeff R 1 = 1 :=
   rfl
 #align power_series.constant_coeff_one PowerSeries.constantCoeff_one
+-/
 
+#print PowerSeries.constantCoeff_X /-
 @[simp]
 theorem constantCoeff_X : constantCoeff R X = 0 :=
   MvPowerSeries.coeff_zero_X _
 #align power_series.constant_coeff_X PowerSeries.constantCoeff_X
+-/
 
+#print PowerSeries.coeff_zero_mul_X /-
 theorem coeff_zero_mul_X (φ : PowerSeries R) : coeff R 0 (φ * X) = 0 := by simp
 #align power_series.coeff_zero_mul_X PowerSeries.coeff_zero_mul_X
+-/
 
+#print PowerSeries.coeff_zero_X_mul /-
 theorem coeff_zero_X_mul (φ : PowerSeries R) : coeff R 0 (X * φ) = 0 := by simp
 #align power_series.coeff_zero_X_mul PowerSeries.coeff_zero_X_mul
+-/
 
 -- The following section duplicates the api of `data.polynomial.coeff` and should attempt to keep
 -- up to date with that
 section
 
+#print PowerSeries.coeff_C_mul_X_pow /-
 theorem coeff_C_mul_X_pow (x : R) (k n : ℕ) :
     coeff R n (C R x * X ^ k : PowerSeries R) = if n = k then x else 0 := by
   simp [X_pow_eq, coeff_monomial]
 #align power_series.coeff_C_mul_X_pow PowerSeries.coeff_C_mul_X_pow
+-/
 
+#print PowerSeries.coeff_mul_X_pow /-
 @[simp]
 theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * X ^ n) = coeff R d p :=
   by
@@ -1452,7 +1759,9 @@ theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * X
     rw [Finset.Nat.mem_antidiagonal, add_right_cancel_iff] at h1 ; subst h1
   · exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
 #align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_X_pow
+-/
 
+#print PowerSeries.coeff_X_pow_mul /-
 @[simp]
 theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (X ^ n * p) = coeff R d p :=
   by
@@ -1462,7 +1771,9 @@ theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (X ^ n
   · rw [add_comm]
     exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
 #align power_series.coeff_X_pow_mul PowerSeries.coeff_X_pow_mul
+-/
 
+#print PowerSeries.coeff_mul_X_pow' /-
 theorem coeff_mul_X_pow' (p : PowerSeries R) (n d : ℕ) :
     coeff R d (p * X ^ n) = ite (n ≤ d) (coeff R (d - n) p) 0 :=
   by
@@ -1472,7 +1783,9 @@ theorem coeff_mul_X_pow' (p : PowerSeries R) (n d : ℕ) :
     rw [coeff_X_pow, if_neg, MulZeroClass.mul_zero]
     exact ((le_of_add_le_right (finset.nat.mem_antidiagonal.mp hx).le).trans_lt <| not_le.mp h).Ne
 #align power_series.coeff_mul_X_pow' PowerSeries.coeff_mul_X_pow'
+-/
 
+#print PowerSeries.coeff_X_pow_mul' /-
 theorem coeff_X_pow_mul' (p : PowerSeries R) (n d : ℕ) :
     coeff R d (X ^ n * p) = ite (n ≤ d) (coeff R (d - n) p) 0 :=
   by
@@ -1484,14 +1797,18 @@ theorem coeff_X_pow_mul' (p : PowerSeries R) (n d : ℕ) :
     rw [add_comm] at this 
     exact ((le_of_add_le_right this.le).trans_lt <| not_le.mp h).Ne
 #align power_series.coeff_X_pow_mul' PowerSeries.coeff_X_pow_mul'
+-/
 
 end
 
+#print PowerSeries.isUnit_constantCoeff /-
 /-- If a formal power series is invertible, then so is its constant coefficient.-/
 theorem isUnit_constantCoeff (φ : PowerSeries R) (h : IsUnit φ) : IsUnit (constantCoeff R φ) :=
   MvPowerSeries.isUnit_constantCoeff φ h
 #align power_series.is_unit_constant_coeff PowerSeries.isUnit_constantCoeff
+-/
 
+#print PowerSeries.eq_shift_mul_X_add_const /-
 /-- Split off the constant coefficient. -/
 theorem eq_shift_mul_X_add_const (φ : PowerSeries R) :
     φ = (mk fun p => coeff R (p + 1) φ) * X + C R (constantCoeff R φ) :=
@@ -1504,7 +1821,9 @@ theorem eq_shift_mul_X_add_const (φ : PowerSeries R) :
     simp only [coeff_succ_mul_X, coeff_mk, LinearMap.map_add, coeff_C, n.succ_ne_zero, sub_zero,
       if_false, add_zero]
 #align power_series.eq_shift_mul_X_add_const PowerSeries.eq_shift_mul_X_add_const
+-/
 
+#print PowerSeries.eq_X_mul_shift_add_const /-
 /-- Split off the constant coefficient. -/
 theorem eq_X_mul_shift_add_const (φ : PowerSeries R) :
     φ = (X * mk fun p => coeff R (p + 1) φ) + C R (constantCoeff R φ) :=
@@ -1517,6 +1836,7 @@ theorem eq_X_mul_shift_add_const (φ : PowerSeries R) :
     simp only [coeff_succ_X_mul, coeff_mk, LinearMap.map_add, coeff_C, n.succ_ne_zero, sub_zero,
       if_false, add_zero]
 #align power_series.eq_X_mul_shift_add_const PowerSeries.eq_X_mul_shift_add_const
+-/
 
 section Map
 
@@ -1524,35 +1844,48 @@ variable {S : Type _} {T : Type _} [Semiring S] [Semiring T]
 
 variable (f : R →+* S) (g : S →+* T)
 
+#print PowerSeries.map /-
 /-- The map between formal power series induced by a map on the coefficients.-/
 def map : PowerSeries R →+* PowerSeries S :=
   MvPowerSeries.map _ f
 #align power_series.map PowerSeries.map
+-/
 
+#print PowerSeries.map_id /-
 @[simp]
 theorem map_id : (map (RingHom.id R) : PowerSeries R → PowerSeries R) = id :=
   rfl
 #align power_series.map_id PowerSeries.map_id
+-/
 
+#print PowerSeries.map_comp /-
 theorem map_comp : map (g.comp f) = (map g).comp (map f) :=
   rfl
 #align power_series.map_comp PowerSeries.map_comp
+-/
 
+#print PowerSeries.coeff_map /-
 @[simp]
 theorem coeff_map (n : ℕ) (φ : PowerSeries R) : coeff S n (map f φ) = f (coeff R n φ) :=
   rfl
 #align power_series.coeff_map PowerSeries.coeff_map
+-/
 
+#print PowerSeries.map_C /-
 @[simp]
 theorem map_C (r : R) : map f (C _ r) = C _ (f r) := by ext; simp [coeff_C, apply_ite f]
 #align power_series.map_C PowerSeries.map_C
+-/
 
+#print PowerSeries.map_X /-
 @[simp]
 theorem map_X : map f X = X := by ext; simp [coeff_X, apply_ite f]
 #align power_series.map_X PowerSeries.map_X
+-/
 
 end Map
 
+#print PowerSeries.X_pow_dvd_iff /-
 theorem X_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
     (X : PowerSeries R) ^ n ∣ φ ↔ ∀ m, m < n → coeff R m φ = 0 :=
   by
@@ -1562,7 +1895,9 @@ theorem X_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
   · rw [Finsupp.unique_single m]; convert h _ hm
   · apply h; simpa only [Finsupp.single_eq_same] using hm
 #align power_series.X_pow_dvd_iff PowerSeries.X_pow_dvd_iff
+-/
 
+#print PowerSeries.X_dvd_iff /-
 theorem X_dvd_iff {φ : PowerSeries R} : (X : PowerSeries R) ∣ φ ↔ constantCoeff R φ = 0 :=
   by
   rw [← pow_one (X : PowerSeries R), X_pow_dvd_iff, ← coeff_zero_eq_constant_coeff_apply]
@@ -1570,6 +1905,7 @@ theorem X_dvd_iff {φ : PowerSeries R} : (X : PowerSeries R) ∣ φ ↔ constant
   · exact h 0 zero_lt_one
   · intro m hm; rwa [Nat.eq_zero_of_le_zero (Nat.le_of_succ_le_succ hm)]
 #align power_series.X_dvd_iff PowerSeries.X_dvd_iff
+-/
 
 end Semiring
 
@@ -1579,6 +1915,7 @@ variable [CommSemiring R]
 
 open Finset Nat
 
+#print PowerSeries.rescale /-
 /-- The ring homomorphism taking a power series `f(X)` to `f(aX)`. -/
 noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R
     where
@@ -1596,13 +1933,17 @@ noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R
     intro b c H
     rw [← H, pow_add, mul_mul_mul_comm]
 #align power_series.rescale PowerSeries.rescale
+-/
 
+#print PowerSeries.coeff_rescale /-
 @[simp]
 theorem coeff_rescale (f : PowerSeries R) (a : R) (n : ℕ) :
     coeff R n (rescale a f) = a ^ n * coeff R n f :=
   coeff_mk n _
 #align power_series.coeff_rescale PowerSeries.coeff_rescale
+-/
 
+#print PowerSeries.rescale_zero /-
 @[simp]
 theorem rescale_zero : rescale 0 = (C R).comp (constantCoeff R) :=
   by
@@ -1613,19 +1954,27 @@ theorem rescale_zero : rescale 0 = (C R).comp (constantCoeff R) :=
   · simp only [h, one_mul, coeff_zero_eq_constant_coeff, pow_zero]
   · rw [zero_pow' n h, MulZeroClass.zero_mul]
 #align power_series.rescale_zero PowerSeries.rescale_zero
+-/
 
+#print PowerSeries.rescale_zero_apply /-
 theorem rescale_zero_apply : rescale 0 X = C R (constantCoeff R X) := by simp
 #align power_series.rescale_zero_apply PowerSeries.rescale_zero_apply
+-/
 
+#print PowerSeries.rescale_one /-
 @[simp]
 theorem rescale_one : rescale 1 = RingHom.id (PowerSeries R) := by ext;
   simp only [RingHom.id_apply, rescale, one_pow, coeff_mk, one_mul, RingHom.coe_mk]
 #align power_series.rescale_one PowerSeries.rescale_one
+-/
 
+#print PowerSeries.rescale_mk /-
 theorem rescale_mk (f : ℕ → R) (a : R) : rescale a (mk f) = mk fun n : ℕ => a ^ n * f n := by ext;
   rw [coeff_rescale, coeff_mk, coeff_mk]
 #align power_series.rescale_mk PowerSeries.rescale_mk
+-/
 
+#print PowerSeries.rescale_rescale /-
 theorem rescale_rescale (f : PowerSeries R) (a b : R) :
     rescale b (rescale a f) = rescale (a * b) f :=
   by
@@ -1633,10 +1982,13 @@ theorem rescale_rescale (f : PowerSeries R) (a b : R) :
   repeat' rw [coeff_rescale]
   rw [mul_pow, mul_comm _ (b ^ n), mul_assoc]
 #align power_series.rescale_rescale PowerSeries.rescale_rescale
+-/
 
+#print PowerSeries.rescale_mul /-
 theorem rescale_mul (a b : R) : rescale (a * b) = (rescale b).comp (rescale a) := by ext;
   simp [← rescale_rescale]
 #align power_series.rescale_mul PowerSeries.rescale_mul
+-/
 
 section Trunc
 
@@ -1647,11 +1999,14 @@ def trunc (n : ℕ) (φ : PowerSeries R) : R[X] :=
 #align power_series.trunc PowerSeries.trunc
 -/
 
+#print PowerSeries.coeff_trunc /-
 theorem coeff_trunc (m) (n) (φ : PowerSeries R) :
     (trunc n φ).coeff m = if m < n then coeff R m φ else 0 := by
   simp [Trunc, Polynomial.coeff_sum, Polynomial.coeff_monomial, Nat.lt_succ_iff]
 #align power_series.coeff_trunc PowerSeries.coeff_trunc
+-/
 
+#print PowerSeries.trunc_zero /-
 @[simp]
 theorem trunc_zero (n) : trunc n (0 : PowerSeries R) = 0 :=
   Polynomial.ext fun m =>
@@ -1659,7 +2014,9 @@ theorem trunc_zero (n) : trunc n (0 : PowerSeries R) = 0 :=
     rw [coeff_trunc, LinearMap.map_zero, Polynomial.coeff_zero]
     split_ifs <;> rfl
 #align power_series.trunc_zero PowerSeries.trunc_zero
+-/
 
+#print PowerSeries.trunc_one /-
 @[simp]
 theorem trunc_one (n) : trunc (n + 1) (1 : PowerSeries R) = 1 :=
   Polynomial.ext fun m => by
@@ -1670,7 +2027,9 @@ theorem trunc_one (n) : trunc (n + 1) (1 : PowerSeries R) = 1 :=
     · symm; refine' if_neg _
       rintro rfl; apply H; exact Nat.zero_lt_succ _
 #align power_series.trunc_one PowerSeries.trunc_one
+-/
 
+#print PowerSeries.trunc_C /-
 @[simp]
 theorem trunc_C (n) (a : R) : trunc (n + 1) (C R a) = Polynomial.C a :=
   Polynomial.ext fun m => by
@@ -1680,7 +2039,9 @@ theorem trunc_C (n) (a : R) : trunc (n + 1) (C R a) = Polynomial.C a :=
       | rfl
       | try simp_all
 #align power_series.trunc_C PowerSeries.trunc_C
+-/
 
+#print PowerSeries.trunc_add /-
 @[simp]
 theorem trunc_add (n) (φ ψ : PowerSeries R) : trunc n (φ + ψ) = trunc n φ + trunc n ψ :=
   Polynomial.ext fun m =>
@@ -1688,6 +2049,7 @@ theorem trunc_add (n) (φ ψ : PowerSeries R) : trunc n (φ + ψ) = trunc n φ +
     simp only [coeff_trunc, AddMonoidHom.map_add, Polynomial.coeff_add]
     split_ifs with H; · rfl; · rw [zero_add]
 #align power_series.trunc_add PowerSeries.trunc_add
+-/
 
 end Trunc
 
@@ -1704,6 +2066,7 @@ protected def inv.aux : R → PowerSeries R → PowerSeries R :=
 #align power_series.inv.aux PowerSeries.inv.aux
 -/
 
+#print PowerSeries.coeff_inv_aux /-
 theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
     coeff R n (inv.aux a φ) =
       if n = 0 then a
@@ -1738,12 +2101,16 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
     · rw [Prod.mk.inj_iff]; dsimp
       exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
 #align power_series.coeff_inv_aux PowerSeries.coeff_inv_aux
+-/
 
+#print PowerSeries.invOfUnit /-
 /-- A formal power series is invertible if the constant coefficient is invertible.-/
 def invOfUnit (φ : PowerSeries R) (u : Rˣ) : PowerSeries R :=
   MvPowerSeries.invOfUnit φ u
 #align power_series.inv_of_unit PowerSeries.invOfUnit
+-/
 
+#print PowerSeries.coeff_invOfUnit /-
 theorem coeff_invOfUnit (n : ℕ) (φ : PowerSeries R) (u : Rˣ) :
     coeff R n (invOfUnit φ u) =
       if n = 0 then ↑u⁻¹
@@ -1753,28 +2120,37 @@ theorem coeff_invOfUnit (n : ℕ) (φ : PowerSeries R) (u : Rˣ) :
             if x.2 < n then coeff R x.1 φ * coeff R x.2 (invOfUnit φ u) else 0 :=
   coeff_inv_aux n (↑u⁻¹) φ
 #align power_series.coeff_inv_of_unit PowerSeries.coeff_invOfUnit
+-/
 
+#print PowerSeries.constantCoeff_invOfUnit /-
 @[simp]
 theorem constantCoeff_invOfUnit (φ : PowerSeries R) (u : Rˣ) :
     constantCoeff R (invOfUnit φ u) = ↑u⁻¹ := by
   rw [← coeff_zero_eq_constant_coeff_apply, coeff_inv_of_unit, if_pos rfl]
 #align power_series.constant_coeff_inv_of_unit PowerSeries.constantCoeff_invOfUnit
+-/
 
+#print PowerSeries.mul_invOfUnit /-
 theorem mul_invOfUnit (φ : PowerSeries R) (u : Rˣ) (h : constantCoeff R φ = u) :
     φ * invOfUnit φ u = 1 :=
   MvPowerSeries.mul_invOfUnit φ u <| h
 #align power_series.mul_inv_of_unit PowerSeries.mul_invOfUnit
+-/
 
+#print PowerSeries.sub_const_eq_shift_mul_X /-
 /-- Two ways of removing the constant coefficient of a power series are the same. -/
 theorem sub_const_eq_shift_mul_X (φ : PowerSeries R) :
     φ - C R (constantCoeff R φ) = (PowerSeries.mk fun p => coeff R (p + 1) φ) * X :=
   sub_eq_iff_eq_add.mpr (eq_shift_mul_X_add_const φ)
 #align power_series.sub_const_eq_shift_mul_X PowerSeries.sub_const_eq_shift_mul_X
+-/
 
+#print PowerSeries.sub_const_eq_X_mul_shift /-
 theorem sub_const_eq_X_mul_shift (φ : PowerSeries R) :
     φ - C R (constantCoeff R φ) = X * PowerSeries.mk fun p => coeff R (p + 1) φ :=
   sub_eq_iff_eq_add.mpr (eq_X_mul_shift_add_const φ)
 #align power_series.sub_const_eq_X_mul_shift PowerSeries.sub_const_eq_X_mul_shift
+-/
 
 end Ring
 
@@ -1782,6 +2158,7 @@ section CommRing
 
 variable {A : Type _} [CommRing A]
 
+#print PowerSeries.rescale_X /-
 @[simp]
 theorem rescale_X (a : A) : rescale a X = C A a * X :=
   by
@@ -1789,20 +2166,27 @@ theorem rescale_X (a : A) : rescale a X = C A a * X :=
   simp only [coeff_rescale, coeff_C_mul, coeff_X]
   split_ifs with h <;> simp [h]
 #align power_series.rescale_X PowerSeries.rescale_X
+-/
 
+#print PowerSeries.rescale_neg_one_X /-
 theorem rescale_neg_one_X : rescale (-1 : A) X = -X := by
   rw [rescale_X, map_neg, map_one, neg_one_mul]
 #align power_series.rescale_neg_one_X PowerSeries.rescale_neg_one_X
+-/
 
+#print PowerSeries.evalNegHom /-
 /-- The ring homomorphism taking a power series `f(X)` to `f(-X)`. -/
 noncomputable def evalNegHom : PowerSeries A →+* PowerSeries A :=
   rescale (-1 : A)
 #align power_series.eval_neg_hom PowerSeries.evalNegHom
+-/
 
+#print PowerSeries.evalNegHom_X /-
 @[simp]
 theorem evalNegHom_X : evalNegHom (X : PowerSeries A) = -X :=
   rescale_neg_one_X
 #align power_series.eval_neg_hom_X PowerSeries.evalNegHom_X
+-/
 
 end CommRing
 
@@ -1810,6 +2194,7 @@ section Domain
 
 variable [Ring R]
 
+#print PowerSeries.eq_zero_or_eq_zero_of_mul_eq_zero /-
 theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSeries R) (h : φ * ψ = 0) :
     φ = 0 ∨ ψ = 0 := by
   rw [or_iff_not_imp_left]; intro H
@@ -1837,6 +2222,7 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSerie
     simpa [Ne.def, Prod.mk.inj_iff] using (add_right_inj m).mp hij
   · contrapose!; intro h; rw [Finset.Nat.mem_antidiagonal]
 #align power_series.eq_zero_or_eq_zero_of_mul_eq_zero PowerSeries.eq_zero_or_eq_zero_of_mul_eq_zero
+-/
 
 instance [NoZeroDivisors R] : NoZeroDivisors (PowerSeries R)
     where eq_zero_or_eq_zero_of_mul_eq_zero := eq_zero_or_eq_zero_of_mul_eq_zero
@@ -1850,6 +2236,7 @@ section IsDomain
 
 variable [CommRing R] [IsDomain R]
 
+#print PowerSeries.span_X_isPrime /-
 /-- The ideal spanned by the variable in the power series ring
  over an integral domain is a prime ideal.-/
 theorem span_X_isPrime : (Ideal.span ({X} : Set (PowerSeries R))).IsPrime :=
@@ -1859,7 +2246,9 @@ theorem span_X_isPrime : (Ideal.span ({X} : Set (PowerSeries R))).IsPrime :=
   apply Ideal.ext; intro φ
   rw [RingHom.mem_ker, Ideal.mem_span_singleton, X_dvd_iff]
 #align power_series.span_X_is_prime PowerSeries.span_X_isPrime
+-/
 
+#print PowerSeries.X_prime /-
 /-- The variable of the power series ring over an integral domain is prime.-/
 theorem X_prime : Prime (X : PowerSeries R) :=
   by
@@ -1867,7 +2256,9 @@ theorem X_prime : Prime (X : PowerSeries R) :=
   · exact span_X_is_prime
   · intro h; simpa using congr_arg (coeff R 1) h
 #align power_series.X_prime PowerSeries.X_prime
+-/
 
+#print PowerSeries.rescale_injective /-
 theorem rescale_injective {a : R} (ha : a ≠ 0) : Function.Injective (rescale a) :=
   by
   intro p q h
@@ -1879,6 +2270,7 @@ theorem rescale_injective {a : R} (ha : a ≠ 0) : Function.Injective (rescale a
   intro h'
   exact ha (pow_eq_zero h')
 #align power_series.rescale_injective PowerSeries.rescale_injective
+-/
 
 end IsDomain
 
@@ -1886,9 +2278,11 @@ section LocalRing
 
 variable {S : Type _} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalRingHom f]
 
+#print PowerSeries.map.isLocalRingHom /-
 instance map.isLocalRingHom : IsLocalRingHom (map f) :=
   MvPowerSeries.map.isLocalRingHom f
 #align power_series.map.is_local_ring_hom PowerSeries.map.isLocalRingHom
+-/
 
 variable [LocalRing R] [LocalRing S]
 
@@ -1901,13 +2295,17 @@ section Algebra
 
 variable {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
+#print PowerSeries.C_eq_algebraMap /-
 theorem C_eq_algebraMap {r : R} : C R r = (algebraMap R (PowerSeries R)) r :=
   rfl
 #align power_series.C_eq_algebra_map PowerSeries.C_eq_algebraMap
+-/
 
+#print PowerSeries.algebraMap_apply /-
 theorem algebraMap_apply {r : R} : algebraMap R (PowerSeries A) r = C A (algebraMap R A r) :=
   MvPowerSeries.algebraMap_apply
 #align power_series.algebra_map_apply PowerSeries.algebraMap_apply
+-/
 
 instance [Nontrivial R] : Nontrivial (Subalgebra R (PowerSeries R)) :=
   MvPowerSeries.Subalgebra.nontrivial
@@ -1928,10 +2326,13 @@ protected def inv : PowerSeries k → PowerSeries k :=
 instance : Inv (PowerSeries k) :=
   ⟨PowerSeries.inv⟩
 
+#print PowerSeries.inv_eq_inv_aux /-
 theorem inv_eq_inv_aux (φ : PowerSeries k) : φ⁻¹ = inv.aux (constantCoeff k φ)⁻¹ φ :=
   rfl
 #align power_series.inv_eq_inv_aux PowerSeries.inv_eq_inv_aux
+-/
 
+#print PowerSeries.coeff_inv /-
 theorem coeff_inv (n) (φ : PowerSeries k) :
     coeff k n φ⁻¹ =
       if n = 0 then (constantCoeff k φ)⁻¹
@@ -1941,80 +2342,109 @@ theorem coeff_inv (n) (φ : PowerSeries k) :
             if x.2 < n then coeff k x.1 φ * coeff k x.2 φ⁻¹ else 0 :=
   by rw [inv_eq_inv_aux, coeff_inv_aux n (constant_coeff k φ)⁻¹ φ]
 #align power_series.coeff_inv PowerSeries.coeff_inv
+-/
 
+#print PowerSeries.constantCoeff_inv /-
 @[simp]
 theorem constantCoeff_inv (φ : PowerSeries k) : constantCoeff k φ⁻¹ = (constantCoeff k φ)⁻¹ :=
   MvPowerSeries.constantCoeff_inv φ
 #align power_series.constant_coeff_inv PowerSeries.constantCoeff_inv
+-/
 
+#print PowerSeries.inv_eq_zero /-
 theorem inv_eq_zero {φ : PowerSeries k} : φ⁻¹ = 0 ↔ constantCoeff k φ = 0 :=
   MvPowerSeries.inv_eq_zero
 #align power_series.inv_eq_zero PowerSeries.inv_eq_zero
+-/
 
+#print PowerSeries.zero_inv /-
 @[simp]
 theorem zero_inv : (0 : PowerSeries k)⁻¹ = 0 :=
   MvPowerSeries.zero_inv
 #align power_series.zero_inv PowerSeries.zero_inv
+-/
 
+#print PowerSeries.invOfUnit_eq /-
 @[simp]
 theorem invOfUnit_eq (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) :
     invOfUnit φ (Units.mk0 _ h) = φ⁻¹ :=
   MvPowerSeries.invOfUnit_eq _ _
 #align power_series.inv_of_unit_eq PowerSeries.invOfUnit_eq
+-/
 
+#print PowerSeries.invOfUnit_eq' /-
 @[simp]
 theorem invOfUnit_eq' (φ : PowerSeries k) (u : Units k) (h : constantCoeff k φ = u) :
     invOfUnit φ u = φ⁻¹ :=
   MvPowerSeries.invOfUnit_eq' φ _ h
 #align power_series.inv_of_unit_eq' PowerSeries.invOfUnit_eq'
+-/
 
+#print PowerSeries.mul_inv_cancel /-
 @[simp]
 protected theorem mul_inv_cancel (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) : φ * φ⁻¹ = 1 :=
   MvPowerSeries.mul_inv_cancel φ h
 #align power_series.mul_inv_cancel PowerSeries.mul_inv_cancel
+-/
 
+#print PowerSeries.inv_mul_cancel /-
 @[simp]
 protected theorem inv_mul_cancel (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) : φ⁻¹ * φ = 1 :=
   MvPowerSeries.inv_mul_cancel φ h
 #align power_series.inv_mul_cancel PowerSeries.inv_mul_cancel
+-/
 
+#print PowerSeries.eq_mul_inv_iff_mul_eq /-
 theorem eq_mul_inv_iff_mul_eq {φ₁ φ₂ φ₃ : PowerSeries k} (h : constantCoeff k φ₃ ≠ 0) :
     φ₁ = φ₂ * φ₃⁻¹ ↔ φ₁ * φ₃ = φ₂ :=
   MvPowerSeries.eq_mul_inv_iff_mul_eq h
 #align power_series.eq_mul_inv_iff_mul_eq PowerSeries.eq_mul_inv_iff_mul_eq
+-/
 
+#print PowerSeries.eq_inv_iff_mul_eq_one /-
 theorem eq_inv_iff_mul_eq_one {φ ψ : PowerSeries k} (h : constantCoeff k ψ ≠ 0) :
     φ = ψ⁻¹ ↔ φ * ψ = 1 :=
   MvPowerSeries.eq_inv_iff_mul_eq_one h
 #align power_series.eq_inv_iff_mul_eq_one PowerSeries.eq_inv_iff_mul_eq_one
+-/
 
+#print PowerSeries.inv_eq_iff_mul_eq_one /-
 theorem inv_eq_iff_mul_eq_one {φ ψ : PowerSeries k} (h : constantCoeff k ψ ≠ 0) :
     ψ⁻¹ = φ ↔ φ * ψ = 1 :=
   MvPowerSeries.inv_eq_iff_mul_eq_one h
 #align power_series.inv_eq_iff_mul_eq_one PowerSeries.inv_eq_iff_mul_eq_one
+-/
 
+#print PowerSeries.mul_inv_rev /-
 @[simp]
 protected theorem mul_inv_rev (φ ψ : PowerSeries k) : (φ * ψ)⁻¹ = ψ⁻¹ * φ⁻¹ :=
   MvPowerSeries.mul_inv_rev _ _
 #align power_series.mul_inv_rev PowerSeries.mul_inv_rev
+-/
 
 instance : InvOneClass (PowerSeries k) :=
   MvPowerSeries.invOneClass
 
+#print PowerSeries.C_inv /-
 @[simp]
 theorem C_inv (r : k) : (C k r)⁻¹ = C k r⁻¹ :=
   MvPowerSeries.C_inv _
 #align power_series.C_inv PowerSeries.C_inv
+-/
 
+#print PowerSeries.X_inv /-
 @[simp]
 theorem X_inv : (X : PowerSeries k)⁻¹ = 0 :=
   MvPowerSeries.X_inv _
 #align power_series.X_inv PowerSeries.X_inv
+-/
 
+#print PowerSeries.smul_inv /-
 @[simp]
 theorem smul_inv (r : k) (φ : PowerSeries k) : (r • φ)⁻¹ = r⁻¹ • φ⁻¹ :=
   MvPowerSeries.smul_inv _ _
 #align power_series.smul_inv PowerSeries.smul_inv
+-/
 
 end Field
 
@@ -2034,12 +2464,14 @@ open multiplicity
 
 variable [Semiring R] {φ : PowerSeries R}
 
+#print PowerSeries.exists_coeff_ne_zero_iff_ne_zero /-
 theorem exists_coeff_ne_zero_iff_ne_zero : (∃ n : ℕ, coeff R n φ ≠ 0) ↔ φ ≠ 0 :=
   by
   refine' not_iff_not.mp _
   push_neg
   simp [PowerSeries.ext_iff]
 #align power_series.exists_coeff_ne_zero_iff_ne_zero PowerSeries.exists_coeff_ne_zero_iff_ne_zero
+-/
 
 #print PowerSeries.order /-
 /-- The order of a formal power series `φ` is the greatest `n : part_enat`
@@ -2049,12 +2481,15 @@ def order (φ : PowerSeries R) : PartENat :=
 #align power_series.order PowerSeries.order
 -/
 
+#print PowerSeries.order_zero /-
 /-- The order of the `0` power series is infinite.-/
 @[simp]
 theorem order_zero : order (0 : PowerSeries R) = ⊤ :=
   dif_pos rfl
 #align power_series.order_zero PowerSeries.order_zero
+-/
 
+#print PowerSeries.order_finite_iff_ne_zero /-
 theorem order_finite_iff_ne_zero : (order φ).Dom ↔ φ ≠ 0 :=
   by
   simp only [order]
@@ -2066,7 +2501,9 @@ theorem order_finite_iff_ne_zero : (order φ).Dom ↔ φ ≠ 0 :=
   · intro h
     simp [h]
 #align power_series.order_finite_iff_ne_zero PowerSeries.order_finite_iff_ne_zero
+-/
 
+#print PowerSeries.coeff_order /-
 /-- If the order of a formal power series is finite,
 then the coefficient indexed by the order is nonzero.-/
 theorem coeff_order (h : (order φ).Dom) : coeff R (φ.order.get h) φ ≠ 0 :=
@@ -2075,7 +2512,9 @@ theorem coeff_order (h : (order φ).Dom) : coeff R (φ.order.get h) φ ≠ 0 :=
   generalize_proofs h
   exact Nat.find_spec h
 #align power_series.coeff_order PowerSeries.coeff_order
+-/
 
+#print PowerSeries.order_le /-
 /-- If the `n`th coefficient of a formal power series is nonzero,
 then the order of the power series is less than or equal to `n`.-/
 theorem order_le (n : ℕ) (h : coeff R n φ ≠ 0) : order φ ≤ n :=
@@ -2086,13 +2525,17 @@ theorem order_le (n : ℕ) (h : coeff R n φ ≠ 0) : order φ ≤ n :=
     exact ⟨n, le_rfl, h⟩
   · exact exists_coeff_ne_zero_iff_ne_zero.mp ⟨n, h⟩
 #align power_series.order_le PowerSeries.order_le
+-/
 
+#print PowerSeries.coeff_of_lt_order /-
 /-- The `n`th coefficient of a formal power series is `0` if `n` is strictly
 smaller than the order of the power series.-/
 theorem coeff_of_lt_order (n : ℕ) (h : ↑n < order φ) : coeff R n φ = 0 := by contrapose! h;
   exact order_le _ h
 #align power_series.coeff_of_lt_order PowerSeries.coeff_of_lt_order
+-/
 
+#print PowerSeries.order_eq_top /-
 /-- The `0` power series is the unique power series with infinite order.-/
 @[simp]
 theorem order_eq_top {φ : PowerSeries R} : φ.order = ⊤ ↔ φ = 0 :=
@@ -2101,7 +2544,9 @@ theorem order_eq_top {φ : PowerSeries R} : φ.order = ⊤ ↔ φ = 0 :=
   · intro h; ext n; rw [(coeff R n).map_zero, coeff_of_lt_order]; simp [h]
   · rintro rfl; exact order_zero
 #align power_series.order_eq_top PowerSeries.order_eq_top
+-/
 
+#print PowerSeries.nat_le_order /-
 /-- The order of a formal power series is at least `n` if
 the `i`th coefficient is `0` for all `i < n`.-/
 theorem nat_le_order (φ : PowerSeries R) (n : ℕ) (h : ∀ i < n, coeff R i φ = 0) : ↑n ≤ order φ :=
@@ -2111,7 +2556,9 @@ theorem nat_le_order (φ : PowerSeries R) (n : ℕ) (h : ∀ i < n, coeff R i φ
   rw [← PartENat.natCast_get this, PartENat.coe_lt_coe] at H 
   exact coeff_order this (h _ H)
 #align power_series.nat_le_order PowerSeries.nat_le_order
+-/
 
+#print PowerSeries.le_order /-
 /-- The order of a formal power series is at least `n` if
 the `i`th coefficient is `0` for all `i < n`.-/
 theorem le_order (φ : PowerSeries R) (n : PartENat) (h : ∀ i : ℕ, ↑i < n → coeff R i φ = 0) :
@@ -2121,7 +2568,9 @@ theorem le_order (φ : PowerSeries R) (n : PartENat) (h : ∀ i : ℕ, ↑i < n
     ext i; exact h _ (PartENat.natCast_lt_top i)
   · apply nat_le_order; simpa only [PartENat.coe_lt_coe] using h
 #align power_series.le_order PowerSeries.le_order
+-/
 
+#print PowerSeries.order_eq_nat /-
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
 and the `i`th coefficient is `0` for all `i < n`.-/
 theorem order_eq_nat {φ : PowerSeries R} {n : ℕ} :
@@ -2131,7 +2580,9 @@ theorem order_eq_nat {φ : PowerSeries R} {n : ℕ} :
   · simpa using (PartENat.natCast_ne_top _).symm
   simp [order, dif_neg hφ, Nat.find_eq_iff]
 #align power_series.order_eq_nat PowerSeries.order_eq_nat
+-/
 
+#print PowerSeries.order_eq /-
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
 and the `i`th coefficient is `0` for all `i < n`.-/
 theorem order_eq {φ : PowerSeries R} {n : PartENat} :
@@ -2145,7 +2596,9 @@ theorem order_eq {φ : PowerSeries R} {n : PartENat} :
     · rintro ⟨h₁, h₂⟩; ext i; exact h₂ i (PartENat.natCast_lt_top i)
   · simpa [PartENat.natCast_inj] using order_eq_nat
 #align power_series.order_eq PowerSeries.order_eq
+-/
 
+#print PowerSeries.le_order_add /-
 /-- The order of the sum of two formal power series
  is at least the minimum of their orders.-/
 theorem le_order_add (φ ψ : PowerSeries R) : min (order φ) (order ψ) ≤ order (φ + ψ) :=
@@ -2153,6 +2606,7 @@ theorem le_order_add (φ ψ : PowerSeries R) : min (order φ) (order ψ) ≤ ord
   refine' le_order _ _ _
   simp (config := { contextual := true }) [coeff_of_lt_order]
 #align power_series.le_order_add PowerSeries.le_order_add
+-/
 
 private theorem order_add_of_order_eq.aux (φ ψ : PowerSeries R) (h : order φ ≠ order ψ)
     (H : order φ < order ψ) : order (φ + ψ) ≤ order φ ⊓ order ψ :=
@@ -2165,6 +2619,7 @@ private theorem order_add_of_order_eq.aux (φ ψ : PowerSeries R) (h : order φ
       rw [(coeff _ _).map_add, coeff_of_lt_order i hi, coeff_of_lt_order i (lt_trans hi H),
         zero_add]
 
+#print PowerSeries.order_add_of_order_eq /-
 /-- The order of the sum of two formal power series
  is the minimum of their orders if their orders differ.-/
 theorem order_add_of_order_eq (φ ψ : PowerSeries R) (h : order φ ≠ order ψ) :
@@ -2177,7 +2632,9 @@ theorem order_add_of_order_eq (φ ψ : PowerSeries R) (h : order φ ≠ order ψ
   · simpa only [add_comm, inf_comm] using order_add_of_order_eq.aux _ _ h.symm H₂
   exfalso; exact h (le_antisymm (not_lt.1 H₂) (not_lt.1 H₁))
 #align power_series.order_add_of_order_eq PowerSeries.order_add_of_order_eq
+-/
 
+#print PowerSeries.order_mul_ge /-
 /-- The order of the product of two formal power series
  is at least the sum of their orders.-/
 theorem order_mul_ge (φ ψ : PowerSeries R) : order φ + order ψ ≤ order (φ * ψ) :=
@@ -2194,7 +2651,9 @@ theorem order_mul_ge (φ ψ : PowerSeries R) : order φ + order ψ ≤ order (φ
   apply ne_of_lt (lt_of_lt_of_le hn <| add_le_add hi hj)
   rw [← Nat.cast_add, hij]
 #align power_series.order_mul_ge PowerSeries.order_mul_ge
+-/
 
+#print PowerSeries.order_monomial /-
 /-- The order of the monomial `a*X^n` is infinite if `a = 0` and `n` otherwise.-/
 theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
     order (monomial R n a) = if a = 0 then ⊤ else n :=
@@ -2205,12 +2664,16 @@ theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
     · rw [PartENat.natCast_inj] at hi ; rwa [hi, coeff_monomial_same]
     · rw [PartENat.coe_lt_coe] at hi ; rw [coeff_monomial, if_neg]; exact ne_of_lt hi
 #align power_series.order_monomial PowerSeries.order_monomial
+-/
 
+#print PowerSeries.order_monomial_of_ne_zero /-
 /-- The order of the monomial `a*X^n` is `n` if `a ≠ 0`.-/
 theorem order_monomial_of_ne_zero (n : ℕ) (a : R) (h : a ≠ 0) : order (monomial R n a) = n := by
   rw [order_monomial, if_neg h]
 #align power_series.order_monomial_of_ne_zero PowerSeries.order_monomial_of_ne_zero
+-/
 
+#print PowerSeries.coeff_mul_of_lt_order /-
 /-- If `n` is strictly smaller than the order of `ψ`, then the `n`th coefficient of its product
 with any other power series is `0`. -/
 theorem coeff_mul_of_lt_order {φ ψ : PowerSeries R} {n : ℕ} (h : ↑n < ψ.order) :
@@ -2225,12 +2688,16 @@ theorem coeff_mul_of_lt_order {φ ψ : PowerSeries R} {n : ℕ} (h : ↑n < ψ.o
   norm_cast
   linarith
 #align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_order
+-/
 
+#print PowerSeries.coeff_mul_one_sub_of_lt_order /-
 theorem coeff_mul_one_sub_of_lt_order {R : Type _} [CommRing R] {φ ψ : PowerSeries R} (n : ℕ)
     (h : ↑n < ψ.order) : coeff R n (φ * (1 - ψ)) = coeff R n φ := by
   simp [coeff_mul_of_lt_order h, mul_sub]
 #align power_series.coeff_mul_one_sub_of_lt_order PowerSeries.coeff_mul_one_sub_of_lt_order
+-/
 
+#print PowerSeries.coeff_mul_prod_one_sub_of_lt_order /-
 theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type _} [CommRing R] (k : ℕ) (s : Finset ι)
     (φ : PowerSeries R) (f : ι → PowerSeries R) :
     (∀ i ∈ s, ↑k < (f i).order) → coeff R k (φ * ∏ i in s, (1 - f i)) = coeff R k φ :=
@@ -2242,7 +2709,9 @@ theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type _} [CommRing R] (k : ℕ
     rw [Finset.prod_insert ha, ← mul_assoc, mul_right_comm, coeff_mul_one_sub_of_lt_order _ t.1]
     exact ih t.2
 #align power_series.coeff_mul_prod_one_sub_of_lt_order PowerSeries.coeff_mul_prod_one_sub_of_lt_order
+-/
 
+#print PowerSeries.X_pow_order_dvd /-
 -- TODO: link with `X_pow_dvd_iff`
 theorem X_pow_order_dvd (h : (order φ).Dom) : X ^ (order φ).get h ∣ φ :=
   by
@@ -2256,7 +2725,9 @@ theorem X_pow_order_dvd (h : (order φ).Dom) : X ^ (order φ).get h ∣ φ :=
     refine' coeff_of_lt_order _ _
     simpa [PartENat.coe_lt_iff] using fun _ => hn
 #align power_series.X_pow_order_dvd PowerSeries.X_pow_order_dvd
+-/
 
+#print PowerSeries.order_eq_multiplicity_X /-
 theorem order_eq_multiplicity_X {R : Type _} [Semiring R] (φ : PowerSeries R) :
     order φ = multiplicity X φ :=
   by
@@ -2279,6 +2750,7 @@ theorem order_eq_multiplicity_X {R : Type _} [Semiring R] (φ : PowerSeries R) :
     · rw [← hn, PartENat.coe_lt_coe]
       exact Nat.lt_succ_self _
 #align power_series.order_eq_multiplicity_X PowerSeries.order_eq_multiplicity_X
+-/
 
 end OrderBasic
 
@@ -2286,11 +2758,13 @@ section OrderZeroNeOne
 
 variable [Semiring R] [Nontrivial R]
 
+#print PowerSeries.order_one /-
 /-- The order of the formal power series `1` is `0`.-/
 @[simp]
 theorem order_one : order (1 : PowerSeries R) = 0 := by
   simpa using order_monomial_of_ne_zero 0 (1 : R) one_ne_zero
 #align power_series.order_one PowerSeries.order_one
+-/
 
 #print PowerSeries.order_X /-
 /-- The order of the formal power series `X` is `1`.-/
@@ -2300,11 +2774,13 @@ theorem order_X : order (X : PowerSeries R) = 1 := by
 #align power_series.order_X PowerSeries.order_X
 -/
 
+#print PowerSeries.order_X_pow /-
 /-- The order of the formal power series `X^n` is `n`.-/
 @[simp]
 theorem order_X_pow (n : ℕ) : order ((X : PowerSeries R) ^ n) = n := by
   rw [X_pow_eq, order_monomial_of_ne_zero]; exact one_ne_zero
 #align power_series.order_X_pow PowerSeries.order_X_pow
+-/
 
 end OrderZeroNeOne
 
@@ -2313,6 +2789,7 @@ section OrderIsDomain
 -- TODO: generalize to `[semiring R] [no_zero_divisors R]`
 variable [CommRing R] [IsDomain R]
 
+#print PowerSeries.order_mul /-
 /-- The order of the product of two formal power series over an integral domain
  is the sum of their orders.-/
 theorem order_mul (φ ψ : PowerSeries R) : order (φ * ψ) = order φ + order ψ :=
@@ -2320,6 +2797,7 @@ theorem order_mul (φ ψ : PowerSeries R) : order (φ * ψ) = order φ + order 
   simp_rw [order_eq_multiplicity_X]
   exact multiplicity.mul X_prime
 #align power_series.order_mul PowerSeries.order_mul
+-/
 
 end OrderIsDomain
 
@@ -2344,54 +2822,72 @@ theorem coe_def : (φ : PowerSeries R) = PowerSeries.mk (coeff φ) :=
 #align polynomial.coe_def Polynomial.coe_def
 -/
 
+#print Polynomial.coeff_coe /-
 @[simp, norm_cast]
 theorem coeff_coe (n) : PowerSeries.coeff R n φ = coeff φ n :=
   congr_arg (coeff φ) Finsupp.single_eq_same
 #align polynomial.coeff_coe Polynomial.coeff_coe
+-/
 
+#print Polynomial.coe_monomial /-
 @[simp, norm_cast]
 theorem coe_monomial (n : ℕ) (a : R) :
     (monomial n a : PowerSeries R) = PowerSeries.monomial R n a := by ext;
   simp [coeff_coe, PowerSeries.coeff_monomial, Polynomial.coeff_monomial, eq_comm]
 #align polynomial.coe_monomial Polynomial.coe_monomial
+-/
 
+#print Polynomial.coe_zero /-
 @[simp, norm_cast]
 theorem coe_zero : ((0 : R[X]) : PowerSeries R) = 0 :=
   rfl
 #align polynomial.coe_zero Polynomial.coe_zero
+-/
 
+#print Polynomial.coe_one /-
 @[simp, norm_cast]
 theorem coe_one : ((1 : R[X]) : PowerSeries R) = 1 :=
   by
   have := coe_monomial 0 (1 : R)
   rwa [PowerSeries.monomial_zero_eq_C_apply] at this 
 #align polynomial.coe_one Polynomial.coe_one
+-/
 
+#print Polynomial.coe_add /-
 @[simp, norm_cast]
 theorem coe_add : ((φ + ψ : R[X]) : PowerSeries R) = φ + ψ := by ext; simp
 #align polynomial.coe_add Polynomial.coe_add
+-/
 
+#print Polynomial.coe_mul /-
 @[simp, norm_cast]
 theorem coe_mul : ((φ * ψ : R[X]) : PowerSeries R) = φ * ψ :=
   PowerSeries.ext fun n => by simp only [coeff_coe, PowerSeries.coeff_mul, coeff_mul]
 #align polynomial.coe_mul Polynomial.coe_mul
+-/
 
+#print Polynomial.coe_C /-
 @[simp, norm_cast]
 theorem coe_C (a : R) : ((C a : R[X]) : PowerSeries R) = PowerSeries.C R a :=
   by
   have := coe_monomial 0 a
   rwa [PowerSeries.monomial_zero_eq_C_apply] at this 
 #align polynomial.coe_C Polynomial.coe_C
+-/
 
+#print Polynomial.coe_bit0 /-
 @[simp, norm_cast]
 theorem coe_bit0 : ((bit0 φ : R[X]) : PowerSeries R) = bit0 (φ : PowerSeries R) :=
   coe_add φ φ
 #align polynomial.coe_bit0 Polynomial.coe_bit0
+-/
 
+#print Polynomial.coe_bit1 /-
 @[simp, norm_cast]
 theorem coe_bit1 : ((bit1 φ : R[X]) : PowerSeries R) = bit1 (φ : PowerSeries R) := by
   rw [bit1, bit1, coe_add, coe_one, coe_bit0]
 #align polynomial.coe_bit1 Polynomial.coe_bit1
+-/
 
 #print Polynomial.coe_X /-
 @[simp, norm_cast]
@@ -2400,10 +2896,12 @@ theorem coe_X : ((X : R[X]) : PowerSeries R) = PowerSeries.X :=
 #align polynomial.coe_X Polynomial.coe_X
 -/
 
+#print Polynomial.constantCoeff_coe /-
 @[simp]
 theorem constantCoeff_coe : PowerSeries.constantCoeff R φ = φ.coeff 0 :=
   rfl
 #align polynomial.constant_coeff_coe Polynomial.constantCoeff_coe
+-/
 
 variable (R)
 
@@ -2422,16 +2920,21 @@ theorem coe_inj : (φ : PowerSeries R) = ψ ↔ φ = ψ :=
 #align polynomial.coe_inj Polynomial.coe_inj
 -/
 
+#print Polynomial.coe_eq_zero_iff /-
 @[simp]
 theorem coe_eq_zero_iff : (φ : PowerSeries R) = 0 ↔ φ = 0 := by rw [← coe_zero, coe_inj]
 #align polynomial.coe_eq_zero_iff Polynomial.coe_eq_zero_iff
+-/
 
+#print Polynomial.coe_eq_one_iff /-
 @[simp]
 theorem coe_eq_one_iff : (φ : PowerSeries R) = 1 ↔ φ = 1 := by rw [← coe_one, coe_inj]
 #align polynomial.coe_eq_one_iff Polynomial.coe_eq_one_iff
+-/
 
 variable (φ ψ)
 
+#print Polynomial.coeToPowerSeries.ringHom /-
 /-- The coercion from polynomials to power series
 as a ring homomorphism.
 -/
@@ -2443,19 +2946,25 @@ def coeToPowerSeries.ringHom : R[X] →+* PowerSeries R
   map_add' := coe_add
   map_mul' := coe_mul
 #align polynomial.coe_to_power_series.ring_hom Polynomial.coeToPowerSeries.ringHom
+-/
 
+#print Polynomial.coeToPowerSeries.ringHom_apply /-
 @[simp]
 theorem coeToPowerSeries.ringHom_apply : coeToPowerSeries.ringHom φ = φ :=
   rfl
 #align polynomial.coe_to_power_series.ring_hom_apply Polynomial.coeToPowerSeries.ringHom_apply
+-/
 
+#print Polynomial.coe_pow /-
 @[simp, norm_cast]
 theorem coe_pow (n : ℕ) : ((φ ^ n : R[X]) : PowerSeries R) = (φ : PowerSeries R) ^ n :=
   coeToPowerSeries.ringHom.map_pow _ _
 #align polynomial.coe_pow Polynomial.coe_pow
+-/
 
 variable (A : Type _) [Semiring A] [Algebra R A]
 
+#print Polynomial.coeToPowerSeries.algHom /-
 /-- The coercion from polynomials to power series
 as an algebra homomorphism.
 -/
@@ -2463,12 +2972,15 @@ def coeToPowerSeries.algHom : R[X] →ₐ[R] PowerSeries A :=
   { (PowerSeries.map (algebraMap R A)).comp coeToPowerSeries.ringHom with
     commutes' := fun r => by simp [algebraMap_apply, PowerSeries.algebraMap_apply] }
 #align polynomial.coe_to_power_series.alg_hom Polynomial.coeToPowerSeries.algHom
+-/
 
+#print Polynomial.coeToPowerSeries.algHom_apply /-
 @[simp]
 theorem coeToPowerSeries.algHom_apply :
     coeToPowerSeries.algHom A φ = PowerSeries.map (algebraMap R A) ↑φ :=
   rfl
 #align polynomial.coe_to_power_series.alg_hom_apply Polynomial.coeToPowerSeries.algHom_apply
+-/
 
 end Polynomial
 
@@ -2476,30 +2988,40 @@ namespace PowerSeries
 
 variable {R A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : PowerSeries R)
 
+#print PowerSeries.algebraPolynomial /-
 instance algebraPolynomial : Algebra R[X] (PowerSeries A) :=
   RingHom.toAlgebra (Polynomial.coeToPowerSeries.algHom A).toRingHom
 #align power_series.algebra_polynomial PowerSeries.algebraPolynomial
+-/
 
+#print PowerSeries.algebraPowerSeries /-
 instance algebraPowerSeries : Algebra (PowerSeries R) (PowerSeries A) :=
   (map (algebraMap R A)).toAlgebra
 #align power_series.algebra_power_series PowerSeries.algebraPowerSeries
+-/
 
+#print PowerSeries.algebraPolynomial' /-
 -- see Note [lower instance priority]
 instance (priority := 100) algebraPolynomial' {A : Type _} [CommSemiring A] [Algebra R A[X]] :
     Algebra R (PowerSeries A) :=
   RingHom.toAlgebra <| Polynomial.coeToPowerSeries.ringHom.comp (algebraMap R A[X])
 #align power_series.algebra_polynomial' PowerSeries.algebraPolynomial'
+-/
 
 variable (A)
 
+#print PowerSeries.algebraMap_apply' /-
 theorem algebraMap_apply' (p : R[X]) : algebraMap R[X] (PowerSeries A) p = map (algebraMap R A) p :=
   rfl
 #align power_series.algebra_map_apply' PowerSeries.algebraMap_apply'
+-/
 
+#print PowerSeries.algebraMap_apply'' /-
 theorem algebraMap_apply'' :
     algebraMap (PowerSeries R) (PowerSeries A) f = map (algebraMap R A) f :=
   rfl
 #align power_series.algebra_map_apply'' PowerSeries.algebraMap_apply''
+-/
 
 end PowerSeries
 

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

@@ -2233,7 +2233,7 @@ theorem coeff_mul_one_sub_of_lt_order {R : Type _} [CommRing R] {φ ψ : PowerSe
 
 theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type _} [CommRing R] (k : ℕ) (s : Finset ι)
     (φ : PowerSeries R) (f : ι → PowerSeries R) :
-    (∀ i ∈ s, ↑k < (f i).order) → coeff R k (φ * ∏ i in s, 1 - f i) = coeff R k φ :=
+    (∀ i ∈ s, ↑k < (f i).order) → coeff R k (φ * ∏ i in s, (1 - f i)) = coeff R k φ :=
   by
   apply Finset.induction_on s
   · simp

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

@@ -1236,7 +1236,6 @@ theorem coeff_monomial (m n : ℕ) (a : R) : coeff R m (monomial R n a) = if m =
   calc
     coeff R m (monomial R n a) = _ := MvPowerSeries.coeff_monomial _ _ _
     _ = if m = n then a else 0 := by simp only [Finsupp.unique_single_eq_iff]
-    
 #align power_series.coeff_monomial PowerSeries.coeff_monomial
 
 theorem monomial_eq_mk (n : ℕ) (a : R) : monomial R n a = mk fun m => if m = n then a else 0 :=

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

@@ -512,7 +512,7 @@ theorem X_inj [Nontrivial R] {s t : σ} : (X s : MvPowerSeries σ R) = X t ↔ s
   ⟨by
     intro h; replace h := congr_arg (coeff R (single s 1)) h;
     rw [coeff_X, if_pos rfl, coeff_X] at h 
-    split_ifs  at h  with H
+    split_ifs at h  with H
     · rw [Finsupp.single_eq_single_iff] at H 
       cases H; · exact H.1; · exfalso; exact one_ne_zero H.1
     · exfalso; exact one_ne_zero h, congr_arg X⟩
@@ -710,11 +710,11 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
         · exact MulZeroClass.zero_mul _
       ·
         classical
-          contrapose! H
-          ext t
-          by_cases hst : s = t
-          · subst t; simpa using tsub_add_cancel_of_le H
-          · simp [Finsupp.single_apply, hst]
+        contrapose! H
+        ext t
+        by_cases hst : s = t
+        · subst t; simpa using tsub_add_cancel_of_le H
+        · simp [Finsupp.single_apply, hst]
 #align mv_power_series.X_pow_dvd_iff MvPowerSeries.X_pow_dvd_iff
 
 theorem X_dvd_iff {s : σ} {φ : MvPowerSeries σ R} :
@@ -1557,11 +1557,11 @@ end Map
 theorem X_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
     (X : PowerSeries R) ^ n ∣ φ ↔ ∀ m, m < n → coeff R m φ = 0 :=
   by
-  convert@MvPowerSeries.X_pow_dvd_iff Unit R _ () n φ; apply propext
+  convert @MvPowerSeries.X_pow_dvd_iff Unit R _ () n φ; apply propext
   classical
-    constructor <;> intro h m hm
-    · rw [Finsupp.unique_single m]; convert h _ hm
-    · apply h; simpa only [Finsupp.single_eq_same] using hm
+  constructor <;> intro h m hm
+  · rw [Finsupp.unique_single m]; convert h _ hm
+  · apply h; simpa only [Finsupp.single_eq_same] using hm
 #align power_series.X_pow_dvd_iff PowerSeries.X_pow_dvd_iff
 
 theorem X_dvd_iff {φ : PowerSeries R} : (X : PowerSeries R) ∣ φ ↔ constantCoeff R φ = 0 :=
@@ -1827,9 +1827,9 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSerie
   · rintro ⟨i, j⟩ hij hne
     by_cases hj : j < n; · rw [ih j hj, MulZeroClass.mul_zero]
     by_cases hi : i < m
-    · specialize hm₂ _ hi; push_neg  at hm₂ ; rw [hm₂, MulZeroClass.zero_mul]
+    · specialize hm₂ _ hi; push_neg at hm₂ ; rw [hm₂, MulZeroClass.zero_mul]
     rw [Finset.Nat.mem_antidiagonal] at hij 
-    push_neg  at hi hj 
+    push_neg at hi hj 
     suffices m < i by
       have : m + n < i + j := add_lt_add_of_lt_of_le this hj
       exfalso; exact ne_of_lt this hij.symm

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

@@ -266,9 +266,9 @@ theorem commute_monomial {a : R} {n} : Commute φ (monomial R n a) ↔ ∀ m, Co
   by
   refine' ext_iff.trans ⟨fun h m => _, fun h m => _⟩
   · have := h (m + n)
-    rwa [coeff_add_mul_monomial, add_comm, coeff_add_monomial_mul] at this
+    rwa [coeff_add_mul_monomial, add_comm, coeff_add_monomial_mul] at this 
   · rw [coeff_mul_monomial, coeff_monomial_mul]
-    split_ifs <;> [apply h;rfl]
+    split_ifs <;> [apply h; rfl]
 #align mv_power_series.commute_monomial MvPowerSeries.commute_monomial
 
 protected theorem one_mul : (1 : MvPowerSeries σ R) * φ = φ :=
@@ -340,10 +340,10 @@ theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
   ext k
   simp only [coeff_mul_monomial, coeff_monomial]
   split_ifs with h₁ h₂ h₃ h₃ h₂ <;> try rfl
-  · rw [← h₂, tsub_add_cancel_of_le h₁] at h₃; exact (h₃ rfl).elim
-  · rw [h₃, add_tsub_cancel_right] at h₂; exact (h₂ rfl).elim
+  · rw [← h₂, tsub_add_cancel_of_le h₁] at h₃ ; exact (h₃ rfl).elim
+  · rw [h₃, add_tsub_cancel_right] at h₂ ; exact (h₂ rfl).elim
   · exact MulZeroClass.zero_mul b
-  · rw [h₂] at h₁; exact (h₁ <| le_add_left le_rfl).elim
+  · rw [h₂] at h₁ ; exact (h₁ <| le_add_left le_rfl).elim
 #align mv_power_series.monomial_mul_monomial MvPowerSeries.monomial_mul_monomial
 
 variable (σ) (R)
@@ -510,9 +510,10 @@ theorem smul_eq_C_mul (f : MvPowerSeries σ R) (a : R) : a • f = C σ R a * f
 #print MvPowerSeries.X_inj /-
 theorem X_inj [Nontrivial R] {s t : σ} : (X s : MvPowerSeries σ R) = X t ↔ s = t :=
   ⟨by
-    intro h; replace h := congr_arg (coeff R (single s 1)) h; rw [coeff_X, if_pos rfl, coeff_X] at h
-    split_ifs  at h with H
-    · rw [Finsupp.single_eq_single_iff] at H
+    intro h; replace h := congr_arg (coeff R (single s 1)) h;
+    rw [coeff_X, if_pos rfl, coeff_X] at h 
+    split_ifs  at h  with H
+    · rw [Finsupp.single_eq_single_iff] at H 
       cases H; · exact H.1; · exfalso; exact one_ne_zero H.1
     · exfalso; exact one_ne_zero h, congr_arg X⟩
 #align mv_power_series.X_inj MvPowerSeries.X_inj
@@ -642,7 +643,7 @@ def trunc : MvPowerSeries σ R →+ MvPolynomial σ R
     where
   toFun := truncFun n
   map_zero' := by ext; simp [coeff_trunc_fun]
-  map_add' := by intros ; ext; simp [coeff_trunc_fun, ite_add]; split_ifs <;> rfl
+  map_add' := by intros; ext; simp [coeff_trunc_fun, ite_add]; split_ifs <;> rfl
 #align mv_power_series.trunc MvPowerSeries.trunc
 -/
 
@@ -668,7 +669,10 @@ theorem trunc_c (hnn : n ≠ 0) (a : R) : trunc R n (C σ R a) = MvPolynomial.C
   MvPolynomial.ext _ _ fun m =>
     by
     rw [coeff_trunc, coeff_C, MvPolynomial.coeff_C]
-    split_ifs with H <;> first |rfl|try simp_all
+    split_ifs with H <;>
+      first
+      | rfl
+      | try simp_all
     exfalso; apply H; subst m; exact Ne.bot_lt hnn
 #align mv_power_series.trunc_C MvPowerSeries.trunc_c
 
@@ -685,21 +689,21 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
   · rintro ⟨φ, rfl⟩ m h
     rw [coeff_mul, Finset.sum_eq_zero]
     rintro ⟨i, j⟩ hij; rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
-    contrapose! h; subst i; rw [Finsupp.mem_antidiagonal] at hij
+    contrapose! h; subst i; rw [Finsupp.mem_antidiagonal] at hij 
     rw [← hij, Finsupp.add_apply, Finsupp.single_eq_same]; exact Nat.le_add_right n _
   · intro h; refine' ⟨fun m => coeff R (m + single s n) φ, _⟩
     ext m; by_cases H : m - single s n + single s n = m
     · rw [coeff_mul, Finset.sum_eq_single (single s n, m - single s n)]
       · rw [coeff_X_pow, if_pos rfl, one_mul]
         simpa using congr_arg (fun m : σ →₀ ℕ => coeff R m φ) H.symm
-      · rintro ⟨i, j⟩ hij hne; rw [Finsupp.mem_antidiagonal] at hij
+      · rintro ⟨i, j⟩ hij hne; rw [Finsupp.mem_antidiagonal] at hij 
         rw [coeff_X_pow]; split_ifs with hi
         · exfalso; apply hne; rw [← hij, ← hi, Prod.mk.inj_iff]; refine' ⟨rfl, _⟩
           ext t; simp only [add_tsub_cancel_left, Finsupp.add_apply, Finsupp.tsub_apply]
         · exact MulZeroClass.zero_mul _
       · intro hni; exfalso; apply hni; rwa [Finsupp.mem_antidiagonal, add_comm]
     · rw [h, coeff_mul, Finset.sum_eq_zero]
-      · rintro ⟨i, j⟩ hij; rw [Finsupp.mem_antidiagonal] at hij
+      · rintro ⟨i, j⟩ hij; rw [Finsupp.mem_antidiagonal] at hij 
         rw [coeff_X_pow]; split_ifs with hi
         · exfalso; apply H; rw [← hij, hi]; ext
           rw [coe_add, coe_add, Pi.add_apply, Pi.add_apply, add_tsub_cancel_left, add_comm]
@@ -740,10 +744,8 @@ well-founded recursion on the coeffients of the inverse.
 protected noncomputable def inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerSeries σ R
   | n =>
     if n = 0 then a
-    else
-      -a *
-        ∑ x in n.antidiagonal, if h : x.2 < n then coeff R x.1 φ * inv.aux x.2 else 0termination_by'
-  ⟨_, Finsupp.lt_wf σ⟩
+    else -a * ∑ x in n.antidiagonal, if h : x.2 < n then coeff R x.1 φ * inv.aux x.2 else 0
+termination_by' ⟨_, Finsupp.lt_wf σ⟩
 #align mv_power_series.inv.aux MvPowerSeries.inv.aux
 -/
 
@@ -793,7 +795,7 @@ theorem mul_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) (h : constantCoeff σ
         Finset.insert_erase this, Finset.sum_insert (Finset.not_mem_erase _ _),
         Finset.insert_erase this, if_neg (not_lt_of_ge <| le_rfl), zero_add, add_comm, ←
         sub_eq_add_neg, sub_eq_zero, Finset.sum_congr rfl]
-      rintro ⟨i, j⟩ hij; rw [Finset.mem_erase, Finsupp.mem_antidiagonal] at hij
+      rintro ⟨i, j⟩ hij; rw [Finset.mem_erase, Finsupp.mem_antidiagonal] at hij 
       cases' hij with h₁ h₂
       subst n; rw [if_pos]
       suffices (0 : _) + j < i + j by simpa
@@ -817,7 +819,7 @@ instance [LocalRing R] : LocalRing (MvPowerSeries σ R) :=
     by
     intro φ
     rcases LocalRing.isUnit_or_isUnit_one_sub_self (constant_coeff σ R φ) with (⟨u, h⟩ | ⟨u, h⟩) <;>
-        [left;right] <;>
+        [left; right] <;>
       · refine' isUnit_of_mul_eq_one _ _ (mul_inv_of_unit _ u _)
         simpa using h.symm
 
@@ -835,9 +837,9 @@ instance map.isLocalRingHom : IsLocalRingHom (map σ f) :=
   ⟨by
     rintro φ ⟨ψ, h⟩
     replace h := congr_arg (constant_coeff σ S) h
-    rw [constant_coeff_map] at h
+    rw [constant_coeff_map] at h 
     have : IsUnit (constant_coeff σ S ↑ψ) := @is_unit_constant_coeff σ S _ (↑ψ) ψ.is_unit
-    rw [h] at this
+    rw [h] at this 
     rcases isUnit_of_map_unit f _ this with ⟨c, hc⟩
     exact isUnit_of_mul_eq_one φ (inv_of_unit φ c) (mul_inv_of_unit φ c hc.symm)⟩
 #align mv_power_series.map.is_local_ring_hom MvPowerSeries.map.isLocalRingHom
@@ -926,12 +928,12 @@ protected theorem mul_inv_rev (φ ψ : MvPowerSeries σ k) : (φ * ψ)⁻¹ = ψ
   by
   by_cases h : constant_coeff σ k (φ * ψ) = 0
   · rw [inv_eq_zero.mpr h]
-    simp only [map_mul, mul_eq_zero] at h
+    simp only [map_mul, mul_eq_zero] at h 
     -- we don't have `no_zero_divisors (mw_power_series σ k)` yet,
       cases h <;>
       simp [inv_eq_zero.mpr h]
   · rw [MvPowerSeries.inv_eq_iff_mul_eq_one h]
-    simp only [not_or, map_mul, mul_eq_zero] at h
+    simp only [not_or, map_mul, mul_eq_zero] at h 
     rw [← mul_assoc, mul_assoc _⁻¹, MvPowerSeries.inv_mul_cancel _ h.left, mul_one,
       MvPowerSeries.inv_mul_cancel _ h.right]
 #align mv_power_series.mul_inv_rev MvPowerSeries.mul_inv_rev
@@ -990,7 +992,11 @@ theorem coe_monomial (n : σ →₀ ℕ) (a : R) :
   MvPowerSeries.ext fun m =>
     by
     rw [coeff_coe, coeff_monomial, MvPowerSeries.coeff_monomial]
-    split_ifs with h₁ h₂ <;> first |rfl|subst m <;> contradiction
+    split_ifs with h₁ h₂ <;>
+        first
+        | rfl
+        | subst m <;>
+      contradiction
 #align mv_polynomial.coe_monomial MvPolynomial.coe_monomial
 
 @[simp, norm_cast]
@@ -1349,14 +1355,14 @@ theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
   by
   symm
   apply Finset.sum_bij fun (p : ℕ × ℕ) h => (single () p.1, single () p.2)
-  · rintro ⟨i, j⟩ hij; rw [Finset.Nat.mem_antidiagonal] at hij
+  · rintro ⟨i, j⟩ hij; rw [Finset.Nat.mem_antidiagonal] at hij 
     rw [Finsupp.mem_antidiagonal, ← Finsupp.single_add, hij]
   · rintro ⟨i, j⟩ hij; rfl
   · rintro ⟨i, j⟩ ⟨k, l⟩ hij hkl
     simpa only [Prod.mk.inj_iff, Finsupp.unique_single_eq_iff] using id
   · rintro ⟨f, g⟩ hfg
     refine' ⟨(f (), g ()), _, _⟩
-    · rw [Finsupp.mem_antidiagonal] at hfg
+    · rw [Finsupp.mem_antidiagonal] at hfg 
       rw [Finset.Nat.mem_antidiagonal, ← Finsupp.add_apply, hfg, Finsupp.single_eq_same]
     · rw [Prod.mk.inj_iff]; dsimp
       exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
@@ -1444,7 +1450,7 @@ theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * X
   by
   rw [coeff_mul, Finset.sum_eq_single (d, n), coeff_X_pow, if_pos rfl, mul_one]
   · rintro ⟨i, j⟩ h1 h2; rw [coeff_X_pow, if_neg, MulZeroClass.mul_zero]; rintro rfl; apply h2
-    rw [Finset.Nat.mem_antidiagonal, add_right_cancel_iff] at h1; subst h1
+    rw [Finset.Nat.mem_antidiagonal, add_right_cancel_iff] at h1 ; subst h1
   · exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
 #align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_X_pow
 
@@ -1453,7 +1459,7 @@ theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (X ^ n
   by
   rw [coeff_mul, Finset.sum_eq_single (n, d), coeff_X_pow, if_pos rfl, one_mul]
   · rintro ⟨i, j⟩ h1 h2; rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]; rintro rfl; apply h2
-    rw [Finset.Nat.mem_antidiagonal, add_comm, add_right_cancel_iff] at h1; subst h1
+    rw [Finset.Nat.mem_antidiagonal, add_comm, add_right_cancel_iff] at h1 ; subst h1
   · rw [add_comm]
     exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
 #align power_series.coeff_X_pow_mul PowerSeries.coeff_X_pow_mul
@@ -1476,7 +1482,7 @@ theorem coeff_X_pow_mul' (p : PowerSeries R) (n d : ℕ) :
   · refine' (coeff_mul _ _ _).trans (Finset.sum_eq_zero fun x hx => _)
     rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
     have := finset.nat.mem_antidiagonal.mp hx
-    rw [add_comm] at this
+    rw [add_comm] at this 
     exact ((le_of_add_le_right this.le).trans_lt <| not_le.mp h).Ne
 #align power_series.coeff_X_pow_mul' PowerSeries.coeff_X_pow_mul'
 
@@ -1582,7 +1588,7 @@ noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R
   map_one' := by
     ext1; simp only [mul_boole, PowerSeries.coeff_mk, PowerSeries.coeff_one]
     split_ifs; · rw [h, pow_zero]; rfl
-  map_add' := by intros ; ext; exact mul_add _ _ _
+  map_add' := by intros; ext; exact mul_add _ _ _
   map_mul' f g := by
     ext
     rw [PowerSeries.coeff_mul, PowerSeries.coeff_mk, PowerSeries.coeff_mul, Finset.mul_sum]
@@ -1670,7 +1676,10 @@ theorem trunc_one (n) : trunc (n + 1) (1 : PowerSeries R) = 1 :=
 theorem trunc_C (n) (a : R) : trunc (n + 1) (C R a) = Polynomial.C a :=
   Polynomial.ext fun m => by
     rw [coeff_trunc, coeff_C, Polynomial.coeff_C]
-    split_ifs with H <;> first |rfl|try simp_all
+    split_ifs with H <;>
+      first
+      | rfl
+      | try simp_all
 #align power_series.trunc_C PowerSeries.trunc_C
 
 @[simp]
@@ -1710,14 +1719,14 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
   congr 1
   symm
   apply Finset.sum_bij fun (p : ℕ × ℕ) h => (single () p.1, single () p.2)
-  · rintro ⟨i, j⟩ hij; rw [Finset.Nat.mem_antidiagonal] at hij
+  · rintro ⟨i, j⟩ hij; rw [Finset.Nat.mem_antidiagonal] at hij 
     rw [Finsupp.mem_antidiagonal, ← Finsupp.single_add, hij]
   · rintro ⟨i, j⟩ hij
     by_cases H : j < n
     · rw [if_pos H, if_pos]; · rfl
       constructor
       · rintro ⟨⟩; simpa [Finsupp.single_eq_same] using le_of_lt H
-      · intro hh; rw [lt_iff_not_ge] at H; apply H
+      · intro hh; rw [lt_iff_not_ge] at H ; apply H
         simpa [Finsupp.single_eq_same] using hh ()
     · rw [if_neg H, if_neg]; rintro ⟨h₁, h₂⟩; apply h₂; rintro ⟨⟩
       simpa [Finsupp.single_eq_same] using not_lt.1 H
@@ -1725,7 +1734,7 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
     simpa only [Prod.mk.inj_iff, Finsupp.unique_single_eq_iff] using id
   · rintro ⟨f, g⟩ hfg
     refine' ⟨(f (), g ()), _, _⟩
-    · rw [Finsupp.mem_antidiagonal] at hfg
+    · rw [Finsupp.mem_antidiagonal] at hfg 
       rw [Finset.Nat.mem_antidiagonal, ← Finsupp.add_apply, hfg, Finsupp.single_eq_same]
     · rw [Prod.mk.inj_iff]; dsimp
       exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
@@ -1812,15 +1821,15 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSerie
   ext n; rw [(coeff R n).map_zero]; apply Nat.strong_induction_on n
   clear n; intro n ih
   replace h := congr_arg (coeff R (m + n)) h
-  rw [LinearMap.map_zero, coeff_mul, Finset.sum_eq_single (m, n)] at h
+  rw [LinearMap.map_zero, coeff_mul, Finset.sum_eq_single (m, n)] at h 
   · replace h := eq_zero_or_eq_zero_of_mul_eq_zero h
-    rw [or_iff_not_imp_left] at h; exact h hm₁
+    rw [or_iff_not_imp_left] at h ; exact h hm₁
   · rintro ⟨i, j⟩ hij hne
     by_cases hj : j < n; · rw [ih j hj, MulZeroClass.mul_zero]
     by_cases hi : i < m
-    · specialize hm₂ _ hi; push_neg  at hm₂; rw [hm₂, MulZeroClass.zero_mul]
-    rw [Finset.Nat.mem_antidiagonal] at hij
-    push_neg  at hi hj
+    · specialize hm₂ _ hi; push_neg  at hm₂ ; rw [hm₂, MulZeroClass.zero_mul]
+    rw [Finset.Nat.mem_antidiagonal] at hij 
+    push_neg  at hi hj 
     suffices m < i by
       have : m + n < i + j := add_lt_add_of_lt_of_le this hj
       exfalso; exact ne_of_lt this hij.symm
@@ -1866,7 +1875,7 @@ theorem rescale_injective {a : R} (ha : a ≠ 0) : Function.Injective (rescale a
   rw [PowerSeries.ext_iff] at *
   intro n
   specialize h n
-  rw [coeff_rescale, coeff_rescale, mul_eq_mul_left_iff] at h
+  rw [coeff_rescale, coeff_rescale, mul_eq_mul_left_iff] at h 
   apply h.resolve_right
   intro h'
   exact ha (pow_eq_zero h')
@@ -2098,9 +2107,9 @@ theorem order_eq_top {φ : PowerSeries R} : φ.order = ⊤ ↔ φ = 0 :=
 the `i`th coefficient is `0` for all `i < n`.-/
 theorem nat_le_order (φ : PowerSeries R) (n : ℕ) (h : ∀ i < n, coeff R i φ = 0) : ↑n ≤ order φ :=
   by
-  by_contra H; rw [not_le] at H
+  by_contra H; rw [not_le] at H 
   have : (order φ).Dom := PartENat.dom_of_le_natCast H.le
-  rw [← PartENat.natCast_get this, PartENat.coe_lt_coe] at H
+  rw [← PartENat.natCast_get this, PartENat.coe_lt_coe] at H 
   exact coeff_order this (h _ H)
 #align power_series.nat_le_order PowerSeries.nat_le_order
 
@@ -2151,7 +2160,7 @@ private theorem order_add_of_order_eq.aux (φ ψ : PowerSeries R) (h : order φ
   by
   suffices order (φ + ψ) = order φ by rw [le_inf_iff, this]; exact ⟨le_rfl, le_of_lt H⟩
   · rw [order_eq]; constructor
-    · intro i hi; rw [← hi] at H; rw [(coeff _ _).map_add, coeff_of_lt_order i H, add_zero]
+    · intro i hi; rw [← hi] at H ; rw [(coeff _ _).map_add, coeff_of_lt_order i H, add_zero]
       exact (order_eq_nat.1 hi.symm).1
     · intro i hi
       rw [(coeff _ _).map_add, coeff_of_lt_order i hi, coeff_of_lt_order i (lt_trans hi H),
@@ -2181,7 +2190,7 @@ theorem order_mul_ge (φ ψ : PowerSeries R) : order φ + order ψ ≤ order (φ
   · rw [coeff_of_lt_order i hi, MulZeroClass.zero_mul]
   by_cases hj : ↑j < order ψ
   · rw [coeff_of_lt_order j hj, MulZeroClass.mul_zero]
-  rw [not_lt] at hi hj; rw [Finset.Nat.mem_antidiagonal] at hij
+  rw [not_lt] at hi hj ; rw [Finset.Nat.mem_antidiagonal] at hij 
   exfalso
   apply ne_of_lt (lt_of_lt_of_le hn <| add_le_add hi hj)
   rw [← Nat.cast_add, hij]
@@ -2194,8 +2203,8 @@ theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
   split_ifs with h
   · rw [h, order_eq_top, LinearMap.map_zero]
   · rw [order_eq]; constructor <;> intro i hi
-    · rw [PartENat.natCast_inj] at hi; rwa [hi, coeff_monomial_same]
-    · rw [PartENat.coe_lt_coe] at hi; rw [coeff_monomial, if_neg]; exact ne_of_lt hi
+    · rw [PartENat.natCast_inj] at hi ; rwa [hi, coeff_monomial_same]
+    · rw [PartENat.coe_lt_coe] at hi ; rw [coeff_monomial, if_neg]; exact ne_of_lt hi
 #align power_series.order_monomial PowerSeries.order_monomial
 
 /-- The order of the monomial `a*X^n` is `n` if `a ≠ 0`.-/
@@ -2213,7 +2222,7 @@ theorem coeff_mul_of_lt_order {φ ψ : PowerSeries R} {n : ℕ} (h : ↑n < ψ.o
   rw [coeff_mul]
   apply Finset.sum_congr rfl fun x hx => _
   refine' mul_eq_zero_of_right (coeff R x.fst φ) (coeff_of_lt_order x.snd (lt_of_le_of_lt _ h))
-  rw [Finset.Nat.mem_antidiagonal] at hx
+  rw [Finset.Nat.mem_antidiagonal] at hx 
   norm_cast
   linarith
 #align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_order
@@ -2230,7 +2239,7 @@ theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type _} [CommRing R] (k : ℕ
   apply Finset.induction_on s
   · simp
   · intro a s ha ih t
-    simp only [Finset.mem_insert, forall_eq_or_imp] at t
+    simp only [Finset.mem_insert, forall_eq_or_imp] at t 
     rw [Finset.prod_insert ha, ← mul_assoc, mul_right_comm, coeff_mul_one_sub_of_lt_order _ t.1]
     exact ih t.2
 #align power_series.coeff_mul_prod_one_sub_of_lt_order PowerSeries.coeff_mul_prod_one_sub_of_lt_order
@@ -2263,7 +2272,7 @@ theorem order_eq_multiplicity_X {R : Type _} [Semiring R] (φ : PowerSeries R) :
       (PartENat.find_le _ _ _)
   rintro ⟨ψ, H⟩
   have := congr_arg (coeff R n) H
-  rw [← (ψ.commute_X.pow_right _).Eq, coeff_mul_of_lt_order, ← hn] at this
+  rw [← (ψ.commute_X.pow_right _).Eq, coeff_mul_of_lt_order, ← hn] at this 
   · exact coeff_order _ this
   · rw [X_pow_eq, order_monomial]
     split_ifs
@@ -2356,7 +2365,7 @@ theorem coe_zero : ((0 : R[X]) : PowerSeries R) = 0 :=
 theorem coe_one : ((1 : R[X]) : PowerSeries R) = 1 :=
   by
   have := coe_monomial 0 (1 : R)
-  rwa [PowerSeries.monomial_zero_eq_C_apply] at this
+  rwa [PowerSeries.monomial_zero_eq_C_apply] at this 
 #align polynomial.coe_one Polynomial.coe_one
 
 @[simp, norm_cast]
@@ -2372,7 +2381,7 @@ theorem coe_mul : ((φ * ψ : R[X]) : PowerSeries R) = φ * ψ :=
 theorem coe_C (a : R) : ((C a : R[X]) : PowerSeries R) = PowerSeries.C R a :=
   by
   have := coe_monomial 0 a
-  rwa [PowerSeries.monomial_zero_eq_C_apply] at this
+  rwa [PowerSeries.monomial_zero_eq_C_apply] at this 
 #align polynomial.coe_C Polynomial.coe_C
 
 @[simp, norm_cast]

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

@@ -2456,13 +2456,11 @@ def coeToPowerSeries.algHom : R[X] →ₐ[R] PowerSeries A :=
     commutes' := fun r => by simp [algebraMap_apply, PowerSeries.algebraMap_apply] }
 #align polynomial.coe_to_power_series.alg_hom Polynomial.coeToPowerSeries.algHom
 
-#print Polynomial.coeToPowerSeries.algHom_apply /-
 @[simp]
 theorem coeToPowerSeries.algHom_apply :
     coeToPowerSeries.algHom A φ = PowerSeries.map (algebraMap R A) ↑φ :=
   rfl
 #align polynomial.coe_to_power_series.alg_hom_apply Polynomial.coeToPowerSeries.algHom_apply
--/
 
 end Polynomial
 

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

@@ -76,7 +76,7 @@ Occasionally this leads to proofs that are uglier than expected.
 
 noncomputable section
 
-open Classical BigOperators Polynomial
+open scoped Classical BigOperators Polynomial
 
 #print MvPowerSeries /-
 /-- Multivariate formal power series, where `σ` is the index set of the variables

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

@@ -140,43 +140,22 @@ def coeff (n : σ →₀ ℕ) : MvPowerSeries σ R →ₗ[R] R :=
 
 variable {R}
 
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 /-- Two multivariate formal power series are equal if all their coefficients are equal.-/
 @[ext]
 theorem ext {φ ψ} (h : ∀ n : σ →₀ ℕ, coeff R n φ = coeff R n ψ) : φ = ψ :=
   funext h
 #align mv_power_series.ext MvPowerSeries.ext
 
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 /-- Two multivariate formal power series are equal
  if and only if all their coefficients are equal.-/
 theorem ext_iff {φ ψ : MvPowerSeries σ R} : φ = ψ ↔ ∀ n : σ →₀ ℕ, coeff R n φ = coeff R n ψ :=
   Function.funext_iff
 #align mv_power_series.ext_iff MvPowerSeries.ext_iff
 
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 theorem monomial_def [DecidableEq σ] (n : σ →₀ ℕ) : monomial R n = LinearMap.stdBasis R _ n := by
   convert rfl
 #align mv_power_series.monomial_def MvPowerSeries.monomial_def
 
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 -- unify the `decidable` arguments
 theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
     coeff R m (monomial R n a) = if m = n then a else 0 := by
@@ -184,46 +163,25 @@ theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
     Pi.zero_apply]
 #align mv_power_series.coeff_monomial MvPowerSeries.coeff_monomial
 
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 @[simp]
 theorem coeff_monomial_same (n : σ →₀ ℕ) (a : R) : coeff R n (monomial R n a) = a :=
   LinearMap.stdBasis_same R _ n a
 #align mv_power_series.coeff_monomial_same MvPowerSeries.coeff_monomial_same
 
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 theorem coeff_monomial_ne {m n : σ →₀ ℕ} (h : m ≠ n) (a : R) : coeff R m (monomial R n a) = 0 :=
   LinearMap.stdBasis_ne R _ _ _ h a
 #align mv_power_series.coeff_monomial_ne MvPowerSeries.coeff_monomial_ne
 
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 theorem eq_of_coeff_monomial_ne_zero {m n : σ →₀ ℕ} {a : R} (h : coeff R m (monomial R n a) ≠ 0) :
     m = n :=
   by_contra fun h' => h <| coeff_monomial_ne h' a
 #align mv_power_series.eq_of_coeff_monomial_ne_zero MvPowerSeries.eq_of_coeff_monomial_ne_zero
 
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 @[simp]
 theorem coeff_comp_monomial (n : σ →₀ ℕ) : (coeff R n).comp (monomial R n) = LinearMap.id :=
   LinearMap.ext <| coeff_monomial_same n
 #align mv_power_series.coeff_comp_monomial MvPowerSeries.coeff_comp_monomial
 
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 @[simp]
 theorem coeff_zero (n : σ →₀ ℕ) : coeff R n (0 : MvPowerSeries σ R) = 0 :=
   rfl
@@ -234,29 +192,14 @@ variable (m n : σ →₀ ℕ) (φ ψ : MvPowerSeries σ R)
 instance : One (MvPowerSeries σ R) :=
   ⟨monomial R (0 : σ →₀ ℕ) 1⟩
 
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 theorem coeff_one [DecidableEq σ] : coeff R n (1 : MvPowerSeries σ R) = if n = 0 then 1 else 0 :=
   coeff_monomial _ _ _
 #align mv_power_series.coeff_one MvPowerSeries.coeff_one
 
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 theorem coeff_zero_one : coeff R (0 : σ →₀ ℕ) 1 = 1 :=
   coeff_monomial_same 0 1
 #align mv_power_series.coeff_zero_one MvPowerSeries.coeff_zero_one
 
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 theorem monomial_zero_one : monomial R (0 : σ →₀ ℕ) 1 = 1 :=
   rfl
 #align mv_power_series.monomial_zero_one MvPowerSeries.monomial_zero_one
@@ -271,37 +214,19 @@ instance : AddMonoidWithOne (MvPowerSeries σ R) :=
 instance : Mul (MvPowerSeries σ R) :=
   ⟨fun φ ψ n => ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ⟩
 
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 theorem coeff_mul :
     coeff R n (φ * ψ) = ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ :=
   rfl
 #align mv_power_series.coeff_mul MvPowerSeries.coeff_mul
 
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 protected theorem zero_mul : (0 : MvPowerSeries σ R) * φ = 0 :=
   ext fun n => by simp [coeff_mul]
 #align mv_power_series.zero_mul MvPowerSeries.zero_mul
 
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 protected theorem mul_zero : φ * 0 = 0 :=
   ext fun n => by simp [coeff_mul]
 #align mv_power_series.mul_zero MvPowerSeries.mul_zero
 
-/- warning: mv_power_series.coeff_monomial_mul -> MvPowerSeries.coeff_monomial_mul is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_monomial_mul MvPowerSeries.coeff_monomial_mulₓ'. -/
 theorem coeff_monomial_mul (a : R) :
     coeff R m (monomial R n a * φ) = if n ≤ m then a * coeff R (m - n) φ else 0 :=
   by
@@ -313,9 +238,6 @@ theorem coeff_monomial_mul (a : R) :
   simp only [Finset.sum_singleton, coeff_monomial_same, Finset.sum_empty]
 #align mv_power_series.coeff_monomial_mul MvPowerSeries.coeff_monomial_mul
 
-/- warning: mv_power_series.coeff_mul_monomial -> MvPowerSeries.coeff_mul_monomial is a dubious translation:
-<too large>
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 theorem coeff_mul_monomial (a : R) :
     coeff R m (φ * monomial R n a) = if n ≤ m then coeff R (m - n) φ * a else 0 :=
   by
@@ -327,27 +249,18 @@ theorem coeff_mul_monomial (a : R) :
   simp only [Finset.sum_singleton, coeff_monomial_same, Finset.sum_empty]
 #align mv_power_series.coeff_mul_monomial MvPowerSeries.coeff_mul_monomial
 
-/- warning: mv_power_series.coeff_add_monomial_mul -> MvPowerSeries.coeff_add_monomial_mul is a dubious translation:
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 theorem coeff_add_monomial_mul (a : R) : coeff R (m + n) (monomial R m a * φ) = a * coeff R n φ :=
   by
   rw [coeff_monomial_mul, if_pos, add_tsub_cancel_left]
   exact le_add_right le_rfl
 #align mv_power_series.coeff_add_monomial_mul MvPowerSeries.coeff_add_monomial_mul
 
-/- warning: mv_power_series.coeff_add_mul_monomial -> MvPowerSeries.coeff_add_mul_monomial is a dubious translation:
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 theorem coeff_add_mul_monomial (a : R) : coeff R (m + n) (φ * monomial R n a) = coeff R m φ * a :=
   by
   rw [coeff_mul_monomial, if_pos, add_tsub_cancel_right]
   exact le_add_left le_rfl
 #align mv_power_series.coeff_add_mul_monomial MvPowerSeries.coeff_add_mul_monomial
 
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 @[simp]
 theorem commute_monomial {a : R} {n} : Commute φ (monomial R n a) ↔ ∀ m, Commute (coeff R m φ) a :=
   by
@@ -358,52 +271,22 @@ theorem commute_monomial {a : R} {n} : Commute φ (monomial R n a) ↔ ∀ m, Co
     split_ifs <;> [apply h;rfl]
 #align mv_power_series.commute_monomial MvPowerSeries.commute_monomial
 
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 protected theorem one_mul : (1 : MvPowerSeries σ R) * φ = φ :=
   ext fun n => by simpa using coeff_add_monomial_mul 0 n φ 1
 #align mv_power_series.one_mul MvPowerSeries.one_mul
 
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 protected theorem mul_one : φ * 1 = φ :=
   ext fun n => by simpa using coeff_add_mul_monomial n 0 φ 1
 #align mv_power_series.mul_one MvPowerSeries.mul_one
 
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 protected theorem mul_add (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : φ₁ * (φ₂ + φ₃) = φ₁ * φ₂ + φ₁ * φ₃ :=
   ext fun n => by simp only [coeff_mul, mul_add, Finset.sum_add_distrib, LinearMap.map_add]
 #align mv_power_series.mul_add MvPowerSeries.mul_add
 
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 protected theorem add_mul (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : (φ₁ + φ₂) * φ₃ = φ₁ * φ₃ + φ₂ * φ₃ :=
   ext fun n => by simp only [coeff_mul, add_mul, Finset.sum_add_distrib, LinearMap.map_add]
 #align mv_power_series.add_mul MvPowerSeries.add_mul
 
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 protected theorem mul_assoc (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : φ₁ * φ₂ * φ₃ = φ₁ * (φ₂ * φ₃) :=
   by
   ext1 n
@@ -451,9 +334,6 @@ section Semiring
 
 variable [Semiring R]
 
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-<too large>
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 theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
     monomial R m a * monomial R n b = monomial R (m + n) (a * b) :=
   by
@@ -468,12 +348,6 @@ theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
 
 variable (σ) (R)
 
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 /-- The constant multivariate formal power series.-/
 def C : R →+* MvPowerSeries σ R :=
   { monomial R (0 : σ →₀ ℕ) with
@@ -484,38 +358,20 @@ def C : R →+* MvPowerSeries σ R :=
 
 variable {σ} {R}
 
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 @[simp]
 theorem monomial_zero_eq_C : ⇑(monomial R (0 : σ →₀ ℕ)) = C σ R :=
   rfl
 #align mv_power_series.monomial_zero_eq_C MvPowerSeries.monomial_zero_eq_C
 
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 theorem monomial_zero_eq_C_apply (a : R) : monomial R (0 : σ →₀ ℕ) a = C σ R a :=
   rfl
 #align mv_power_series.monomial_zero_eq_C_apply MvPowerSeries.monomial_zero_eq_C_apply
 
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 theorem coeff_C [DecidableEq σ] (n : σ →₀ ℕ) (a : R) :
     coeff R n (C σ R a) = if n = 0 then a else 0 :=
   coeff_monomial _ _ _
 #align mv_power_series.coeff_C MvPowerSeries.coeff_C
 
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 theorem coeff_zero_C (a : R) : coeff R (0 : σ →₀ ℕ) (C σ R a) = a :=
   coeff_monomial_same 0 a
 #align mv_power_series.coeff_zero_C MvPowerSeries.coeff_zero_C
@@ -527,75 +383,33 @@ def X (s : σ) : MvPowerSeries σ R :=
 #align mv_power_series.X MvPowerSeries.X
 -/
 
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 theorem coeff_X [DecidableEq σ] (n : σ →₀ ℕ) (s : σ) :
     coeff R n (X s : MvPowerSeries σ R) = if n = single s 1 then 1 else 0 :=
   coeff_monomial _ _ _
 #align mv_power_series.coeff_X MvPowerSeries.coeff_X
 
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 theorem coeff_index_single_X [DecidableEq σ] (s t : σ) :
     coeff R (single t 1) (X s : MvPowerSeries σ R) = if t = s then 1 else 0 := by
   simp only [coeff_X, single_left_inj one_ne_zero]
 #align mv_power_series.coeff_index_single_X MvPowerSeries.coeff_index_single_X
 
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 @[simp]
 theorem coeff_index_single_self_X (s : σ) : coeff R (single s 1) (X s : MvPowerSeries σ R) = 1 :=
   coeff_monomial_same _ _
 #align mv_power_series.coeff_index_single_self_X MvPowerSeries.coeff_index_single_self_X
 
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 theorem coeff_zero_X (s : σ) : coeff R (0 : σ →₀ ℕ) (X s : MvPowerSeries σ R) = 0 := by
   rw [coeff_X, if_neg]; intro h; exact one_ne_zero (single_eq_zero.mp h.symm)
 #align mv_power_series.coeff_zero_X MvPowerSeries.coeff_zero_X
 
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 theorem commute_X (φ : MvPowerSeries σ R) (s : σ) : Commute φ (X s) :=
   φ.commute_monomial.mpr fun m => Commute.one_right _
 #align mv_power_series.commute_X MvPowerSeries.commute_X
 
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 theorem X_def (s : σ) : X s = monomial R (single s 1) 1 :=
   rfl
 #align mv_power_series.X_def MvPowerSeries.X_def
 
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 theorem X_pow_eq (s : σ) (n : ℕ) : (X s : MvPowerSeries σ R) ^ n = monomial R (single s n) 1 :=
   by
   induction' n with n ih
@@ -603,60 +417,33 @@ theorem X_pow_eq (s : σ) (n : ℕ) : (X s : MvPowerSeries σ R) ^ n = monomial
   · rw [pow_succ', ih, Nat.succ_eq_add_one, Finsupp.single_add, X, monomial_mul_monomial, one_mul]
 #align mv_power_series.X_pow_eq MvPowerSeries.X_pow_eq
 
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 theorem coeff_X_pow [DecidableEq σ] (m : σ →₀ ℕ) (s : σ) (n : ℕ) :
     coeff R m ((X s : MvPowerSeries σ R) ^ n) = if m = single s n then 1 else 0 := by
   rw [X_pow_eq s n, coeff_monomial]
 #align mv_power_series.coeff_X_pow MvPowerSeries.coeff_X_pow
 
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 @[simp]
 theorem coeff_mul_C (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
     coeff R n (φ * C σ R a) = coeff R n φ * a := by simpa using coeff_add_mul_monomial n 0 φ a
 #align mv_power_series.coeff_mul_C MvPowerSeries.coeff_mul_C
 
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 @[simp]
 theorem coeff_C_mul (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
     coeff R n (C σ R a * φ) = a * coeff R n φ := by simpa using coeff_add_monomial_mul 0 n φ a
 #align mv_power_series.coeff_C_mul MvPowerSeries.coeff_C_mul
 
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 theorem coeff_zero_mul_X (φ : MvPowerSeries σ R) (s : σ) : coeff R (0 : σ →₀ ℕ) (φ * X s) = 0 :=
   by
   have : ¬single s 1 ≤ 0 := fun h => by simpa using h s
   simp only [X, coeff_mul_monomial, if_neg this]
 #align mv_power_series.coeff_zero_mul_X MvPowerSeries.coeff_zero_mul_X
 
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 theorem coeff_zero_X_mul (φ : MvPowerSeries σ R) (s : σ) : coeff R (0 : σ →₀ ℕ) (X s * φ) = 0 := by
   rw [← (φ.commute_X s).Eq, coeff_zero_mul_X]
 #align mv_power_series.coeff_zero_X_mul MvPowerSeries.coeff_zero_X_mul
 
 variable (σ) (R)
 
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 /-- The constant coefficient of a formal power series.-/
 def constantCoeff : MvPowerSeries σ R →+* R :=
   { coeff R (0 : σ →₀ ℕ) with
@@ -668,34 +455,16 @@ def constantCoeff : MvPowerSeries σ R →+* R :=
 
 variable {σ} {R}
 
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 @[simp]
 theorem coeff_zero_eq_constantCoeff : ⇑(coeff R (0 : σ →₀ ℕ)) = constantCoeff σ R :=
   rfl
 #align mv_power_series.coeff_zero_eq_constant_coeff MvPowerSeries.coeff_zero_eq_constantCoeff
 
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 theorem coeff_zero_eq_constantCoeff_apply (φ : MvPowerSeries σ R) :
     coeff R (0 : σ →₀ ℕ) φ = constantCoeff σ R φ :=
   rfl
 #align mv_power_series.coeff_zero_eq_constant_coeff_apply MvPowerSeries.coeff_zero_eq_constantCoeff_apply
 
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-Case conversion may be inaccurate. Consider using '#align mv_power_series.constant_coeff_C MvPowerSeries.constantCoeff_Cₓ'. -/
 @[simp]
 theorem constantCoeff_C (a : R) : constantCoeff σ R (C σ R a) = a :=
   rfl
@@ -708,45 +477,21 @@ theorem constantCoeff_comp_C : (constantCoeff σ R).comp (C σ R) = RingHom.id R
 #align mv_power_series.constant_coeff_comp_C MvPowerSeries.constantCoeff_comp_C
 -/
 
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 @[simp]
 theorem constantCoeff_zero : constantCoeff σ R 0 = 0 :=
   rfl
 #align mv_power_series.constant_coeff_zero MvPowerSeries.constantCoeff_zero
 
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 @[simp]
 theorem constantCoeff_one : constantCoeff σ R 1 = 1 :=
   rfl
 #align mv_power_series.constant_coeff_one MvPowerSeries.constantCoeff_one
 
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 @[simp]
 theorem constantCoeff_X (s : σ) : constantCoeff σ R (X s) = 0 :=
   coeff_zero_X s
 #align mv_power_series.constant_coeff_X MvPowerSeries.constantCoeff_X
 
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 /-- If a multivariate formal power series is invertible,
  then so is its constant coefficient.-/
 theorem isUnit_constantCoeff (φ : MvPowerSeries σ R) (h : IsUnit φ) :
@@ -754,20 +499,11 @@ theorem isUnit_constantCoeff (φ : MvPowerSeries σ R) (h : IsUnit φ) :
   h.map _
 #align mv_power_series.is_unit_constant_coeff MvPowerSeries.isUnit_constantCoeff
 
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 @[simp]
 theorem coeff_smul (f : MvPowerSeries σ R) (n) (a : R) : coeff _ n (a • f) = a * coeff _ n f :=
   rfl
 #align mv_power_series.coeff_smul MvPowerSeries.coeff_smul
 
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 theorem smul_eq_C_mul (f : MvPowerSeries σ R) (a : R) : a • f = C σ R a * f := by ext; simp
 #align mv_power_series.smul_eq_C_mul MvPowerSeries.smul_eq_C_mul
 
@@ -792,12 +528,6 @@ variable (f : R →+* S) (g : S →+* T)
 
 variable (σ)
 
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 /-- The map between multivariate formal power series induced by a map on the coefficients.-/
 def map : MvPowerSeries σ R →+* MvPowerSeries σ S
     where
@@ -818,66 +548,36 @@ def map : MvPowerSeries σ R →+* MvPowerSeries σ S
 
 variable {σ}
 
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 @[simp]
 theorem map_id : map σ (RingHom.id R) = RingHom.id _ :=
   rfl
 #align mv_power_series.map_id MvPowerSeries.map_id
 
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 theorem map_comp : map σ (g.comp f) = (map σ g).comp (map σ f) :=
   rfl
 #align mv_power_series.map_comp MvPowerSeries.map_comp
 
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 @[simp]
 theorem coeff_map (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) : coeff S n (map σ f φ) = f (coeff R n φ) :=
   rfl
 #align mv_power_series.coeff_map MvPowerSeries.coeff_map
 
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 @[simp]
 theorem constantCoeff_map (φ : MvPowerSeries σ R) :
     constantCoeff σ S (map σ f φ) = f (constantCoeff σ R φ) :=
   rfl
 #align mv_power_series.constant_coeff_map MvPowerSeries.constantCoeff_map
 
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 @[simp]
 theorem map_monomial (n : σ →₀ ℕ) (a : R) : map σ f (monomial R n a) = monomial S n (f a) := by
   ext m; simp [coeff_monomial, apply_ite f]
 #align mv_power_series.map_monomial MvPowerSeries.map_monomial
 
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 @[simp]
 theorem map_C (a : R) : map σ f (C σ R a) = C σ S (f a) :=
   map_monomial _ _ _
 #align mv_power_series.map_C MvPowerSeries.map_C
 
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 @[simp]
 theorem map_X (s : σ) : map σ f (X s) = X s := by simp [MvPowerSeries.X]
 #align mv_power_series.map_X MvPowerSeries.map_X
@@ -895,19 +595,10 @@ instance : Algebra R (MvPowerSeries σ A) :=
     smul_def' := fun a σ => by ext n; simp [(coeff A n).map_smul_of_tower a, Algebra.smul_def]
     toRingHom := (MvPowerSeries.map σ (algebraMap R A)).comp (C σ R) }
 
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 theorem c_eq_algebraMap : C σ R = algebraMap R (MvPowerSeries σ R) :=
   rfl
 #align mv_power_series.C_eq_algebra_map MvPowerSeries.c_eq_algebraMap
 
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 theorem algebraMap_apply {r : R} : algebraMap R (MvPowerSeries σ A) r = C σ A (algebraMap R A r) :=
   by
   change (MvPowerSeries.map σ (algebraMap R A)).comp (C σ R) r = _
@@ -938,9 +629,6 @@ def truncFun (φ : MvPowerSeries σ R) : MvPolynomial σ R :=
 #align mv_power_series.trunc_fun MvPowerSeries.truncFun
 -/
 
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 theorem coeff_truncFun (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
     (truncFun n φ).coeff m = if m < n then coeff R m φ else 0 := by
   simp [trunc_fun, MvPolynomial.coeff_sum]
@@ -960,16 +648,10 @@ def trunc : MvPowerSeries σ R →+ MvPolynomial σ R
 
 variable {R}
 
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 theorem coeff_trunc (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
     (trunc R n φ).coeff m = if m < n then coeff R m φ else 0 := by simp [Trunc, coeff_trunc_fun]
 #align mv_power_series.coeff_trunc MvPowerSeries.coeff_trunc
 
-/- warning: mv_power_series.trunc_one -> MvPowerSeries.trunc_one is a dubious translation:
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 @[simp]
 theorem trunc_one (hnn : n ≠ 0) : trunc R n 1 = 1 :=
   MvPolynomial.ext _ _ fun m => by
@@ -981,9 +663,6 @@ theorem trunc_one (hnn : n ≠ 0) : trunc R n 1 = 1 :=
       rintro rfl; apply H; exact Ne.bot_lt hnn
 #align mv_power_series.trunc_one MvPowerSeries.trunc_one
 
-/- warning: mv_power_series.trunc_C -> MvPowerSeries.trunc_c is a dubious translation:
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 @[simp]
 theorem trunc_c (hnn : n ≠ 0) (a : R) : trunc R n (C σ R a) = MvPolynomial.C a :=
   MvPolynomial.ext _ _ fun m =>
@@ -999,12 +678,6 @@ section Semiring
 
 variable [Semiring R]
 
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-Case conversion may be inaccurate. Consider using '#align mv_power_series.X_pow_dvd_iff MvPowerSeries.X_pow_dvd_iffₓ'. -/
 theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
     (X s : MvPowerSeries σ R) ^ n ∣ φ ↔ ∀ m : σ →₀ ℕ, m s < n → coeff R m φ = 0 :=
   by
@@ -1040,12 +713,6 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
           · simp [Finsupp.single_apply, hst]
 #align mv_power_series.X_pow_dvd_iff MvPowerSeries.X_pow_dvd_iff
 
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-Case conversion may be inaccurate. Consider using '#align mv_power_series.X_dvd_iff MvPowerSeries.X_dvd_iffₓ'. -/
 theorem X_dvd_iff {s : σ} {φ : MvPowerSeries σ R} :
     (X s : MvPowerSeries σ R) ∣ φ ↔ ∀ m : σ →₀ ℕ, m s = 0 → coeff R m φ = 0 :=
   by
@@ -1080,9 +747,6 @@ protected noncomputable def inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerS
 #align mv_power_series.inv.aux MvPowerSeries.inv.aux
 -/
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_inv_aux MvPowerSeries.coeff_inv_auxₓ'. -/
 theorem coeff_inv_aux [DecidableEq σ] (n : σ →₀ ℕ) (a : R) (φ : MvPowerSeries σ R) :
     coeff R n (inv.aux a φ) =
       if n = 0 then a
@@ -1094,21 +758,12 @@ theorem coeff_inv_aux [DecidableEq σ] (n : σ →₀ ℕ) (a : R) (φ : MvPower
     convert rfl
 #align mv_power_series.coeff_inv_aux MvPowerSeries.coeff_inv_aux
 
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 -- unify `decidable` instances
 /-- A multivariate formal power series is invertible if the constant coefficient is invertible.-/
 def invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) : MvPowerSeries σ R :=
   inv.aux (↑u⁻¹) φ
 #align mv_power_series.inv_of_unit MvPowerSeries.invOfUnit
 
-/- warning: mv_power_series.coeff_inv_of_unit -> MvPowerSeries.coeff_invOfUnit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_inv_of_unit MvPowerSeries.coeff_invOfUnitₓ'. -/
 theorem coeff_invOfUnit [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (u : Rˣ) :
     coeff R n (invOfUnit φ u) =
       if n = 0 then ↑u⁻¹
@@ -1119,24 +774,12 @@ theorem coeff_invOfUnit [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries
   coeff_inv_aux n (↑u⁻¹) φ
 #align mv_power_series.coeff_inv_of_unit MvPowerSeries.coeff_invOfUnit
 
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 @[simp]
 theorem constantCoeff_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) :
     constantCoeff σ R (invOfUnit φ u) = ↑u⁻¹ := by
   rw [← coeff_zero_eq_constant_coeff_apply, coeff_inv_of_unit, if_pos rfl]
 #align mv_power_series.constant_coeff_inv_of_unit MvPowerSeries.constantCoeff_invOfUnit
 
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 theorem mul_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) (h : constantCoeff σ R φ = u) :
     φ * invOfUnit φ u = 1 :=
   ext fun n =>
@@ -1185,12 +828,6 @@ section LocalRing
 
 variable {S : Type _} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalRingHom f]
 
-/- warning: mv_power_series.map.is_local_ring_hom -> MvPowerSeries.map.isLocalRingHom is a dubious translation:
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 -- Thanks to the linter for informing us that  this instance does
 -- not actually need R and S to be local rings!
 /-- The map `A[[X]] → B[[X]]` induced by a local ring hom `A → B` is local -/
@@ -1221,9 +858,6 @@ protected def inv (φ : MvPowerSeries σ k) : MvPowerSeries σ k :=
 instance : Inv (MvPowerSeries σ k) :=
   ⟨MvPowerSeries.inv⟩
 
-/- warning: mv_power_series.coeff_inv -> MvPowerSeries.coeff_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_inv MvPowerSeries.coeff_invₓ'. -/
 theorem coeff_inv [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ k) :
     coeff k n φ⁻¹ =
       if n = 0 then (constantCoeff σ k φ)⁻¹
@@ -1233,21 +867,12 @@ theorem coeff_inv [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ k)
   coeff_inv_aux n _ φ
 #align mv_power_series.coeff_inv MvPowerSeries.coeff_inv
 
-/- warning: mv_power_series.constant_coeff_inv -> MvPowerSeries.constantCoeff_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_power_series.constant_coeff_inv MvPowerSeries.constantCoeff_invₓ'. -/
 @[simp]
 theorem constantCoeff_inv (φ : MvPowerSeries σ k) :
     constantCoeff σ k φ⁻¹ = (constantCoeff σ k φ)⁻¹ := by
   rw [← coeff_zero_eq_constant_coeff_apply, coeff_inv, if_pos rfl]
 #align mv_power_series.constant_coeff_inv MvPowerSeries.constantCoeff_inv
 
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 theorem inv_eq_zero {φ : MvPowerSeries σ k} : φ⁻¹ = 0 ↔ constantCoeff σ k φ = 0 :=
   ⟨fun h => by simpa using congr_arg (constant_coeff σ k) h, fun h =>
     ext fun n => by rw [coeff_inv];
@@ -1255,31 +880,16 @@ theorem inv_eq_zero {φ : MvPowerSeries σ k} : φ⁻¹ = 0 ↔ constantCoeff σ
         simp only [h, MvPowerSeries.coeff_zero, MulZeroClass.zero_mul, inv_zero, neg_zero]⟩
 #align mv_power_series.inv_eq_zero MvPowerSeries.inv_eq_zero
 
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 @[simp]
 theorem zero_inv : (0 : MvPowerSeries σ k)⁻¹ = 0 := by rw [inv_eq_zero, constant_coeff_zero]
 #align mv_power_series.zero_inv MvPowerSeries.zero_inv
 
-/- warning: mv_power_series.inv_of_unit_eq -> MvPowerSeries.invOfUnit_eq is a dubious translation:
-<too large>
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 @[simp]
 theorem invOfUnit_eq (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
     invOfUnit φ (Units.mk0 _ h) = φ⁻¹ :=
   rfl
 #align mv_power_series.inv_of_unit_eq MvPowerSeries.invOfUnit_eq
 
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-Case conversion may be inaccurate. Consider using '#align mv_power_series.inv_of_unit_eq' MvPowerSeries.invOfUnit_eq'ₓ'. -/
 @[simp]
 theorem invOfUnit_eq' (φ : MvPowerSeries σ k) (u : Units k) (h : constantCoeff σ k φ = u) :
     invOfUnit φ u = φ⁻¹ := by
@@ -1287,66 +897,30 @@ theorem invOfUnit_eq' (φ : MvPowerSeries σ k) (u : Units k) (h : constantCoeff
   congr 1; rw [Units.ext_iff]; exact h.symm
 #align mv_power_series.inv_of_unit_eq' MvPowerSeries.invOfUnit_eq'
 
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 @[simp]
 protected theorem mul_inv_cancel (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
     φ * φ⁻¹ = 1 := by rw [← inv_of_unit_eq φ h, mul_inv_of_unit φ (Units.mk0 _ h) rfl]
 #align mv_power_series.mul_inv_cancel MvPowerSeries.mul_inv_cancel
 
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 @[simp]
 protected theorem inv_mul_cancel (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
     φ⁻¹ * φ = 1 := by rw [mul_comm, φ.mul_inv_cancel h]
 #align mv_power_series.inv_mul_cancel MvPowerSeries.inv_mul_cancel
 
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 protected theorem eq_mul_inv_iff_mul_eq {φ₁ φ₂ φ₃ : MvPowerSeries σ k}
     (h : constantCoeff σ k φ₃ ≠ 0) : φ₁ = φ₂ * φ₃⁻¹ ↔ φ₁ * φ₃ = φ₂ :=
   ⟨fun k => by simp [k, mul_assoc, MvPowerSeries.inv_mul_cancel _ h], fun k => by
     simp [← k, mul_assoc, MvPowerSeries.mul_inv_cancel _ h]⟩
 #align mv_power_series.eq_mul_inv_iff_mul_eq MvPowerSeries.eq_mul_inv_iff_mul_eq
 
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 protected theorem eq_inv_iff_mul_eq_one {φ ψ : MvPowerSeries σ k} (h : constantCoeff σ k ψ ≠ 0) :
     φ = ψ⁻¹ ↔ φ * ψ = 1 := by rw [← MvPowerSeries.eq_mul_inv_iff_mul_eq h, one_mul]
 #align mv_power_series.eq_inv_iff_mul_eq_one MvPowerSeries.eq_inv_iff_mul_eq_one
 
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 protected theorem inv_eq_iff_mul_eq_one {φ ψ : MvPowerSeries σ k} (h : constantCoeff σ k ψ ≠ 0) :
     ψ⁻¹ = φ ↔ φ * ψ = 1 := by rw [eq_comm, MvPowerSeries.eq_inv_iff_mul_eq_one h]
 #align mv_power_series.inv_eq_iff_mul_eq_one MvPowerSeries.inv_eq_iff_mul_eq_one
 
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 @[simp]
 protected theorem mul_inv_rev (φ ψ : MvPowerSeries σ k) : (φ * ψ)⁻¹ = ψ⁻¹ * φ⁻¹ :=
   by
@@ -1366,9 +940,6 @@ instance : InvOneClass (MvPowerSeries σ k) :=
   { MvPowerSeries.hasOne, MvPowerSeries.hasInv with
     inv_one := by rw [MvPowerSeries.inv_eq_iff_mul_eq_one, mul_one]; simp }
 
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 @[simp]
 theorem C_inv (r : k) : (C σ k r)⁻¹ = C σ k r⁻¹ :=
   by
@@ -1378,22 +949,10 @@ theorem C_inv (r : k) : (C σ k r)⁻¹ = C σ k r⁻¹ :=
   simpa using hr
 #align mv_power_series.C_inv MvPowerSeries.C_inv
 
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 @[simp]
 theorem X_inv (s : σ) : (X s : MvPowerSeries σ k)⁻¹ = 0 := by rw [inv_eq_zero, constant_coeff_X]
 #align mv_power_series.X_inv MvPowerSeries.X_inv
 
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 @[simp]
 theorem smul_inv (r : k) (φ : MvPowerSeries σ k) : (r • φ)⁻¹ = r⁻¹ • φ⁻¹ := by
   simp [smul_eq_C_mul, mul_comm]
@@ -1416,30 +975,15 @@ instance coeToMvPowerSeries : Coe (MvPolynomial σ R) (MvPowerSeries σ R) :=
 #align mv_polynomial.coe_to_mv_power_series MvPolynomial.coeToMvPowerSeries
 -/
 
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 theorem coe_def : (φ : MvPowerSeries σ R) = fun n => coeff n φ :=
   rfl
 #align mv_polynomial.coe_def MvPolynomial.coe_def
 
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 @[simp, norm_cast]
 theorem coeff_coe (n : σ →₀ ℕ) : MvPowerSeries.coeff R n ↑φ = coeff n φ :=
   rfl
 #align mv_polynomial.coeff_coe MvPolynomial.coeff_coe
 
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 @[simp, norm_cast]
 theorem coe_monomial (n : σ →₀ ℕ) (a : R) :
     (monomial n a : MvPowerSeries σ R) = MvPowerSeries.monomial R n a :=
@@ -1449,88 +993,43 @@ theorem coe_monomial (n : σ →₀ ℕ) (a : R) :
     split_ifs with h₁ h₂ <;> first |rfl|subst m <;> contradiction
 #align mv_polynomial.coe_monomial MvPolynomial.coe_monomial
 
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 @[simp, norm_cast]
 theorem coe_zero : ((0 : MvPolynomial σ R) : MvPowerSeries σ R) = 0 :=
   rfl
 #align mv_polynomial.coe_zero MvPolynomial.coe_zero
 
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 @[simp, norm_cast]
 theorem coe_one : ((1 : MvPolynomial σ R) : MvPowerSeries σ R) = 1 :=
   coe_monomial _ _
 #align mv_polynomial.coe_one MvPolynomial.coe_one
 
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 @[simp, norm_cast]
 theorem coe_add : ((φ + ψ : MvPolynomial σ R) : MvPowerSeries σ R) = φ + ψ :=
   rfl
 #align mv_polynomial.coe_add MvPolynomial.coe_add
 
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 @[simp, norm_cast]
 theorem coe_mul : ((φ * ψ : MvPolynomial σ R) : MvPowerSeries σ R) = φ * ψ :=
   MvPowerSeries.ext fun n => by simp only [coeff_coe, MvPowerSeries.coeff_mul, coeff_mul]
 #align mv_polynomial.coe_mul MvPolynomial.coe_mul
 
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 @[simp, norm_cast]
 theorem coe_C (a : R) : ((C a : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.C σ R a :=
   coe_monomial _ _
 #align mv_polynomial.coe_C MvPolynomial.coe_C
 
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 @[simp, norm_cast]
 theorem coe_bit0 :
     ((bit0 φ : MvPolynomial σ R) : MvPowerSeries σ R) = bit0 (φ : MvPowerSeries σ R) :=
   coe_add _ _
 #align mv_polynomial.coe_bit0 MvPolynomial.coe_bit0
 
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 @[simp, norm_cast]
 theorem coe_bit1 :
     ((bit1 φ : MvPolynomial σ R) : MvPowerSeries σ R) = bit1 (φ : MvPowerSeries σ R) := by
   rw [bit1, bit1, coe_add, coe_one, coe_bit0]
 #align mv_polynomial.coe_bit1 MvPolynomial.coe_bit1
 
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 @[simp, norm_cast]
 theorem coe_X (s : σ) : ((X s : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.X s :=
   coe_monomial _ _
@@ -1538,55 +1037,25 @@ theorem coe_X (s : σ) : ((X s : MvPolynomial σ R) : MvPowerSeries σ R) = MvPo
 
 variable (σ R)
 
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 theorem coe_injective : Function.Injective (coe : MvPolynomial σ R → MvPowerSeries σ R) :=
   fun x y h => by ext; simp_rw [← coeff_coe, h]
 #align mv_polynomial.coe_injective MvPolynomial.coe_injective
 
 variable {σ R φ ψ}
 
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 @[simp, norm_cast]
 theorem coe_inj : (φ : MvPowerSeries σ R) = ψ ↔ φ = ψ :=
   (coe_injective σ R).eq_iff
 #align mv_polynomial.coe_inj MvPolynomial.coe_inj
 
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 @[simp]
 theorem coe_eq_zero_iff : (φ : MvPowerSeries σ R) = 0 ↔ φ = 0 := by rw [← coe_zero, coe_inj]
 #align mv_polynomial.coe_eq_zero_iff MvPolynomial.coe_eq_zero_iff
 
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 @[simp]
 theorem coe_eq_one_iff : (φ : MvPowerSeries σ R) = 1 ↔ φ = 1 := by rw [← coe_one, coe_inj]
 #align mv_polynomial.coe_eq_one_iff MvPolynomial.coe_eq_one_iff
 
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 /-- The coercion from multivariable polynomials to multivariable power series
 as a ring homomorphism.
 -/
@@ -1599,12 +1068,6 @@ def coeToMvPowerSeries.ringHom : MvPolynomial σ R →+* MvPowerSeries σ R
   map_mul' := coe_mul
 #align mv_polynomial.coe_to_mv_power_series.ring_hom MvPolynomial.coeToMvPowerSeries.ringHom
 
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 @[simp, norm_cast]
 theorem coe_pow (n : ℕ) :
     ((φ ^ n : MvPolynomial σ R) : MvPowerSeries σ R) = (φ : MvPowerSeries σ R) ^ n :=
@@ -1613,12 +1076,6 @@ theorem coe_pow (n : ℕ) :
 
 variable (φ ψ)
 
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 @[simp]
 theorem coeToMvPowerSeries.ringHom_apply : coeToMvPowerSeries.ringHom φ = φ :=
   rfl
@@ -1628,12 +1085,6 @@ section Algebra
 
 variable (A : Type _) [CommSemiring A] [Algebra R A]
 
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 /-- The coercion from multivariable polynomials to multivariable power series
 as an algebra homomorphism.
 -/
@@ -1642,9 +1093,6 @@ def coeToMvPowerSeries.algHom : MvPolynomial σ R →ₐ[R] MvPowerSeries σ A :
     commutes' := fun r => by simp [algebraMap_apply, MvPowerSeries.algebraMap_apply] }
 #align mv_polynomial.coe_to_mv_power_series.alg_hom MvPolynomial.coeToMvPowerSeries.algHom
 
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 @[simp]
 theorem coeToMvPowerSeries.algHom_apply :
     coeToMvPowerSeries.algHom A φ = MvPowerSeries.map σ (algebraMap R A) ↑φ :=
@@ -1659,39 +1107,21 @@ namespace MvPowerSeries
 
 variable {σ R A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : MvPowerSeries σ R)
 
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 instance algebraMvPolynomial : Algebra (MvPolynomial σ R) (MvPowerSeries σ A) :=
   RingHom.toAlgebra (MvPolynomial.coeToMvPowerSeries.algHom A).toRingHom
 #align mv_power_series.algebra_mv_polynomial MvPowerSeries.algebraMvPolynomial
 
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-Case conversion may be inaccurate. Consider using '#align mv_power_series.algebra_mv_power_series MvPowerSeries.algebraMvPowerSeriesₓ'. -/
 instance algebraMvPowerSeries : Algebra (MvPowerSeries σ R) (MvPowerSeries σ A) :=
   (map σ (algebraMap R A)).toAlgebra
 #align mv_power_series.algebra_mv_power_series MvPowerSeries.algebraMvPowerSeries
 
 variable (A)
 
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 theorem algebraMap_apply' (p : MvPolynomial σ R) :
     algebraMap (MvPolynomial σ R) (MvPowerSeries σ A) p = map σ (algebraMap R A) p :=
   rfl
 #align mv_power_series.algebra_map_apply' MvPowerSeries.algebraMap_apply'
 
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-<too large>
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 theorem algebraMap_apply'' :
     algebraMap (MvPowerSeries σ R) (MvPowerSeries σ A) f = map σ (algebraMap R A) f :=
   rfl
@@ -1774,24 +1204,12 @@ theorem coeff_def {s : Unit →₀ ℕ} {n : ℕ} (h : s () = n) : coeff R n = M
 #align power_series.coeff_def PowerSeries.coeff_def
 -/
 
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 /-- Two formal power series are equal if all their coefficients are equal.-/
 @[ext]
 theorem ext {φ ψ : PowerSeries R} (h : ∀ n, coeff R n φ = coeff R n ψ) : φ = ψ :=
   MvPowerSeries.ext fun n => by rw [← coeff_def]; · apply h; rfl
 #align power_series.ext PowerSeries.ext
 
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-Case conversion may be inaccurate. Consider using '#align power_series.ext_iff PowerSeries.ext_iffₓ'. -/
 /-- Two formal power series are equal if all their coefficients are equal.-/
 theorem ext_iff {φ ψ : PowerSeries R} : φ = ψ ↔ ∀ n, coeff R n φ = coeff R n ψ :=
   ⟨fun h n => congr_arg (coeff R n) h, ext⟩
@@ -1803,20 +1221,11 @@ def mk {R} (f : ℕ → R) : PowerSeries R := fun s => f (s ())
 #align power_series.mk PowerSeries.mk
 -/
 
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 @[simp]
 theorem coeff_mk (n : ℕ) (f : ℕ → R) : coeff R n (mk f) = f n :=
   congr_arg f Finsupp.single_eq_same
 #align power_series.coeff_mk PowerSeries.coeff_mk
 
-/- warning: power_series.coeff_monomial -> PowerSeries.coeff_monomial is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_monomial PowerSeries.coeff_monomialₓ'. -/
 theorem coeff_monomial (m n : ℕ) (a : R) : coeff R m (monomial R n a) = if m = n then a else 0 :=
   calc
     coeff R m (monomial R n a) = _ := MvPowerSeries.coeff_monomial _ _ _
@@ -1824,19 +1233,10 @@ theorem coeff_monomial (m n : ℕ) (a : R) : coeff R m (monomial R n a) = if m =
     
 #align power_series.coeff_monomial PowerSeries.coeff_monomial
 
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 theorem monomial_eq_mk (n : ℕ) (a : R) : monomial R n a = mk fun m => if m = n then a else 0 :=
   ext fun m => by rw [coeff_monomial, coeff_mk]
 #align power_series.monomial_eq_mk PowerSeries.monomial_eq_mk
 
-/- warning: power_series.coeff_monomial_same -> PowerSeries.coeff_monomial_same is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_monomial_same PowerSeries.coeff_monomial_sameₓ'. -/
 @[simp]
 theorem coeff_monomial_same (n : ℕ) (a : R) : coeff R n (monomial R n a) = a :=
   MvPowerSeries.coeff_monomial_same _ _
@@ -1851,23 +1251,11 @@ theorem coeff_comp_monomial (n : ℕ) : (coeff R n).comp (monomial R n) = Linear
 
 variable (R)
 
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 /-- The constant coefficient of a formal power series. -/
 def constantCoeff : PowerSeries R →+* R :=
   MvPowerSeries.constantCoeff Unit R
 #align power_series.constant_coeff PowerSeries.constantCoeff
 
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 /-- The constant formal power series.-/
 def C : R →+* PowerSeries R :=
   MvPowerSeries.C Unit R
@@ -1882,182 +1270,80 @@ def X : PowerSeries R :=
 #align power_series.X PowerSeries.X
 -/
 
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 theorem commute_X (φ : PowerSeries R) : Commute φ X :=
   φ.commute_X _
 #align power_series.commute_X PowerSeries.commute_X
 
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 @[simp]
 theorem coeff_zero_eq_constantCoeff : ⇑(coeff R 0) = constantCoeff R := by
   rw [coeff, Finsupp.single_zero]; rfl
 #align power_series.coeff_zero_eq_constant_coeff PowerSeries.coeff_zero_eq_constantCoeff
 
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-Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_eq_constant_coeff_apply PowerSeries.coeff_zero_eq_constantCoeff_applyₓ'. -/
 theorem coeff_zero_eq_constantCoeff_apply (φ : PowerSeries R) : coeff R 0 φ = constantCoeff R φ :=
   by rw [coeff_zero_eq_constant_coeff] <;> rfl
 #align power_series.coeff_zero_eq_constant_coeff_apply PowerSeries.coeff_zero_eq_constantCoeff_apply
 
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 @[simp]
 theorem monomial_zero_eq_C : ⇑(monomial R 0) = C R := by
   rw [monomial, Finsupp.single_zero, MvPowerSeries.monomial_zero_eq_C, C]
 #align power_series.monomial_zero_eq_C PowerSeries.monomial_zero_eq_C
 
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-Case conversion may be inaccurate. Consider using '#align power_series.monomial_zero_eq_C_apply PowerSeries.monomial_zero_eq_C_applyₓ'. -/
 theorem monomial_zero_eq_C_apply (a : R) : monomial R 0 a = C R a := by simp
 #align power_series.monomial_zero_eq_C_apply PowerSeries.monomial_zero_eq_C_apply
 
-/- warning: power_series.coeff_C -> PowerSeries.coeff_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_C PowerSeries.coeff_Cₓ'. -/
 theorem coeff_C (n : ℕ) (a : R) : coeff R n (C R a : PowerSeries R) = if n = 0 then a else 0 := by
   rw [← monomial_zero_eq_C_apply, coeff_monomial]
 #align power_series.coeff_C PowerSeries.coeff_C
 
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-Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_C PowerSeries.coeff_zero_Cₓ'. -/
 @[simp]
 theorem coeff_zero_C (a : R) : coeff R 0 (C R a) = a := by
   rw [← monomial_zero_eq_C_apply, coeff_monomial_same 0 a]
 #align power_series.coeff_zero_C PowerSeries.coeff_zero_C
 
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 theorem X_eq : (X : PowerSeries R) = monomial R 1 1 :=
   rfl
 #align power_series.X_eq PowerSeries.X_eq
 
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 theorem coeff_X (n : ℕ) : coeff R n (X : PowerSeries R) = if n = 1 then 1 else 0 := by
   rw [X_eq, coeff_monomial]
 #align power_series.coeff_X PowerSeries.coeff_X
 
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 @[simp]
 theorem coeff_zero_X : coeff R 0 (X : PowerSeries R) = 0 := by
   rw [coeff, Finsupp.single_zero, X, MvPowerSeries.coeff_zero_X]
 #align power_series.coeff_zero_X PowerSeries.coeff_zero_X
 
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 @[simp]
 theorem coeff_one_X : coeff R 1 (X : PowerSeries R) = 1 := by rw [coeff_X, if_pos rfl]
 #align power_series.coeff_one_X PowerSeries.coeff_one_X
 
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 @[simp]
 theorem X_ne_zero [Nontrivial R] : (X : PowerSeries R) ≠ 0 := fun H => by
   simpa only [coeff_one_X, one_ne_zero, map_zero] using congr_arg (coeff R 1) H
 #align power_series.X_ne_zero PowerSeries.X_ne_zero
 
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 theorem X_pow_eq (n : ℕ) : (X : PowerSeries R) ^ n = monomial R n 1 :=
   MvPowerSeries.X_pow_eq _ n
 #align power_series.X_pow_eq PowerSeries.X_pow_eq
 
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-Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow PowerSeries.coeff_X_powₓ'. -/
 theorem coeff_X_pow (m n : ℕ) : coeff R m ((X : PowerSeries R) ^ n) = if m = n then 1 else 0 := by
   rw [X_pow_eq, coeff_monomial]
 #align power_series.coeff_X_pow PowerSeries.coeff_X_pow
 
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-Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow_self PowerSeries.coeff_X_pow_selfₓ'. -/
 @[simp]
 theorem coeff_X_pow_self (n : ℕ) : coeff R n ((X : PowerSeries R) ^ n) = 1 := by
   rw [coeff_X_pow, if_pos rfl]
 #align power_series.coeff_X_pow_self PowerSeries.coeff_X_pow_self
 
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-Case conversion may be inaccurate. Consider using '#align power_series.coeff_one PowerSeries.coeff_oneₓ'. -/
 @[simp]
 theorem coeff_one (n : ℕ) : coeff R n (1 : PowerSeries R) = if n = 0 then 1 else 0 :=
   coeff_C n 1
 #align power_series.coeff_one PowerSeries.coeff_one
 
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-Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_one PowerSeries.coeff_zero_oneₓ'. -/
 theorem coeff_zero_one : coeff R 0 (1 : PowerSeries R) = 1 :=
   coeff_zero_C 1
 #align power_series.coeff_zero_one PowerSeries.coeff_zero_one
 
-/- warning: power_series.coeff_mul -> PowerSeries.coeff_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul PowerSeries.coeff_mulₓ'. -/
 theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
     coeff R n (φ * ψ) = ∑ p in Finset.Nat.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ :=
   by
@@ -2076,43 +1362,25 @@ theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
       exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
 #align power_series.coeff_mul PowerSeries.coeff_mul
 
-/- warning: power_series.coeff_mul_C -> PowerSeries.coeff_mul_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_C PowerSeries.coeff_mul_Cₓ'. -/
 @[simp]
 theorem coeff_mul_C (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (φ * C R a) = coeff R n φ * a :=
   MvPowerSeries.coeff_mul_C _ φ a
 #align power_series.coeff_mul_C PowerSeries.coeff_mul_C
 
-/- warning: power_series.coeff_C_mul -> PowerSeries.coeff_C_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_C_mul PowerSeries.coeff_C_mulₓ'. -/
 @[simp]
 theorem coeff_C_mul (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (C R a * φ) = a * coeff R n φ :=
   MvPowerSeries.coeff_C_mul _ φ a
 #align power_series.coeff_C_mul PowerSeries.coeff_C_mul
 
-/- warning: power_series.coeff_smul -> PowerSeries.coeff_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_smul PowerSeries.coeff_smulₓ'. -/
 @[simp]
 theorem coeff_smul {S : Type _} [Semiring S] [Module R S] (n : ℕ) (φ : PowerSeries S) (a : R) :
     coeff S n (a • φ) = a • coeff S n φ :=
   rfl
 #align power_series.coeff_smul PowerSeries.coeff_smul
 
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-Case conversion may be inaccurate. Consider using '#align power_series.smul_eq_C_mul PowerSeries.smul_eq_C_mulₓ'. -/
 theorem smul_eq_C_mul (f : PowerSeries R) (a : R) : a • f = C R a * f := by ext; simp
 #align power_series.smul_eq_C_mul PowerSeries.smul_eq_C_mul
 
-/- warning: power_series.coeff_succ_mul_X -> PowerSeries.coeff_succ_mul_X is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_succ_mul_X PowerSeries.coeff_succ_mul_Xₓ'. -/
 @[simp]
 theorem coeff_succ_mul_X (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (φ * X) = coeff R n φ :=
   by
@@ -2121,9 +1389,6 @@ theorem coeff_succ_mul_X (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (φ *
   rw [mul_one]
 #align power_series.coeff_succ_mul_X PowerSeries.coeff_succ_mul_X
 
-/- warning: power_series.coeff_succ_X_mul -> PowerSeries.coeff_succ_X_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_succ_X_mul PowerSeries.coeff_succ_X_mulₓ'. -/
 @[simp]
 theorem coeff_succ_X_mul (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (X * φ) = coeff R n φ :=
   by
@@ -2132,12 +1397,6 @@ theorem coeff_succ_X_mul (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (X * 
   rw [one_mul]
 #align power_series.coeff_succ_X_mul PowerSeries.coeff_succ_X_mul
 
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-Case conversion may be inaccurate. Consider using '#align power_series.constant_coeff_C PowerSeries.constantCoeff_Cₓ'. -/
 @[simp]
 theorem constantCoeff_C (a : R) : constantCoeff R (C R a) = a :=
   rfl
@@ -2150,54 +1409,24 @@ theorem constantCoeff_comp_C : (constantCoeff R).comp (C R) = RingHom.id R :=
 #align power_series.constant_coeff_comp_C PowerSeries.constantCoeff_comp_C
 -/
 
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-Case conversion may be inaccurate. Consider using '#align power_series.constant_coeff_zero PowerSeries.constantCoeff_zeroₓ'. -/
 @[simp]
 theorem constantCoeff_zero : constantCoeff R 0 = 0 :=
   rfl
 #align power_series.constant_coeff_zero PowerSeries.constantCoeff_zero
 
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-Case conversion may be inaccurate. Consider using '#align power_series.constant_coeff_one PowerSeries.constantCoeff_oneₓ'. -/
 @[simp]
 theorem constantCoeff_one : constantCoeff R 1 = 1 :=
   rfl
 #align power_series.constant_coeff_one PowerSeries.constantCoeff_one
 
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-Case conversion may be inaccurate. Consider using '#align power_series.constant_coeff_X PowerSeries.constantCoeff_Xₓ'. -/
 @[simp]
 theorem constantCoeff_X : constantCoeff R X = 0 :=
   MvPowerSeries.coeff_zero_X _
 #align power_series.constant_coeff_X PowerSeries.constantCoeff_X
 
-/- warning: power_series.coeff_zero_mul_X -> PowerSeries.coeff_zero_mul_X is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_mul_X PowerSeries.coeff_zero_mul_Xₓ'. -/
 theorem coeff_zero_mul_X (φ : PowerSeries R) : coeff R 0 (φ * X) = 0 := by simp
 #align power_series.coeff_zero_mul_X PowerSeries.coeff_zero_mul_X
 
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-Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_X_mul PowerSeries.coeff_zero_X_mulₓ'. -/
 theorem coeff_zero_X_mul (φ : PowerSeries R) : coeff R 0 (X * φ) = 0 := by simp
 #align power_series.coeff_zero_X_mul PowerSeries.coeff_zero_X_mul
 
@@ -2205,17 +1434,11 @@ theorem coeff_zero_X_mul (φ : PowerSeries R) : coeff R 0 (X * φ) = 0 := by sim
 -- up to date with that
 section
 
-/- warning: power_series.coeff_C_mul_X_pow -> PowerSeries.coeff_C_mul_X_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_C_mul_X_pow PowerSeries.coeff_C_mul_X_powₓ'. -/
 theorem coeff_C_mul_X_pow (x : R) (k n : ℕ) :
     coeff R n (C R x * X ^ k : PowerSeries R) = if n = k then x else 0 := by
   simp [X_pow_eq, coeff_monomial]
 #align power_series.coeff_C_mul_X_pow PowerSeries.coeff_C_mul_X_pow
 
-/- warning: power_series.coeff_mul_X_pow -> PowerSeries.coeff_mul_X_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_X_powₓ'. -/
 @[simp]
 theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * X ^ n) = coeff R d p :=
   by
@@ -2225,9 +1448,6 @@ theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * X
   · exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
 #align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_X_pow
 
-/- warning: power_series.coeff_X_pow_mul -> PowerSeries.coeff_X_pow_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow_mul PowerSeries.coeff_X_pow_mulₓ'. -/
 @[simp]
 theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (X ^ n * p) = coeff R d p :=
   by
@@ -2238,9 +1458,6 @@ theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (X ^ n
     exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
 #align power_series.coeff_X_pow_mul PowerSeries.coeff_X_pow_mul
 
-/- warning: power_series.coeff_mul_X_pow' -> PowerSeries.coeff_mul_X_pow' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_X_pow' PowerSeries.coeff_mul_X_pow'ₓ'. -/
 theorem coeff_mul_X_pow' (p : PowerSeries R) (n d : ℕ) :
     coeff R d (p * X ^ n) = ite (n ≤ d) (coeff R (d - n) p) 0 :=
   by
@@ -2251,9 +1468,6 @@ theorem coeff_mul_X_pow' (p : PowerSeries R) (n d : ℕ) :
     exact ((le_of_add_le_right (finset.nat.mem_antidiagonal.mp hx).le).trans_lt <| not_le.mp h).Ne
 #align power_series.coeff_mul_X_pow' PowerSeries.coeff_mul_X_pow'
 
-/- warning: power_series.coeff_X_pow_mul' -> PowerSeries.coeff_X_pow_mul' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow_mul' PowerSeries.coeff_X_pow_mul'ₓ'. -/
 theorem coeff_X_pow_mul' (p : PowerSeries R) (n d : ℕ) :
     coeff R d (X ^ n * p) = ite (n ≤ d) (coeff R (d - n) p) 0 :=
   by
@@ -2268,20 +1482,11 @@ theorem coeff_X_pow_mul' (p : PowerSeries R) (n d : ℕ) :
 
 end
 
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 /-- If a formal power series is invertible, then so is its constant coefficient.-/
 theorem isUnit_constantCoeff (φ : PowerSeries R) (h : IsUnit φ) : IsUnit (constantCoeff R φ) :=
   MvPowerSeries.isUnit_constantCoeff φ h
 #align power_series.is_unit_constant_coeff PowerSeries.isUnit_constantCoeff
 
-/- warning: power_series.eq_shift_mul_X_add_const -> PowerSeries.eq_shift_mul_X_add_const is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.eq_shift_mul_X_add_const PowerSeries.eq_shift_mul_X_add_constₓ'. -/
 /-- Split off the constant coefficient. -/
 theorem eq_shift_mul_X_add_const (φ : PowerSeries R) :
     φ = (mk fun p => coeff R (p + 1) φ) * X + C R (constantCoeff R φ) :=
@@ -2295,9 +1500,6 @@ theorem eq_shift_mul_X_add_const (φ : PowerSeries R) :
       if_false, add_zero]
 #align power_series.eq_shift_mul_X_add_const PowerSeries.eq_shift_mul_X_add_const
 
-/- warning: power_series.eq_X_mul_shift_add_const -> PowerSeries.eq_X_mul_shift_add_const is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.eq_X_mul_shift_add_const PowerSeries.eq_X_mul_shift_add_constₓ'. -/
 /-- Split off the constant coefficient. -/
 theorem eq_X_mul_shift_add_const (φ : PowerSeries R) :
     φ = (X * mk fun p => coeff R (p + 1) φ) + C R (constantCoeff R φ) :=
@@ -2317,71 +1519,35 @@ variable {S : Type _} {T : Type _} [Semiring S] [Semiring T]
 
 variable (f : R →+* S) (g : S →+* T)
 
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 /-- The map between formal power series induced by a map on the coefficients.-/
 def map : PowerSeries R →+* PowerSeries S :=
   MvPowerSeries.map _ f
 #align power_series.map PowerSeries.map
 
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 @[simp]
 theorem map_id : (map (RingHom.id R) : PowerSeries R → PowerSeries R) = id :=
   rfl
 #align power_series.map_id PowerSeries.map_id
 
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 theorem map_comp : map (g.comp f) = (map g).comp (map f) :=
   rfl
 #align power_series.map_comp PowerSeries.map_comp
 
-/- warning: power_series.coeff_map -> PowerSeries.coeff_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_map PowerSeries.coeff_mapₓ'. -/
 @[simp]
 theorem coeff_map (n : ℕ) (φ : PowerSeries R) : coeff S n (map f φ) = f (coeff R n φ) :=
   rfl
 #align power_series.coeff_map PowerSeries.coeff_map
 
-/- warning: power_series.map_C -> PowerSeries.map_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.map_C PowerSeries.map_Cₓ'. -/
 @[simp]
 theorem map_C (r : R) : map f (C _ r) = C _ (f r) := by ext; simp [coeff_C, apply_ite f]
 #align power_series.map_C PowerSeries.map_C
 
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 @[simp]
 theorem map_X : map f X = X := by ext; simp [coeff_X, apply_ite f]
 #align power_series.map_X PowerSeries.map_X
 
 end Map
 
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-Case conversion may be inaccurate. Consider using '#align power_series.X_pow_dvd_iff PowerSeries.X_pow_dvd_iffₓ'. -/
 theorem X_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
     (X : PowerSeries R) ^ n ∣ φ ↔ ∀ m, m < n → coeff R m φ = 0 :=
   by
@@ -2392,12 +1558,6 @@ theorem X_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
     · apply h; simpa only [Finsupp.single_eq_same] using hm
 #align power_series.X_pow_dvd_iff PowerSeries.X_pow_dvd_iff
 
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-Case conversion may be inaccurate. Consider using '#align power_series.X_dvd_iff PowerSeries.X_dvd_iffₓ'. -/
 theorem X_dvd_iff {φ : PowerSeries R} : (X : PowerSeries R) ∣ φ ↔ constantCoeff R φ = 0 :=
   by
   rw [← pow_one (X : PowerSeries R), X_pow_dvd_iff, ← coeff_zero_eq_constant_coeff_apply]
@@ -2414,12 +1574,6 @@ variable [CommSemiring R]
 
 open Finset Nat
 
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-Case conversion may be inaccurate. Consider using '#align power_series.rescale PowerSeries.rescaleₓ'. -/
 /-- The ring homomorphism taking a power series `f(X)` to `f(aX)`. -/
 noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R
     where
@@ -2438,21 +1592,12 @@ noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R
     rw [← H, pow_add, mul_mul_mul_comm]
 #align power_series.rescale PowerSeries.rescale
 
-/- warning: power_series.coeff_rescale -> PowerSeries.coeff_rescale is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_rescale PowerSeries.coeff_rescaleₓ'. -/
 @[simp]
 theorem coeff_rescale (f : PowerSeries R) (a : R) (n : ℕ) :
     coeff R n (rescale a f) = a ^ n * coeff R n f :=
   coeff_mk n _
 #align power_series.coeff_rescale PowerSeries.coeff_rescale
 
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-Case conversion may be inaccurate. Consider using '#align power_series.rescale_zero PowerSeries.rescale_zeroₓ'. -/
 @[simp]
 theorem rescale_zero : rescale 0 = (C R).comp (constantCoeff R) :=
   by
@@ -2464,36 +1609,18 @@ theorem rescale_zero : rescale 0 = (C R).comp (constantCoeff R) :=
   · rw [zero_pow' n h, MulZeroClass.zero_mul]
 #align power_series.rescale_zero PowerSeries.rescale_zero
 
-/- warning: power_series.rescale_zero_apply -> PowerSeries.rescale_zero_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.rescale_zero_apply PowerSeries.rescale_zero_applyₓ'. -/
 theorem rescale_zero_apply : rescale 0 X = C R (constantCoeff R X) := by simp
 #align power_series.rescale_zero_apply PowerSeries.rescale_zero_apply
 
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-Case conversion may be inaccurate. Consider using '#align power_series.rescale_one PowerSeries.rescale_oneₓ'. -/
 @[simp]
 theorem rescale_one : rescale 1 = RingHom.id (PowerSeries R) := by ext;
   simp only [RingHom.id_apply, rescale, one_pow, coeff_mk, one_mul, RingHom.coe_mk]
 #align power_series.rescale_one PowerSeries.rescale_one
 
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-Case conversion may be inaccurate. Consider using '#align power_series.rescale_mk PowerSeries.rescale_mkₓ'. -/
 theorem rescale_mk (f : ℕ → R) (a : R) : rescale a (mk f) = mk fun n : ℕ => a ^ n * f n := by ext;
   rw [coeff_rescale, coeff_mk, coeff_mk]
 #align power_series.rescale_mk PowerSeries.rescale_mk
 
-/- warning: power_series.rescale_rescale -> PowerSeries.rescale_rescale is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.rescale_rescale PowerSeries.rescale_rescaleₓ'. -/
 theorem rescale_rescale (f : PowerSeries R) (a b : R) :
     rescale b (rescale a f) = rescale (a * b) f :=
   by
@@ -2502,12 +1629,6 @@ theorem rescale_rescale (f : PowerSeries R) (a b : R) :
   rw [mul_pow, mul_comm _ (b ^ n), mul_assoc]
 #align power_series.rescale_rescale PowerSeries.rescale_rescale
 
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-Case conversion may be inaccurate. Consider using '#align power_series.rescale_mul PowerSeries.rescale_mulₓ'. -/
 theorem rescale_mul (a b : R) : rescale (a * b) = (rescale b).comp (rescale a) := by ext;
   simp [← rescale_rescale]
 #align power_series.rescale_mul PowerSeries.rescale_mul
@@ -2521,23 +1642,11 @@ def trunc (n : ℕ) (φ : PowerSeries R) : R[X] :=
 #align power_series.trunc PowerSeries.trunc
 -/
 
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 theorem coeff_trunc (m) (n) (φ : PowerSeries R) :
     (trunc n φ).coeff m = if m < n then coeff R m φ else 0 := by
   simp [Trunc, Polynomial.coeff_sum, Polynomial.coeff_monomial, Nat.lt_succ_iff]
 #align power_series.coeff_trunc PowerSeries.coeff_trunc
 
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 @[simp]
 theorem trunc_zero (n) : trunc n (0 : PowerSeries R) = 0 :=
   Polynomial.ext fun m =>
@@ -2546,12 +1655,6 @@ theorem trunc_zero (n) : trunc n (0 : PowerSeries R) = 0 :=
     split_ifs <;> rfl
 #align power_series.trunc_zero PowerSeries.trunc_zero
 
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 @[simp]
 theorem trunc_one (n) : trunc (n + 1) (1 : PowerSeries R) = 1 :=
   Polynomial.ext fun m => by
@@ -2563,12 +1666,6 @@ theorem trunc_one (n) : trunc (n + 1) (1 : PowerSeries R) = 1 :=
       rintro rfl; apply H; exact Nat.zero_lt_succ _
 #align power_series.trunc_one PowerSeries.trunc_one
 
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 @[simp]
 theorem trunc_C (n) (a : R) : trunc (n + 1) (C R a) = Polynomial.C a :=
   Polynomial.ext fun m => by
@@ -2576,12 +1673,6 @@ theorem trunc_C (n) (a : R) : trunc (n + 1) (C R a) = Polynomial.C a :=
     split_ifs with H <;> first |rfl|try simp_all
 #align power_series.trunc_C PowerSeries.trunc_C
 
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 @[simp]
 theorem trunc_add (n) (φ ψ : PowerSeries R) : trunc n (φ + ψ) = trunc n φ + trunc n ψ :=
   Polynomial.ext fun m =>
@@ -2605,9 +1696,6 @@ protected def inv.aux : R → PowerSeries R → PowerSeries R :=
 #align power_series.inv.aux PowerSeries.inv.aux
 -/
 
-/- warning: power_series.coeff_inv_aux -> PowerSeries.coeff_inv_aux is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_inv_aux PowerSeries.coeff_inv_auxₓ'. -/
 theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
     coeff R n (inv.aux a φ) =
       if n = 0 then a
@@ -2643,20 +1731,11 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
       exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
 #align power_series.coeff_inv_aux PowerSeries.coeff_inv_aux
 
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 /-- A formal power series is invertible if the constant coefficient is invertible.-/
 def invOfUnit (φ : PowerSeries R) (u : Rˣ) : PowerSeries R :=
   MvPowerSeries.invOfUnit φ u
 #align power_series.inv_of_unit PowerSeries.invOfUnit
 
-/- warning: power_series.coeff_inv_of_unit -> PowerSeries.coeff_invOfUnit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_inv_of_unit PowerSeries.coeff_invOfUnitₓ'. -/
 theorem coeff_invOfUnit (n : ℕ) (φ : PowerSeries R) (u : Rˣ) :
     coeff R n (invOfUnit φ u) =
       if n = 0 then ↑u⁻¹
@@ -2667,41 +1746,23 @@ theorem coeff_invOfUnit (n : ℕ) (φ : PowerSeries R) (u : Rˣ) :
   coeff_inv_aux n (↑u⁻¹) φ
 #align power_series.coeff_inv_of_unit PowerSeries.coeff_invOfUnit
 
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 @[simp]
 theorem constantCoeff_invOfUnit (φ : PowerSeries R) (u : Rˣ) :
     constantCoeff R (invOfUnit φ u) = ↑u⁻¹ := by
   rw [← coeff_zero_eq_constant_coeff_apply, coeff_inv_of_unit, if_pos rfl]
 #align power_series.constant_coeff_inv_of_unit PowerSeries.constantCoeff_invOfUnit
 
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-Case conversion may be inaccurate. Consider using '#align power_series.mul_inv_of_unit PowerSeries.mul_invOfUnitₓ'. -/
 theorem mul_invOfUnit (φ : PowerSeries R) (u : Rˣ) (h : constantCoeff R φ = u) :
     φ * invOfUnit φ u = 1 :=
   MvPowerSeries.mul_invOfUnit φ u <| h
 #align power_series.mul_inv_of_unit PowerSeries.mul_invOfUnit
 
-/- warning: power_series.sub_const_eq_shift_mul_X -> PowerSeries.sub_const_eq_shift_mul_X is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.sub_const_eq_shift_mul_X PowerSeries.sub_const_eq_shift_mul_Xₓ'. -/
 /-- Two ways of removing the constant coefficient of a power series are the same. -/
 theorem sub_const_eq_shift_mul_X (φ : PowerSeries R) :
     φ - C R (constantCoeff R φ) = (PowerSeries.mk fun p => coeff R (p + 1) φ) * X :=
   sub_eq_iff_eq_add.mpr (eq_shift_mul_X_add_const φ)
 #align power_series.sub_const_eq_shift_mul_X PowerSeries.sub_const_eq_shift_mul_X
 
-/- warning: power_series.sub_const_eq_X_mul_shift -> PowerSeries.sub_const_eq_X_mul_shift is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.sub_const_eq_X_mul_shift PowerSeries.sub_const_eq_X_mul_shiftₓ'. -/
 theorem sub_const_eq_X_mul_shift (φ : PowerSeries R) :
     φ - C R (constantCoeff R φ) = X * PowerSeries.mk fun p => coeff R (p + 1) φ :=
   sub_eq_iff_eq_add.mpr (eq_X_mul_shift_add_const φ)
@@ -2713,9 +1774,6 @@ section CommRing
 
 variable {A : Type _} [CommRing A]
 
-/- warning: power_series.rescale_X -> PowerSeries.rescale_X is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.rescale_X PowerSeries.rescale_Xₓ'. -/
 @[simp]
 theorem rescale_X (a : A) : rescale a X = C A a * X :=
   by
@@ -2724,33 +1782,15 @@ theorem rescale_X (a : A) : rescale a X = C A a * X :=
   split_ifs with h <;> simp [h]
 #align power_series.rescale_X PowerSeries.rescale_X
 
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 theorem rescale_neg_one_X : rescale (-1 : A) X = -X := by
   rw [rescale_X, map_neg, map_one, neg_one_mul]
 #align power_series.rescale_neg_one_X PowerSeries.rescale_neg_one_X
 
-/- warning: power_series.eval_neg_hom -> PowerSeries.evalNegHom is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align power_series.eval_neg_hom PowerSeries.evalNegHomₓ'. -/
 /-- The ring homomorphism taking a power series `f(X)` to `f(-X)`. -/
 noncomputable def evalNegHom : PowerSeries A →+* PowerSeries A :=
   rescale (-1 : A)
 #align power_series.eval_neg_hom PowerSeries.evalNegHom
 
-/- warning: power_series.eval_neg_hom_X -> PowerSeries.evalNegHom_X is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align power_series.eval_neg_hom_X PowerSeries.evalNegHom_Xₓ'. -/
 @[simp]
 theorem evalNegHom_X : evalNegHom (X : PowerSeries A) = -X :=
   rescale_neg_one_X
@@ -2762,12 +1802,6 @@ section Domain
 
 variable [Ring R]
 
-/- warning: power_series.eq_zero_or_eq_zero_of_mul_eq_zero -> PowerSeries.eq_zero_or_eq_zero_of_mul_eq_zero is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align power_series.eq_zero_or_eq_zero_of_mul_eq_zero PowerSeries.eq_zero_or_eq_zero_of_mul_eq_zeroₓ'. -/
 theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSeries R) (h : φ * ψ = 0) :
     φ = 0 ∨ ψ = 0 := by
   rw [or_iff_not_imp_left]; intro H
@@ -2808,12 +1842,6 @@ section IsDomain
 
 variable [CommRing R] [IsDomain R]
 
-/- warning: power_series.span_X_is_prime -> PowerSeries.span_X_isPrime is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align power_series.span_X_is_prime PowerSeries.span_X_isPrimeₓ'. -/
 /-- The ideal spanned by the variable in the power series ring
  over an integral domain is a prime ideal.-/
 theorem span_X_isPrime : (Ideal.span ({X} : Set (PowerSeries R))).IsPrime :=
@@ -2824,12 +1852,6 @@ theorem span_X_isPrime : (Ideal.span ({X} : Set (PowerSeries R))).IsPrime :=
   rw [RingHom.mem_ker, Ideal.mem_span_singleton, X_dvd_iff]
 #align power_series.span_X_is_prime PowerSeries.span_X_isPrime
 
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-Case conversion may be inaccurate. Consider using '#align power_series.X_prime PowerSeries.X_primeₓ'. -/
 /-- The variable of the power series ring over an integral domain is prime.-/
 theorem X_prime : Prime (X : PowerSeries R) :=
   by
@@ -2838,12 +1860,6 @@ theorem X_prime : Prime (X : PowerSeries R) :=
   · intro h; simpa using congr_arg (coeff R 1) h
 #align power_series.X_prime PowerSeries.X_prime
 
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-Case conversion may be inaccurate. Consider using '#align power_series.rescale_injective PowerSeries.rescale_injectiveₓ'. -/
 theorem rescale_injective {a : R} (ha : a ≠ 0) : Function.Injective (rescale a) :=
   by
   intro p q h
@@ -2862,12 +1878,6 @@ section LocalRing
 
 variable {S : Type _} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalRingHom f]
 
-/- warning: power_series.map.is_local_ring_hom -> PowerSeries.map.isLocalRingHom is a dubious translation:
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-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) [_inst_3 : IsLocalRingHom.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f], IsLocalRingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PowerSeries.semiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (PowerSeries.map.{u1, u2} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f)
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-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) [_inst_3 : IsLocalRingHom.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f], IsLocalRingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PowerSeries.instSemiringPowerSeries.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (PowerSeries.map.{u1, u2} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f)
-Case conversion may be inaccurate. Consider using '#align power_series.map.is_local_ring_hom PowerSeries.map.isLocalRingHomₓ'. -/
 instance map.isLocalRingHom : IsLocalRingHom (map f) :=
   MvPowerSeries.map.isLocalRingHom f
 #align power_series.map.is_local_ring_hom PowerSeries.map.isLocalRingHom
@@ -2883,22 +1893,10 @@ section Algebra
 
 variable {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
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-Case conversion may be inaccurate. Consider using '#align power_series.C_eq_algebra_map PowerSeries.C_eq_algebraMapₓ'. -/
 theorem C_eq_algebraMap {r : R} : C R r = (algebraMap R (PowerSeries R)) r :=
   rfl
 #align power_series.C_eq_algebra_map PowerSeries.C_eq_algebraMap
 
-/- warning: power_series.algebra_map_apply -> PowerSeries.algebraMap_apply is a dubious translation:
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 theorem algebraMap_apply {r : R} : algebraMap R (PowerSeries A) r = C A (algebraMap R A r) :=
   MvPowerSeries.algebraMap_apply
 #align power_series.algebra_map_apply PowerSeries.algebraMap_apply
@@ -2922,19 +1920,10 @@ protected def inv : PowerSeries k → PowerSeries k :=
 instance : Inv (PowerSeries k) :=
   ⟨PowerSeries.inv⟩
 
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 theorem inv_eq_inv_aux (φ : PowerSeries k) : φ⁻¹ = inv.aux (constantCoeff k φ)⁻¹ φ :=
   rfl
 #align power_series.inv_eq_inv_aux PowerSeries.inv_eq_inv_aux
 
-/- warning: power_series.coeff_inv -> PowerSeries.coeff_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_inv PowerSeries.coeff_invₓ'. -/
 theorem coeff_inv (n) (φ : PowerSeries k) :
     coeff k n φ⁻¹ =
       if n = 0 then (constantCoeff k φ)⁻¹
@@ -2945,117 +1934,57 @@ theorem coeff_inv (n) (φ : PowerSeries k) :
   by rw [inv_eq_inv_aux, coeff_inv_aux n (constant_coeff k φ)⁻¹ φ]
 #align power_series.coeff_inv PowerSeries.coeff_inv
 
-/- warning: power_series.constant_coeff_inv -> PowerSeries.constantCoeff_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.constant_coeff_inv PowerSeries.constantCoeff_invₓ'. -/
 @[simp]
 theorem constantCoeff_inv (φ : PowerSeries k) : constantCoeff k φ⁻¹ = (constantCoeff k φ)⁻¹ :=
   MvPowerSeries.constantCoeff_inv φ
 #align power_series.constant_coeff_inv PowerSeries.constantCoeff_inv
 
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-Case conversion may be inaccurate. Consider using '#align power_series.inv_eq_zero PowerSeries.inv_eq_zeroₓ'. -/
 theorem inv_eq_zero {φ : PowerSeries k} : φ⁻¹ = 0 ↔ constantCoeff k φ = 0 :=
   MvPowerSeries.inv_eq_zero
 #align power_series.inv_eq_zero PowerSeries.inv_eq_zero
 
-/- warning: power_series.zero_inv -> PowerSeries.zero_inv is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align power_series.zero_inv PowerSeries.zero_invₓ'. -/
 @[simp]
 theorem zero_inv : (0 : PowerSeries k)⁻¹ = 0 :=
   MvPowerSeries.zero_inv
 #align power_series.zero_inv PowerSeries.zero_inv
 
-/- warning: power_series.inv_of_unit_eq -> PowerSeries.invOfUnit_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.inv_of_unit_eq PowerSeries.invOfUnit_eqₓ'. -/
 @[simp]
 theorem invOfUnit_eq (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) :
     invOfUnit φ (Units.mk0 _ h) = φ⁻¹ :=
   MvPowerSeries.invOfUnit_eq _ _
 #align power_series.inv_of_unit_eq PowerSeries.invOfUnit_eq
 
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-Case conversion may be inaccurate. Consider using '#align power_series.inv_of_unit_eq' PowerSeries.invOfUnit_eq'ₓ'. -/
 @[simp]
 theorem invOfUnit_eq' (φ : PowerSeries k) (u : Units k) (h : constantCoeff k φ = u) :
     invOfUnit φ u = φ⁻¹ :=
   MvPowerSeries.invOfUnit_eq' φ _ h
 #align power_series.inv_of_unit_eq' PowerSeries.invOfUnit_eq'
 
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-Case conversion may be inaccurate. Consider using '#align power_series.mul_inv_cancel PowerSeries.mul_inv_cancelₓ'. -/
 @[simp]
 protected theorem mul_inv_cancel (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) : φ * φ⁻¹ = 1 :=
   MvPowerSeries.mul_inv_cancel φ h
 #align power_series.mul_inv_cancel PowerSeries.mul_inv_cancel
 
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-Case conversion may be inaccurate. Consider using '#align power_series.inv_mul_cancel PowerSeries.inv_mul_cancelₓ'. -/
 @[simp]
 protected theorem inv_mul_cancel (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) : φ⁻¹ * φ = 1 :=
   MvPowerSeries.inv_mul_cancel φ h
 #align power_series.inv_mul_cancel PowerSeries.inv_mul_cancel
 
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-Case conversion may be inaccurate. Consider using '#align power_series.eq_mul_inv_iff_mul_eq PowerSeries.eq_mul_inv_iff_mul_eqₓ'. -/
 theorem eq_mul_inv_iff_mul_eq {φ₁ φ₂ φ₃ : PowerSeries k} (h : constantCoeff k φ₃ ≠ 0) :
     φ₁ = φ₂ * φ₃⁻¹ ↔ φ₁ * φ₃ = φ₂ :=
   MvPowerSeries.eq_mul_inv_iff_mul_eq h
 #align power_series.eq_mul_inv_iff_mul_eq PowerSeries.eq_mul_inv_iff_mul_eq
 
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-Case conversion may be inaccurate. Consider using '#align power_series.eq_inv_iff_mul_eq_one PowerSeries.eq_inv_iff_mul_eq_oneₓ'. -/
 theorem eq_inv_iff_mul_eq_one {φ ψ : PowerSeries k} (h : constantCoeff k ψ ≠ 0) :
     φ = ψ⁻¹ ↔ φ * ψ = 1 :=
   MvPowerSeries.eq_inv_iff_mul_eq_one h
 #align power_series.eq_inv_iff_mul_eq_one PowerSeries.eq_inv_iff_mul_eq_one
 
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-Case conversion may be inaccurate. Consider using '#align power_series.inv_eq_iff_mul_eq_one PowerSeries.inv_eq_iff_mul_eq_oneₓ'. -/
 theorem inv_eq_iff_mul_eq_one {φ ψ : PowerSeries k} (h : constantCoeff k ψ ≠ 0) :
     ψ⁻¹ = φ ↔ φ * ψ = 1 :=
   MvPowerSeries.inv_eq_iff_mul_eq_one h
 #align power_series.inv_eq_iff_mul_eq_one PowerSeries.inv_eq_iff_mul_eq_one
 
-/- warning: power_series.mul_inv_rev -> PowerSeries.mul_inv_rev is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align power_series.mul_inv_rev PowerSeries.mul_inv_revₓ'. -/
 @[simp]
 protected theorem mul_inv_rev (φ ψ : PowerSeries k) : (φ * ψ)⁻¹ = ψ⁻¹ * φ⁻¹ :=
   MvPowerSeries.mul_inv_rev _ _
@@ -3064,31 +1993,16 @@ protected theorem mul_inv_rev (φ ψ : PowerSeries k) : (φ * ψ)⁻¹ = ψ⁻¹
 instance : InvOneClass (PowerSeries k) :=
   MvPowerSeries.invOneClass
 
-/- warning: power_series.C_inv -> PowerSeries.C_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.C_inv PowerSeries.C_invₓ'. -/
 @[simp]
 theorem C_inv (r : k) : (C k r)⁻¹ = C k r⁻¹ :=
   MvPowerSeries.C_inv _
 #align power_series.C_inv PowerSeries.C_inv
 
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-Case conversion may be inaccurate. Consider using '#align power_series.X_inv PowerSeries.X_invₓ'. -/
 @[simp]
 theorem X_inv : (X : PowerSeries k)⁻¹ = 0 :=
   MvPowerSeries.X_inv _
 #align power_series.X_inv PowerSeries.X_inv
 
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-Case conversion may be inaccurate. Consider using '#align power_series.smul_inv PowerSeries.smul_invₓ'. -/
 @[simp]
 theorem smul_inv (r : k) (φ : PowerSeries k) : (r • φ)⁻¹ = r⁻¹ • φ⁻¹ :=
   MvPowerSeries.smul_inv _ _
@@ -3112,12 +2026,6 @@ open multiplicity
 
 variable [Semiring R] {φ : PowerSeries R}
 
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 theorem exists_coeff_ne_zero_iff_ne_zero : (∃ n : ℕ, coeff R n φ ≠ 0) ↔ φ ≠ 0 :=
   by
   refine' not_iff_not.mp _
@@ -3133,24 +2041,12 @@ def order (φ : PowerSeries R) : PartENat :=
 #align power_series.order PowerSeries.order
 -/
 
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 /-- The order of the `0` power series is infinite.-/
 @[simp]
 theorem order_zero : order (0 : PowerSeries R) = ⊤ :=
   dif_pos rfl
 #align power_series.order_zero PowerSeries.order_zero
 
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 theorem order_finite_iff_ne_zero : (order φ).Dom ↔ φ ≠ 0 :=
   by
   simp only [order]
@@ -3163,12 +2059,6 @@ theorem order_finite_iff_ne_zero : (order φ).Dom ↔ φ ≠ 0 :=
     simp [h]
 #align power_series.order_finite_iff_ne_zero PowerSeries.order_finite_iff_ne_zero
 
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 /-- If the order of a formal power series is finite,
 then the coefficient indexed by the order is nonzero.-/
 theorem coeff_order (h : (order φ).Dom) : coeff R (φ.order.get h) φ ≠ 0 :=
@@ -3178,12 +2068,6 @@ theorem coeff_order (h : (order φ).Dom) : coeff R (φ.order.get h) φ ≠ 0 :=
   exact Nat.find_spec h
 #align power_series.coeff_order PowerSeries.coeff_order
 
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 /-- If the `n`th coefficient of a formal power series is nonzero,
 then the order of the power series is less than or equal to `n`.-/
 theorem order_le (n : ℕ) (h : coeff R n φ ≠ 0) : order φ ≤ n :=
@@ -3195,24 +2079,12 @@ theorem order_le (n : ℕ) (h : coeff R n φ ≠ 0) : order φ ≤ n :=
   · exact exists_coeff_ne_zero_iff_ne_zero.mp ⟨n, h⟩
 #align power_series.order_le PowerSeries.order_le
 
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 /-- The `n`th coefficient of a formal power series is `0` if `n` is strictly
 smaller than the order of the power series.-/
 theorem coeff_of_lt_order (n : ℕ) (h : ↑n < order φ) : coeff R n φ = 0 := by contrapose! h;
   exact order_le _ h
 #align power_series.coeff_of_lt_order PowerSeries.coeff_of_lt_order
 
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 /-- The `0` power series is the unique power series with infinite order.-/
 @[simp]
 theorem order_eq_top {φ : PowerSeries R} : φ.order = ⊤ ↔ φ = 0 :=
@@ -3222,12 +2094,6 @@ theorem order_eq_top {φ : PowerSeries R} : φ.order = ⊤ ↔ φ = 0 :=
   · rintro rfl; exact order_zero
 #align power_series.order_eq_top PowerSeries.order_eq_top
 
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-Case conversion may be inaccurate. Consider using '#align power_series.nat_le_order PowerSeries.nat_le_orderₓ'. -/
 /-- The order of a formal power series is at least `n` if
 the `i`th coefficient is `0` for all `i < n`.-/
 theorem nat_le_order (φ : PowerSeries R) (n : ℕ) (h : ∀ i < n, coeff R i φ = 0) : ↑n ≤ order φ :=
@@ -3238,12 +2104,6 @@ theorem nat_le_order (φ : PowerSeries R) (n : ℕ) (h : ∀ i < n, coeff R i φ
   exact coeff_order this (h _ H)
 #align power_series.nat_le_order PowerSeries.nat_le_order
 
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-Case conversion may be inaccurate. Consider using '#align power_series.le_order PowerSeries.le_orderₓ'. -/
 /-- The order of a formal power series is at least `n` if
 the `i`th coefficient is `0` for all `i < n`.-/
 theorem le_order (φ : PowerSeries R) (n : PartENat) (h : ∀ i : ℕ, ↑i < n → coeff R i φ = 0) :
@@ -3254,9 +2114,6 @@ theorem le_order (φ : PowerSeries R) (n : PartENat) (h : ∀ i : ℕ, ↑i < n
   · apply nat_le_order; simpa only [PartENat.coe_lt_coe] using h
 #align power_series.le_order PowerSeries.le_order
 
-/- warning: power_series.order_eq_nat -> PowerSeries.order_eq_nat is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.order_eq_nat PowerSeries.order_eq_natₓ'. -/
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
 and the `i`th coefficient is `0` for all `i < n`.-/
 theorem order_eq_nat {φ : PowerSeries R} {n : ℕ} :
@@ -3267,9 +2124,6 @@ theorem order_eq_nat {φ : PowerSeries R} {n : ℕ} :
   simp [order, dif_neg hφ, Nat.find_eq_iff]
 #align power_series.order_eq_nat PowerSeries.order_eq_nat
 
-/- warning: power_series.order_eq -> PowerSeries.order_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.order_eq PowerSeries.order_eqₓ'. -/
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
 and the `i`th coefficient is `0` for all `i < n`.-/
 theorem order_eq {φ : PowerSeries R} {n : PartENat} :
@@ -3284,12 +2138,6 @@ theorem order_eq {φ : PowerSeries R} {n : PartENat} :
   · simpa [PartENat.natCast_inj] using order_eq_nat
 #align power_series.order_eq PowerSeries.order_eq
 
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-Case conversion may be inaccurate. Consider using '#align power_series.le_order_add PowerSeries.le_order_addₓ'. -/
 /-- The order of the sum of two formal power series
  is at least the minimum of their orders.-/
 theorem le_order_add (φ ψ : PowerSeries R) : min (order φ) (order ψ) ≤ order (φ + ψ) :=
@@ -3309,12 +2157,6 @@ private theorem order_add_of_order_eq.aux (φ ψ : PowerSeries R) (h : order φ
       rw [(coeff _ _).map_add, coeff_of_lt_order i hi, coeff_of_lt_order i (lt_trans hi H),
         zero_add]
 
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-Case conversion may be inaccurate. Consider using '#align power_series.order_add_of_order_eq PowerSeries.order_add_of_order_eqₓ'. -/
 /-- The order of the sum of two formal power series
  is the minimum of their orders if their orders differ.-/
 theorem order_add_of_order_eq (φ ψ : PowerSeries R) (h : order φ ≠ order ψ) :
@@ -3328,12 +2170,6 @@ theorem order_add_of_order_eq (φ ψ : PowerSeries R) (h : order φ ≠ order ψ
   exfalso; exact h (le_antisymm (not_lt.1 H₂) (not_lt.1 H₁))
 #align power_series.order_add_of_order_eq PowerSeries.order_add_of_order_eq
 
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 /-- The order of the product of two formal power series
  is at least the sum of their orders.-/
 theorem order_mul_ge (φ ψ : PowerSeries R) : order φ + order ψ ≤ order (φ * ψ) :=
@@ -3351,12 +2187,6 @@ theorem order_mul_ge (φ ψ : PowerSeries R) : order φ + order ψ ≤ order (φ
   rw [← Nat.cast_add, hij]
 #align power_series.order_mul_ge PowerSeries.order_mul_ge
 
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 /-- The order of the monomial `a*X^n` is infinite if `a = 0` and `n` otherwise.-/
 theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
     order (monomial R n a) = if a = 0 then ⊤ else n :=
@@ -3368,23 +2198,11 @@ theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
     · rw [PartENat.coe_lt_coe] at hi; rw [coeff_monomial, if_neg]; exact ne_of_lt hi
 #align power_series.order_monomial PowerSeries.order_monomial
 
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 /-- The order of the monomial `a*X^n` is `n` if `a ≠ 0`.-/
 theorem order_monomial_of_ne_zero (n : ℕ) (a : R) (h : a ≠ 0) : order (monomial R n a) = n := by
   rw [order_monomial, if_neg h]
 #align power_series.order_monomial_of_ne_zero PowerSeries.order_monomial_of_ne_zero
 
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-Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_orderₓ'. -/
 /-- If `n` is strictly smaller than the order of `ψ`, then the `n`th coefficient of its product
 with any other power series is `0`. -/
 theorem coeff_mul_of_lt_order {φ ψ : PowerSeries R} {n : ℕ} (h : ↑n < ψ.order) :
@@ -3400,17 +2218,11 @@ theorem coeff_mul_of_lt_order {φ ψ : PowerSeries R} {n : ℕ} (h : ↑n < ψ.o
   linarith
 #align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_order
 
-/- warning: power_series.coeff_mul_one_sub_of_lt_order -> PowerSeries.coeff_mul_one_sub_of_lt_order is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_one_sub_of_lt_order PowerSeries.coeff_mul_one_sub_of_lt_orderₓ'. -/
 theorem coeff_mul_one_sub_of_lt_order {R : Type _} [CommRing R] {φ ψ : PowerSeries R} (n : ℕ)
     (h : ↑n < ψ.order) : coeff R n (φ * (1 - ψ)) = coeff R n φ := by
   simp [coeff_mul_of_lt_order h, mul_sub]
 #align power_series.coeff_mul_one_sub_of_lt_order PowerSeries.coeff_mul_one_sub_of_lt_order
 
-/- warning: power_series.coeff_mul_prod_one_sub_of_lt_order -> PowerSeries.coeff_mul_prod_one_sub_of_lt_order is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_prod_one_sub_of_lt_order PowerSeries.coeff_mul_prod_one_sub_of_lt_orderₓ'. -/
 theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type _} [CommRing R] (k : ℕ) (s : Finset ι)
     (φ : PowerSeries R) (f : ι → PowerSeries R) :
     (∀ i ∈ s, ↑k < (f i).order) → coeff R k (φ * ∏ i in s, 1 - f i) = coeff R k φ :=
@@ -3423,12 +2235,6 @@ theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type _} [CommRing R] (k : ℕ
     exact ih t.2
 #align power_series.coeff_mul_prod_one_sub_of_lt_order PowerSeries.coeff_mul_prod_one_sub_of_lt_order
 
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 -- TODO: link with `X_pow_dvd_iff`
 theorem X_pow_order_dvd (h : (order φ).Dom) : X ^ (order φ).get h ∣ φ :=
   by
@@ -3443,12 +2249,6 @@ theorem X_pow_order_dvd (h : (order φ).Dom) : X ^ (order φ).get h ∣ φ :=
     simpa [PartENat.coe_lt_iff] using fun _ => hn
 #align power_series.X_pow_order_dvd PowerSeries.X_pow_order_dvd
 
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-Case conversion may be inaccurate. Consider using '#align power_series.order_eq_multiplicity_X PowerSeries.order_eq_multiplicity_Xₓ'. -/
 theorem order_eq_multiplicity_X {R : Type _} [Semiring R] (φ : PowerSeries R) :
     order φ = multiplicity X φ :=
   by
@@ -3478,12 +2278,6 @@ section OrderZeroNeOne
 
 variable [Semiring R] [Nontrivial R]
 
-/- warning: power_series.order_one -> PowerSeries.order_one is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align power_series.order_one PowerSeries.order_oneₓ'. -/
 /-- The order of the formal power series `1` is `0`.-/
 @[simp]
 theorem order_one : order (1 : PowerSeries R) = 0 := by
@@ -3498,12 +2292,6 @@ theorem order_X : order (X : PowerSeries R) = 1 := by
 #align power_series.order_X PowerSeries.order_X
 -/
 
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-Case conversion may be inaccurate. Consider using '#align power_series.order_X_pow PowerSeries.order_X_powₓ'. -/
 /-- The order of the formal power series `X^n` is `n`.-/
 @[simp]
 theorem order_X_pow (n : ℕ) : order ((X : PowerSeries R) ^ n) = n := by
@@ -3517,12 +2305,6 @@ section OrderIsDomain
 -- TODO: generalize to `[semiring R] [no_zero_divisors R]`
 variable [CommRing R] [IsDomain R]
 
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 /-- The order of the product of two formal power series over an integral domain
  is the sum of their orders.-/
 theorem order_mul (φ ψ : PowerSeries R) : order (φ * ψ) = order φ + order ψ :=
@@ -3554,43 +2336,22 @@ theorem coe_def : (φ : PowerSeries R) = PowerSeries.mk (coeff φ) :=
 #align polynomial.coe_def Polynomial.coe_def
 -/
 
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 @[simp, norm_cast]
 theorem coeff_coe (n) : PowerSeries.coeff R n φ = coeff φ n :=
   congr_arg (coeff φ) Finsupp.single_eq_same
 #align polynomial.coeff_coe Polynomial.coeff_coe
 
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 @[simp, norm_cast]
 theorem coe_monomial (n : ℕ) (a : R) :
     (monomial n a : PowerSeries R) = PowerSeries.monomial R n a := by ext;
   simp [coeff_coe, PowerSeries.coeff_monomial, Polynomial.coeff_monomial, eq_comm]
 #align polynomial.coe_monomial Polynomial.coe_monomial
 
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 @[simp, norm_cast]
 theorem coe_zero : ((0 : R[X]) : PowerSeries R) = 0 :=
   rfl
 #align polynomial.coe_zero Polynomial.coe_zero
 
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 @[simp, norm_cast]
 theorem coe_one : ((1 : R[X]) : PowerSeries R) = 1 :=
   by
@@ -3598,33 +2359,15 @@ theorem coe_one : ((1 : R[X]) : PowerSeries R) = 1 :=
   rwa [PowerSeries.monomial_zero_eq_C_apply] at this
 #align polynomial.coe_one Polynomial.coe_one
 
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 @[simp, norm_cast]
 theorem coe_add : ((φ + ψ : R[X]) : PowerSeries R) = φ + ψ := by ext; simp
 #align polynomial.coe_add Polynomial.coe_add
 
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 @[simp, norm_cast]
 theorem coe_mul : ((φ * ψ : R[X]) : PowerSeries R) = φ * ψ :=
   PowerSeries.ext fun n => by simp only [coeff_coe, PowerSeries.coeff_mul, coeff_mul]
 #align polynomial.coe_mul Polynomial.coe_mul
 
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 @[simp, norm_cast]
 theorem coe_C (a : R) : ((C a : R[X]) : PowerSeries R) = PowerSeries.C R a :=
   by
@@ -3632,23 +2375,11 @@ theorem coe_C (a : R) : ((C a : R[X]) : PowerSeries R) = PowerSeries.C R a :=
   rwa [PowerSeries.monomial_zero_eq_C_apply] at this
 #align polynomial.coe_C Polynomial.coe_C
 
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 @[simp, norm_cast]
 theorem coe_bit0 : ((bit0 φ : R[X]) : PowerSeries R) = bit0 (φ : PowerSeries R) :=
   coe_add φ φ
 #align polynomial.coe_bit0 Polynomial.coe_bit0
 
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 @[simp, norm_cast]
 theorem coe_bit1 : ((bit1 φ : R[X]) : PowerSeries R) = bit1 (φ : PowerSeries R) := by
   rw [bit1, bit1, coe_add, coe_one, coe_bit0]
@@ -3661,12 +2392,6 @@ theorem coe_X : ((X : R[X]) : PowerSeries R) = PowerSeries.X :=
 #align polynomial.coe_X Polynomial.coe_X
 -/
 
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 @[simp]
 theorem constantCoeff_coe : PowerSeries.constantCoeff R φ = φ.coeff 0 :=
   rfl
@@ -3689,34 +2414,16 @@ theorem coe_inj : (φ : PowerSeries R) = ψ ↔ φ = ψ :=
 #align polynomial.coe_inj Polynomial.coe_inj
 -/
 
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 @[simp]
 theorem coe_eq_zero_iff : (φ : PowerSeries R) = 0 ↔ φ = 0 := by rw [← coe_zero, coe_inj]
 #align polynomial.coe_eq_zero_iff Polynomial.coe_eq_zero_iff
 
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 @[simp]
 theorem coe_eq_one_iff : (φ : PowerSeries R) = 1 ↔ φ = 1 := by rw [← coe_one, coe_inj]
 #align polynomial.coe_eq_one_iff Polynomial.coe_eq_one_iff
 
 variable (φ ψ)
 
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 /-- The coercion from polynomials to power series
 as a ring homomorphism.
 -/
@@ -3729,23 +2436,11 @@ def coeToPowerSeries.ringHom : R[X] →+* PowerSeries R
   map_mul' := coe_mul
 #align polynomial.coe_to_power_series.ring_hom Polynomial.coeToPowerSeries.ringHom
 
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 @[simp]
 theorem coeToPowerSeries.ringHom_apply : coeToPowerSeries.ringHom φ = φ :=
   rfl
 #align polynomial.coe_to_power_series.ring_hom_apply Polynomial.coeToPowerSeries.ringHom_apply
 
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 @[simp, norm_cast]
 theorem coe_pow (n : ℕ) : ((φ ^ n : R[X]) : PowerSeries R) = (φ : PowerSeries R) ^ n :=
   coeToPowerSeries.ringHom.map_pow _ _
@@ -3753,12 +2448,6 @@ theorem coe_pow (n : ℕ) : ((φ ^ n : R[X]) : PowerSeries R) = (φ : PowerSerie
 
 variable (A : Type _) [Semiring A] [Algebra R A]
 
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 /-- The coercion from polynomials to power series
 as an algebra homomorphism.
 -/
@@ -3781,32 +2470,14 @@ namespace PowerSeries
 
 variable {R A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : PowerSeries R)
 
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 instance algebraPolynomial : Algebra R[X] (PowerSeries A) :=
   RingHom.toAlgebra (Polynomial.coeToPowerSeries.algHom A).toRingHom
 #align power_series.algebra_polynomial PowerSeries.algebraPolynomial
 
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 instance algebraPowerSeries : Algebra (PowerSeries R) (PowerSeries A) :=
   (map (algebraMap R A)).toAlgebra
 #align power_series.algebra_power_series PowerSeries.algebraPowerSeries
 
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 -- see Note [lower instance priority]
 instance (priority := 100) algebraPolynomial' {A : Type _} [CommSemiring A] [Algebra R A[X]] :
     Algebra R (PowerSeries A) :=
@@ -3815,16 +2486,10 @@ instance (priority := 100) algebraPolynomial' {A : Type _} [CommSemiring A] [Alg
 
 variable (A)
 
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-<too large>
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 theorem algebraMap_apply' (p : R[X]) : algebraMap R[X] (PowerSeries A) p = map (algebraMap R A) p :=
   rfl
 #align power_series.algebra_map_apply' PowerSeries.algebraMap_apply'
 
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-Case conversion may be inaccurate. Consider using '#align power_series.algebra_map_apply'' PowerSeries.algebraMap_apply''ₓ'. -/
 theorem algebraMap_apply'' :
     algebraMap (PowerSeries R) (PowerSeries A) f = map (algebraMap R A) f :=
   rfl

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

@@ -411,21 +411,13 @@ protected theorem mul_assoc (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : φ₁ * 
   refine' Finset.sum_bij (fun p _ => ⟨(p.2.1, p.2.2 + p.1.2), (p.2.2, p.1.2)⟩) _ _ _ _ <;>
     simp only [mem_antidiagonal, Finset.mem_sigma, heq_iff_eq, Prod.mk.inj_iff, and_imp,
       exists_prop]
-  · rintro ⟨⟨i, j⟩, ⟨k, l⟩⟩
-    dsimp only
-    rintro rfl rfl
+  · rintro ⟨⟨i, j⟩, ⟨k, l⟩⟩; dsimp only; rintro rfl rfl
     simp [add_assoc]
-  · rintro ⟨⟨a, b⟩, ⟨c, d⟩⟩
-    dsimp only
-    rintro rfl rfl
+  · rintro ⟨⟨a, b⟩, ⟨c, d⟩⟩; dsimp only; rintro rfl rfl
     apply mul_assoc
-  · rintro ⟨⟨a, b⟩, ⟨c, d⟩⟩ ⟨⟨i, j⟩, ⟨k, l⟩⟩
-    dsimp only
-    rintro rfl rfl - rfl rfl - rfl rfl
+  · rintro ⟨⟨a, b⟩, ⟨c, d⟩⟩ ⟨⟨i, j⟩, ⟨k, l⟩⟩; dsimp only; rintro rfl rfl - rfl rfl - rfl rfl
     rfl
-  · rintro ⟨⟨i, j⟩, ⟨k, l⟩⟩
-    dsimp only
-    rintro rfl rfl
+  · rintro ⟨⟨i, j⟩, ⟨k, l⟩⟩; dsimp only; rintro rfl rfl
     refine' ⟨⟨(i + k, l), (i, k)⟩, _, _⟩ <;> simp [add_assoc]
 #align mv_power_series.mul_assoc MvPowerSeries.mul_assoc
 
@@ -468,13 +460,10 @@ theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
   ext k
   simp only [coeff_mul_monomial, coeff_monomial]
   split_ifs with h₁ h₂ h₃ h₃ h₂ <;> try rfl
-  · rw [← h₂, tsub_add_cancel_of_le h₁] at h₃
-    exact (h₃ rfl).elim
-  · rw [h₃, add_tsub_cancel_right] at h₂
-    exact (h₂ rfl).elim
+  · rw [← h₂, tsub_add_cancel_of_le h₁] at h₃; exact (h₃ rfl).elim
+  · rw [h₃, add_tsub_cancel_right] at h₂; exact (h₂ rfl).elim
   · exact MulZeroClass.zero_mul b
-  · rw [h₂] at h₁
-    exact (h₁ <| le_add_left le_rfl).elim
+  · rw [h₂] at h₁; exact (h₁ <| le_add_left le_rfl).elim
 #align mv_power_series.monomial_mul_monomial MvPowerSeries.monomial_mul_monomial
 
 variable (σ) (R)
@@ -577,11 +566,8 @@ lean 3 declaration is
 but is expected to have type
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (s : σ), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) (fun (_x : MvPowerSeries.{u1, u2} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_X MvPowerSeries.coeff_zero_Xₓ'. -/
-theorem coeff_zero_X (s : σ) : coeff R (0 : σ →₀ ℕ) (X s : MvPowerSeries σ R) = 0 :=
-  by
-  rw [coeff_X, if_neg]
-  intro h
-  exact one_ne_zero (single_eq_zero.mp h.symm)
+theorem coeff_zero_X (s : σ) : coeff R (0 : σ →₀ ℕ) (X s : MvPowerSeries σ R) = 0 := by
+  rw [coeff_X, if_neg]; intro h; exact one_ne_zero (single_eq_zero.mp h.symm)
 #align mv_power_series.coeff_zero_X MvPowerSeries.coeff_zero_X
 
 /- warning: mv_power_series.commute_X -> MvPowerSeries.commute_X is a dubious translation:
@@ -782,10 +768,7 @@ lean 3 declaration is
 but is expected to have type
   forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : MvPowerSeries.{u2, u1} σ R) (a : R), Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ R) (HSMul.hSMul.{u1, max u2 u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHSMul.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (SMulZeroClass.toSMul.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (SMulWithZero.toSMulZeroClass.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{u1} R _inst_1) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Module.toMulActionWithZero.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))))))) a f) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) a) (MvPowerSeries.{u2, u1} σ R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) a) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) a) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))))) (MvPowerSeries.C.{u2, u1} σ R _inst_1) a) f)
 Case conversion may be inaccurate. Consider using '#align mv_power_series.smul_eq_C_mul MvPowerSeries.smul_eq_C_mulₓ'. -/
-theorem smul_eq_C_mul (f : MvPowerSeries σ R) (a : R) : a • f = C σ R a * f :=
-  by
-  ext
-  simp
+theorem smul_eq_C_mul (f : MvPowerSeries σ R) (a : R) : a • f = C σ R a * f := by ext; simp
 #align mv_power_series.smul_eq_C_mul MvPowerSeries.smul_eq_C_mul
 
 #print MvPowerSeries.X_inj /-
@@ -794,12 +777,8 @@ theorem X_inj [Nontrivial R] {s t : σ} : (X s : MvPowerSeries σ R) = X t ↔ s
     intro h; replace h := congr_arg (coeff R (single s 1)) h; rw [coeff_X, if_pos rfl, coeff_X] at h
     split_ifs  at h with H
     · rw [Finsupp.single_eq_single_iff] at H
-      cases H
-      · exact H.1
-      · exfalso
-        exact one_ne_zero H.1
-    · exfalso
-      exact one_ne_zero h, congr_arg X⟩
+      cases H; · exact H.1; · exfalso; exact one_ne_zero H.1
+    · exfalso; exact one_ne_zero h, congr_arg X⟩
 #align mv_power_series.X_inj MvPowerSeries.X_inj
 -/
 
@@ -826,9 +805,7 @@ def map : MvPowerSeries σ R →+* MvPowerSeries σ S
   map_zero' := ext fun n => f.map_zero
   map_one' :=
     ext fun n =>
-      show f ((coeff R n) 1) = (coeff S n) 1
-        by
-        rw [coeff_one, coeff_one]
+      show f ((coeff R n) 1) = (coeff S n) 1 by rw [coeff_one, coeff_one];
         split_ifs <;> simp [f.map_one, f.map_zero]
   map_add' φ ψ :=
     ext fun n => show f ((coeff R n) (φ + ψ)) = f ((coeff R n) φ) + f ((coeff R n) ψ) by simp
@@ -883,10 +860,8 @@ theorem constantCoeff_map (φ : MvPowerSeries σ R) :
 <too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.map_monomial MvPowerSeries.map_monomialₓ'. -/
 @[simp]
-theorem map_monomial (n : σ →₀ ℕ) (a : R) : map σ f (monomial R n a) = monomial S n (f a) :=
-  by
-  ext m
-  simp [coeff_monomial, apply_ite f]
+theorem map_monomial (n : σ →₀ ℕ) (a : R) : map σ f (monomial R n a) = monomial S n (f a) := by
+  ext m; simp [coeff_monomial, apply_ite f]
 #align mv_power_series.map_monomial MvPowerSeries.map_monomial
 
 /- warning: mv_power_series.map_C -> MvPowerSeries.map_C is a dubious translation:
@@ -916,12 +891,8 @@ variable {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 instance : Algebra R (MvPowerSeries σ A) :=
   {
     MvPowerSeries.module with
-    commutes' := fun a φ => by
-      ext n
-      simp [Algebra.commutes]
-    smul_def' := fun a σ => by
-      ext n
-      simp [(coeff A n).map_smul_of_tower a, Algebra.smul_def]
+    commutes' := fun a φ => by ext n; simp [Algebra.commutes]
+    smul_def' := fun a σ => by ext n; simp [(coeff A n).map_smul_of_tower a, Algebra.smul_def]
     toRingHom := (MvPowerSeries.map σ (algebraMap R A)).comp (C σ R) }
 
 /- warning: mv_power_series.C_eq_algebra_map -> MvPowerSeries.c_eq_algebraMap is a dubious translation:
@@ -982,14 +953,8 @@ variable (R)
 def trunc : MvPowerSeries σ R →+ MvPolynomial σ R
     where
   toFun := truncFun n
-  map_zero' := by
-    ext
-    simp [coeff_trunc_fun]
-  map_add' := by
-    intros
-    ext
-    simp [coeff_trunc_fun, ite_add]
-    split_ifs <;> rfl
+  map_zero' := by ext; simp [coeff_trunc_fun]
+  map_add' := by intros ; ext; simp [coeff_trunc_fun, ite_add]; split_ifs <;> rfl
 #align mv_power_series.trunc MvPowerSeries.trunc
 -/
 
@@ -1010,17 +975,10 @@ theorem trunc_one (hnn : n ≠ 0) : trunc R n 1 = 1 :=
   MvPolynomial.ext _ _ fun m => by
     rw [coeff_trunc, coeff_one]
     split_ifs with H H' H'
-    · subst m
-      simp
-    · symm
-      rw [MvPolynomial.coeff_one]
-      exact if_neg (Ne.symm H')
-    · symm
-      rw [MvPolynomial.coeff_one]
-      refine' if_neg _
-      rintro rfl
-      apply H
-      exact Ne.bot_lt hnn
+    · subst m; simp
+    · symm; rw [MvPolynomial.coeff_one]; exact if_neg (Ne.symm H')
+    · symm; rw [MvPolynomial.coeff_one]; refine' if_neg _
+      rintro rfl; apply H; exact Ne.bot_lt hnn
 #align mv_power_series.trunc_one MvPowerSeries.trunc_one
 
 /- warning: mv_power_series.trunc_C -> MvPowerSeries.trunc_c is a dubious translation:
@@ -1053,44 +1011,24 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
   constructor
   · rintro ⟨φ, rfl⟩ m h
     rw [coeff_mul, Finset.sum_eq_zero]
-    rintro ⟨i, j⟩ hij
-    rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
-    contrapose! h
-    subst i
-    rw [Finsupp.mem_antidiagonal] at hij
-    rw [← hij, Finsupp.add_apply, Finsupp.single_eq_same]
-    exact Nat.le_add_right n _
-  · intro h
-    refine' ⟨fun m => coeff R (m + single s n) φ, _⟩
-    ext m
-    by_cases H : m - single s n + single s n = m
+    rintro ⟨i, j⟩ hij; rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
+    contrapose! h; subst i; rw [Finsupp.mem_antidiagonal] at hij
+    rw [← hij, Finsupp.add_apply, Finsupp.single_eq_same]; exact Nat.le_add_right n _
+  · intro h; refine' ⟨fun m => coeff R (m + single s n) φ, _⟩
+    ext m; by_cases H : m - single s n + single s n = m
     · rw [coeff_mul, Finset.sum_eq_single (single s n, m - single s n)]
       · rw [coeff_X_pow, if_pos rfl, one_mul]
         simpa using congr_arg (fun m : σ →₀ ℕ => coeff R m φ) H.symm
-      · rintro ⟨i, j⟩ hij hne
-        rw [Finsupp.mem_antidiagonal] at hij
-        rw [coeff_X_pow]
-        split_ifs with hi
-        · exfalso
-          apply hne
-          rw [← hij, ← hi, Prod.mk.inj_iff]
-          refine' ⟨rfl, _⟩
-          ext t
-          simp only [add_tsub_cancel_left, Finsupp.add_apply, Finsupp.tsub_apply]
+      · rintro ⟨i, j⟩ hij hne; rw [Finsupp.mem_antidiagonal] at hij
+        rw [coeff_X_pow]; split_ifs with hi
+        · exfalso; apply hne; rw [← hij, ← hi, Prod.mk.inj_iff]; refine' ⟨rfl, _⟩
+          ext t; simp only [add_tsub_cancel_left, Finsupp.add_apply, Finsupp.tsub_apply]
         · exact MulZeroClass.zero_mul _
-      · intro hni
-        exfalso
-        apply hni
-        rwa [Finsupp.mem_antidiagonal, add_comm]
+      · intro hni; exfalso; apply hni; rwa [Finsupp.mem_antidiagonal, add_comm]
     · rw [h, coeff_mul, Finset.sum_eq_zero]
-      · rintro ⟨i, j⟩ hij
-        rw [Finsupp.mem_antidiagonal] at hij
-        rw [coeff_X_pow]
-        split_ifs with hi
-        · exfalso
-          apply H
-          rw [← hij, hi]
-          ext
+      · rintro ⟨i, j⟩ hij; rw [Finsupp.mem_antidiagonal] at hij
+        rw [coeff_X_pow]; split_ifs with hi
+        · exfalso; apply H; rw [← hij, hi]; ext
           rw [coe_add, coe_add, Pi.add_apply, Pi.add_apply, add_tsub_cancel_left, add_comm]
         · exact MulZeroClass.zero_mul _
       ·
@@ -1098,8 +1036,7 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
           contrapose! H
           ext t
           by_cases hst : s = t
-          · subst t
-            simpa using tsub_add_cancel_of_le H
+          · subst t; simpa using tsub_add_cancel_of_le H
           · simp [Finsupp.single_apply, hst]
 #align mv_power_series.X_pow_dvd_iff MvPowerSeries.X_pow_dvd_iff
 
@@ -1203,9 +1140,7 @@ Case conversion may be inaccurate. Consider using '#align mv_power_series.mul_in
 theorem mul_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) (h : constantCoeff σ R φ = u) :
     φ * invOfUnit φ u = 1 :=
   ext fun n =>
-    if H : n = 0 then by
-      rw [H]
-      simp [coeff_mul, support_single_ne_zero, h]
+    if H : n = 0 then by rw [H]; simp [coeff_mul, support_single_ne_zero, h]
     else
       by
       have : ((0 : σ →₀ ℕ), n) ∈ n.antidiagonal := by rw [Finsupp.mem_antidiagonal, zero_add]
@@ -1215,21 +1150,16 @@ theorem mul_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) (h : constantCoeff σ
         Finset.insert_erase this, Finset.sum_insert (Finset.not_mem_erase _ _),
         Finset.insert_erase this, if_neg (not_lt_of_ge <| le_rfl), zero_add, add_comm, ←
         sub_eq_add_neg, sub_eq_zero, Finset.sum_congr rfl]
-      rintro ⟨i, j⟩ hij
-      rw [Finset.mem_erase, Finsupp.mem_antidiagonal] at hij
+      rintro ⟨i, j⟩ hij; rw [Finset.mem_erase, Finsupp.mem_antidiagonal] at hij
       cases' hij with h₁ h₂
-      subst n
-      rw [if_pos]
+      subst n; rw [if_pos]
       suffices (0 : _) + j < i + j by simpa
       apply add_lt_add_right
       constructor
-      · intro s
-        exact Nat.zero_le _
-      · intro H
-        apply h₁
+      · intro s; exact Nat.zero_le _
+      · intro H; apply h₁
         suffices i = 0 by simp [this]
-        ext1 s
-        exact Nat.eq_zero_of_le_zero (H s)
+        ext1 s; exact Nat.eq_zero_of_le_zero (H s)
 #align mv_power_series.mul_inv_of_unit MvPowerSeries.mul_invOfUnit
 
 end Ring
@@ -1320,8 +1250,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align mv_power_series.inv_eq_zero MvPowerSeries.inv_eq_zeroₓ'. -/
 theorem inv_eq_zero {φ : MvPowerSeries σ k} : φ⁻¹ = 0 ↔ constantCoeff σ k φ = 0 :=
   ⟨fun h => by simpa using congr_arg (constant_coeff σ k) h, fun h =>
-    ext fun n => by
-      rw [coeff_inv]
+    ext fun n => by rw [coeff_inv];
       split_ifs <;>
         simp only [h, MvPowerSeries.coeff_zero, MulZeroClass.zero_mul, inv_zero, neg_zero]⟩
 #align mv_power_series.inv_eq_zero MvPowerSeries.inv_eq_zero
@@ -1435,9 +1364,7 @@ protected theorem mul_inv_rev (φ ψ : MvPowerSeries σ k) : (φ * ψ)⁻¹ = ψ
 
 instance : InvOneClass (MvPowerSeries σ k) :=
   { MvPowerSeries.hasOne, MvPowerSeries.hasInv with
-    inv_one := by
-      rw [MvPowerSeries.inv_eq_iff_mul_eq_one, mul_one]
-      simp }
+    inv_one := by rw [MvPowerSeries.inv_eq_iff_mul_eq_one, mul_one]; simp }
 
 /- warning: mv_power_series.C_inv -> MvPowerSeries.C_inv is a dubious translation:
 <too large>
@@ -1618,9 +1545,7 @@ but is expected to have type
   forall (σ : Type.{u2}) (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R], Function.Injective.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPowerSeries.{u2, u1} σ R) (Coe.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.coeToMvPowerSeries.{u2, u1} σ R _inst_1))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_injective MvPolynomial.coe_injectiveₓ'. -/
 theorem coe_injective : Function.Injective (coe : MvPolynomial σ R → MvPowerSeries σ R) :=
-  fun x y h => by
-  ext
-  simp_rw [← coeff_coe, h]
+  fun x y h => by ext; simp_rw [← coeff_coe, h]
 #align mv_polynomial.coe_injective MvPolynomial.coe_injective
 
 variable {σ R φ ψ}
@@ -1858,10 +1783,7 @@ Case conversion may be inaccurate. Consider using '#align power_series.ext Power
 /-- Two formal power series are equal if all their coefficients are equal.-/
 @[ext]
 theorem ext {φ ψ : PowerSeries R} (h : ∀ n, coeff R n φ = coeff R n ψ) : φ = ψ :=
-  MvPowerSeries.ext fun n => by
-    rw [← coeff_def]
-    · apply h
-    rfl
+  MvPowerSeries.ext fun n => by rw [← coeff_def]; · apply h; rfl
 #align power_series.ext PowerSeries.ext
 
 /- warning: power_series.ext_iff -> PowerSeries.ext_iff is a dubious translation:
@@ -1977,10 +1899,8 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (forall (ᾰ : PowerSeries.{u1} R), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_eq_constant_coeff PowerSeries.coeff_zero_eq_constantCoeffₓ'. -/
 @[simp]
-theorem coeff_zero_eq_constantCoeff : ⇑(coeff R 0) = constantCoeff R :=
-  by
-  rw [coeff, Finsupp.single_zero]
-  rfl
+theorem coeff_zero_eq_constantCoeff : ⇑(coeff R 0) = constantCoeff R := by
+  rw [coeff, Finsupp.single_zero]; rfl
 #align power_series.coeff_zero_eq_constant_coeff PowerSeries.coeff_zero_eq_constantCoeff
 
 /- warning: power_series.coeff_zero_eq_constant_coeff_apply -> PowerSeries.coeff_zero_eq_constantCoeff_apply is a dubious translation:
@@ -2143,19 +2063,16 @@ theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
   by
   symm
   apply Finset.sum_bij fun (p : ℕ × ℕ) h => (single () p.1, single () p.2)
-  · rintro ⟨i, j⟩ hij
-    rw [Finset.Nat.mem_antidiagonal] at hij
+  · rintro ⟨i, j⟩ hij; rw [Finset.Nat.mem_antidiagonal] at hij
     rw [Finsupp.mem_antidiagonal, ← Finsupp.single_add, hij]
-  · rintro ⟨i, j⟩ hij
-    rfl
+  · rintro ⟨i, j⟩ hij; rfl
   · rintro ⟨i, j⟩ ⟨k, l⟩ hij hkl
     simpa only [Prod.mk.inj_iff, Finsupp.unique_single_eq_iff] using id
   · rintro ⟨f, g⟩ hfg
     refine' ⟨(f (), g ()), _, _⟩
     · rw [Finsupp.mem_antidiagonal] at hfg
       rw [Finset.Nat.mem_antidiagonal, ← Finsupp.add_apply, hfg, Finsupp.single_eq_same]
-    · rw [Prod.mk.inj_iff]
-      dsimp
+    · rw [Prod.mk.inj_iff]; dsimp
       exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
 #align power_series.coeff_mul PowerSeries.coeff_mul
 
@@ -2190,10 +2107,7 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : PowerSeries.{u1} R) (a : R), Eq.{succ u1} (PowerSeries.{u1} R) (HSMul.hSMul.{u1, u1, u1} R (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHSMul.{u1, u1} R (PowerSeries.{u1} R) (SMulZeroClass.toSMul.{u1, u1} R (PowerSeries.{u1} R) (PowerSeries.instZeroPowerSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (PowerSeries.{u1} R) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (PowerSeries.instZeroPowerSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} R _inst_1) (PowerSeries.instZeroPowerSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Module.toMulActionWithZero.{u1, u1} R (PowerSeries.{u1} R) _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))))))) a f) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (PowerSeries.{u1} R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a) f)
 Case conversion may be inaccurate. Consider using '#align power_series.smul_eq_C_mul PowerSeries.smul_eq_C_mulₓ'. -/
-theorem smul_eq_C_mul (f : PowerSeries R) (a : R) : a • f = C R a * f :=
-  by
-  ext
-  simp
+theorem smul_eq_C_mul (f : PowerSeries R) (a : R) : a • f = C R a * f := by ext; simp
 #align power_series.smul_eq_C_mul PowerSeries.smul_eq_C_mul
 
 /- warning: power_series.coeff_succ_mul_X -> PowerSeries.coeff_succ_mul_X is a dubious translation:
@@ -2306,12 +2220,8 @@ Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul
 theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * X ^ n) = coeff R d p :=
   by
   rw [coeff_mul, Finset.sum_eq_single (d, n), coeff_X_pow, if_pos rfl, mul_one]
-  · rintro ⟨i, j⟩ h1 h2
-    rw [coeff_X_pow, if_neg, MulZeroClass.mul_zero]
-    rintro rfl
-    apply h2
-    rw [Finset.Nat.mem_antidiagonal, add_right_cancel_iff] at h1
-    subst h1
+  · rintro ⟨i, j⟩ h1 h2; rw [coeff_X_pow, if_neg, MulZeroClass.mul_zero]; rintro rfl; apply h2
+    rw [Finset.Nat.mem_antidiagonal, add_right_cancel_iff] at h1; subst h1
   · exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
 #align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_X_pow
 
@@ -2322,12 +2232,8 @@ Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_p
 theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (X ^ n * p) = coeff R d p :=
   by
   rw [coeff_mul, Finset.sum_eq_single (n, d), coeff_X_pow, if_pos rfl, one_mul]
-  · rintro ⟨i, j⟩ h1 h2
-    rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
-    rintro rfl
-    apply h2
-    rw [Finset.Nat.mem_antidiagonal, add_comm, add_right_cancel_iff] at h1
-    subst h1
+  · rintro ⟨i, j⟩ h1 h2; rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]; rintro rfl; apply h2
+    rw [Finset.Nat.mem_antidiagonal, add_comm, add_right_cancel_iff] at h1; subst h1
   · rw [add_comm]
     exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
 #align power_series.coeff_X_pow_mul PowerSeries.coeff_X_pow_mul
@@ -2352,8 +2258,7 @@ theorem coeff_X_pow_mul' (p : PowerSeries R) (n d : ℕ) :
     coeff R d (X ^ n * p) = ite (n ≤ d) (coeff R (d - n) p) 0 :=
   by
   split_ifs
-  · rw [← tsub_add_cancel_of_le h, coeff_X_pow_mul]
-    simp
+  · rw [← tsub_add_cancel_of_le h, coeff_X_pow_mul]; simp
   · refine' (coeff_mul _ _ _).trans (Finset.sum_eq_zero fun x hx => _)
     rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
     have := finset.nat.mem_antidiagonal.mp hx
@@ -2456,10 +2361,7 @@ theorem coeff_map (n : ℕ) (φ : PowerSeries R) : coeff S n (map f φ) = f (coe
 <too large>
 Case conversion may be inaccurate. Consider using '#align power_series.map_C PowerSeries.map_Cₓ'. -/
 @[simp]
-theorem map_C (r : R) : map f (C _ r) = C _ (f r) :=
-  by
-  ext
-  simp [coeff_C, apply_ite f]
+theorem map_C (r : R) : map f (C _ r) = C _ (f r) := by ext; simp [coeff_C, apply_ite f]
 #align power_series.map_C PowerSeries.map_C
 
 /- warning: power_series.map_X -> PowerSeries.map_X is a dubious translation:
@@ -2469,9 +2371,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u2} S) (PowerSeries.X.{u1} R _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u2} S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2))) (PowerSeries.{u1} R) (PowerSeries.{u2} S) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} (PowerSeries.{u2} S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2))) (PowerSeries.{u1} R) (PowerSeries.{u2} S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2))) (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2)))))) (PowerSeries.map.{u1, u2} R _inst_1 S _inst_2 f) (PowerSeries.X.{u1} R _inst_1)) (PowerSeries.X.{u2} S _inst_2)
 Case conversion may be inaccurate. Consider using '#align power_series.map_X PowerSeries.map_Xₓ'. -/
 @[simp]
-theorem map_X : map f X = X := by
-  ext
-  simp [coeff_X, apply_ite f]
+theorem map_X : map f X = X := by ext; simp [coeff_X, apply_ite f]
 #align power_series.map_X PowerSeries.map_X
 
 end Map
@@ -2488,10 +2388,8 @@ theorem X_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
   convert@MvPowerSeries.X_pow_dvd_iff Unit R _ () n φ; apply propext
   classical
     constructor <;> intro h m hm
-    · rw [Finsupp.unique_single m]
-      convert h _ hm
-    · apply h
-      simpa only [Finsupp.single_eq_same] using hm
+    · rw [Finsupp.unique_single m]; convert h _ hm
+    · apply h; simpa only [Finsupp.single_eq_same] using hm
 #align power_series.X_pow_dvd_iff PowerSeries.X_pow_dvd_iff
 
 /- warning: power_series.X_dvd_iff -> PowerSeries.X_dvd_iff is a dubious translation:
@@ -2505,8 +2403,7 @@ theorem X_dvd_iff {φ : PowerSeries R} : (X : PowerSeries R) ∣ φ ↔ constant
   rw [← pow_one (X : PowerSeries R), X_pow_dvd_iff, ← coeff_zero_eq_constant_coeff_apply]
   constructor <;> intro h
   · exact h 0 zero_lt_one
-  · intro m hm
-    rwa [Nat.eq_zero_of_le_zero (Nat.le_of_succ_le_succ hm)]
+  · intro m hm; rwa [Nat.eq_zero_of_le_zero (Nat.le_of_succ_le_succ hm)]
 #align power_series.X_dvd_iff PowerSeries.X_dvd_iff
 
 end Semiring
@@ -2527,19 +2424,11 @@ Case conversion may be inaccurate. Consider using '#align power_series.rescale P
 noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R
     where
   toFun f := PowerSeries.mk fun n => a ^ n * PowerSeries.coeff R n f
-  map_zero' := by
-    ext
-    simp only [LinearMap.map_zero, PowerSeries.coeff_mk, MulZeroClass.mul_zero]
+  map_zero' := by ext; simp only [LinearMap.map_zero, PowerSeries.coeff_mk, MulZeroClass.mul_zero]
   map_one' := by
-    ext1
-    simp only [mul_boole, PowerSeries.coeff_mk, PowerSeries.coeff_one]
-    split_ifs
-    · rw [h, pow_zero]
-    rfl
-  map_add' := by
-    intros
-    ext
-    exact mul_add _ _ _
+    ext1; simp only [mul_boole, PowerSeries.coeff_mk, PowerSeries.coeff_one]
+    split_ifs; · rw [h, pow_zero]; rfl
+  map_add' := by intros ; ext; exact mul_add _ _ _
   map_mul' f g := by
     ext
     rw [PowerSeries.coeff_mul, PowerSeries.coeff_mk, PowerSeries.coeff_mul, Finset.mul_sum]
@@ -2588,9 +2477,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R], Eq.{succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.rescale.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (RingHom.id.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align power_series.rescale_one PowerSeries.rescale_oneₓ'. -/
 @[simp]
-theorem rescale_one : rescale 1 = RingHom.id (PowerSeries R) :=
-  by
-  ext
+theorem rescale_one : rescale 1 = RingHom.id (PowerSeries R) := by ext;
   simp only [RingHom.id_apply, rescale, one_pow, coeff_mk, one_mul, RingHom.coe_mk]
 #align power_series.rescale_one PowerSeries.rescale_one
 
@@ -2600,9 +2487,7 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Nat -> R) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u1} R) (PowerSeries.mk.{u1} R f)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (PowerSeries.rescale.{u1} R _inst_1 a) (PowerSeries.mk.{u1} R f)) (PowerSeries.mk.{u1} R (fun (n : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) a n) (f n)))
 Case conversion may be inaccurate. Consider using '#align power_series.rescale_mk PowerSeries.rescale_mkₓ'. -/
-theorem rescale_mk (f : ℕ → R) (a : R) : rescale a (mk f) = mk fun n : ℕ => a ^ n * f n :=
-  by
-  ext
+theorem rescale_mk (f : ℕ → R) (a : R) : rescale a (mk f) = mk fun n : ℕ => a ^ n * f n := by ext;
   rw [coeff_rescale, coeff_mk, coeff_mk]
 #align power_series.rescale_mk PowerSeries.rescale_mk
 
@@ -2623,9 +2508,7 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (a : R) (b : R), Eq.{succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.rescale.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) a b)) (RingHom.comp.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.rescale.{u1} R _inst_1 b) (PowerSeries.rescale.{u1} R _inst_1 a))
 Case conversion may be inaccurate. Consider using '#align power_series.rescale_mul PowerSeries.rescale_mulₓ'. -/
-theorem rescale_mul (a b : R) : rescale (a * b) = (rescale b).comp (rescale a) :=
-  by
-  ext
+theorem rescale_mul (a b : R) : rescale (a * b) = (rescale b).comp (rescale a) := by ext;
   simp [← rescale_rescale]
 #align power_series.rescale_mul PowerSeries.rescale_mul
 
@@ -2674,15 +2557,10 @@ theorem trunc_one (n) : trunc (n + 1) (1 : PowerSeries R) = 1 :=
   Polynomial.ext fun m => by
     rw [coeff_trunc, coeff_one]
     split_ifs with H H' H' <;> rw [Polynomial.coeff_one]
-    · subst m
-      rw [if_pos rfl]
-    · symm
-      exact if_neg (Ne.elim (Ne.symm H'))
-    · symm
-      refine' if_neg _
-      rintro rfl
-      apply H
-      exact Nat.zero_lt_succ _
+    · subst m; rw [if_pos rfl]
+    · symm; exact if_neg (Ne.elim (Ne.symm H'))
+    · symm; refine' if_neg _
+      rintro rfl; apply H; exact Nat.zero_lt_succ _
 #align power_series.trunc_one PowerSeries.trunc_one
 
 /- warning: power_series.trunc_C -> PowerSeries.trunc_C is a dubious translation:
@@ -2744,24 +2622,16 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
   congr 1
   symm
   apply Finset.sum_bij fun (p : ℕ × ℕ) h => (single () p.1, single () p.2)
-  · rintro ⟨i, j⟩ hij
-    rw [Finset.Nat.mem_antidiagonal] at hij
+  · rintro ⟨i, j⟩ hij; rw [Finset.Nat.mem_antidiagonal] at hij
     rw [Finsupp.mem_antidiagonal, ← Finsupp.single_add, hij]
   · rintro ⟨i, j⟩ hij
     by_cases H : j < n
-    · rw [if_pos H, if_pos]
-      · rfl
+    · rw [if_pos H, if_pos]; · rfl
       constructor
-      · rintro ⟨⟩
-        simpa [Finsupp.single_eq_same] using le_of_lt H
-      · intro hh
-        rw [lt_iff_not_ge] at H
-        apply H
+      · rintro ⟨⟩; simpa [Finsupp.single_eq_same] using le_of_lt H
+      · intro hh; rw [lt_iff_not_ge] at H; apply H
         simpa [Finsupp.single_eq_same] using hh ()
-    · rw [if_neg H, if_neg]
-      rintro ⟨h₁, h₂⟩
-      apply h₂
-      rintro ⟨⟩
+    · rw [if_neg H, if_neg]; rintro ⟨h₁, h₂⟩; apply h₂; rintro ⟨⟩
       simpa [Finsupp.single_eq_same] using not_lt.1 H
   · rintro ⟨i, j⟩ ⟨k, l⟩ hij hkl
     simpa only [Prod.mk.inj_iff, Finsupp.unique_single_eq_iff] using id
@@ -2769,8 +2639,7 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
     refine' ⟨(f (), g ()), _, _⟩
     · rw [Finsupp.mem_antidiagonal] at hfg
       rw [Finset.Nat.mem_antidiagonal, ← Finsupp.add_apply, hfg, Finsupp.single_eq_same]
-    · rw [Prod.mk.inj_iff]
-      dsimp
+    · rw [Prod.mk.inj_iff]; dsimp
       exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
 #align power_series.coeff_inv_aux PowerSeries.coeff_inv_aux
 
@@ -2901,43 +2770,30 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align power_series.eq_zero_or_eq_zero_of_mul_eq_zero PowerSeries.eq_zero_or_eq_zero_of_mul_eq_zeroₓ'. -/
 theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSeries R) (h : φ * ψ = 0) :
     φ = 0 ∨ ψ = 0 := by
-  rw [or_iff_not_imp_left]
-  intro H
-  have ex : ∃ m, coeff R m φ ≠ 0 := by
-    contrapose! H
-    exact ext H
+  rw [or_iff_not_imp_left]; intro H
+  have ex : ∃ m, coeff R m φ ≠ 0 := by contrapose! H; exact ext H
   let m := Nat.find ex
   have hm₁ : coeff R m φ ≠ 0 := Nat.find_spec ex
   have hm₂ : ∀ k < m, ¬coeff R k φ ≠ 0 := fun k => Nat.find_min ex
-  ext n
-  rw [(coeff R n).map_zero]
-  apply Nat.strong_induction_on n
-  clear n
-  intro n ih
+  ext n; rw [(coeff R n).map_zero]; apply Nat.strong_induction_on n
+  clear n; intro n ih
   replace h := congr_arg (coeff R (m + n)) h
   rw [LinearMap.map_zero, coeff_mul, Finset.sum_eq_single (m, n)] at h
   · replace h := eq_zero_or_eq_zero_of_mul_eq_zero h
-    rw [or_iff_not_imp_left] at h
-    exact h hm₁
+    rw [or_iff_not_imp_left] at h; exact h hm₁
   · rintro ⟨i, j⟩ hij hne
-    by_cases hj : j < n
-    · rw [ih j hj, MulZeroClass.mul_zero]
+    by_cases hj : j < n; · rw [ih j hj, MulZeroClass.mul_zero]
     by_cases hi : i < m
-    · specialize hm₂ _ hi
-      push_neg  at hm₂
-      rw [hm₂, MulZeroClass.zero_mul]
+    · specialize hm₂ _ hi; push_neg  at hm₂; rw [hm₂, MulZeroClass.zero_mul]
     rw [Finset.Nat.mem_antidiagonal] at hij
     push_neg  at hi hj
     suffices m < i by
       have : m + n < i + j := add_lt_add_of_lt_of_le this hj
-      exfalso
-      exact ne_of_lt this hij.symm
+      exfalso; exact ne_of_lt this hij.symm
     contrapose! hne
     obtain rfl := le_antisymm hi hne
     simpa [Ne.def, Prod.mk.inj_iff] using (add_right_inj m).mp hij
-  · contrapose!
-    intro h
-    rw [Finset.Nat.mem_antidiagonal]
+  · contrapose!; intro h; rw [Finset.Nat.mem_antidiagonal]
 #align power_series.eq_zero_or_eq_zero_of_mul_eq_zero PowerSeries.eq_zero_or_eq_zero_of_mul_eq_zero
 
 instance [NoZeroDivisors R] : NoZeroDivisors (PowerSeries R)
@@ -2962,12 +2818,9 @@ Case conversion may be inaccurate. Consider using '#align power_series.span_X_is
  over an integral domain is a prime ideal.-/
 theorem span_X_isPrime : (Ideal.span ({X} : Set (PowerSeries R))).IsPrime :=
   by
-  suffices Ideal.span ({X} : Set (PowerSeries R)) = (constant_coeff R).ker
-    by
-    rw [this]
+  suffices Ideal.span ({X} : Set (PowerSeries R)) = (constant_coeff R).ker by rw [this];
     exact RingHom.ker_isPrime _
-  apply Ideal.ext
-  intro φ
+  apply Ideal.ext; intro φ
   rw [RingHom.mem_ker, Ideal.mem_span_singleton, X_dvd_iff]
 #align power_series.span_X_is_prime PowerSeries.span_X_isPrime
 
@@ -2982,8 +2835,7 @@ theorem X_prime : Prime (X : PowerSeries R) :=
   by
   rw [← Ideal.span_singleton_prime]
   · exact span_X_is_prime
-  · intro h
-    simpa using congr_arg (coeff R 1) h
+  · intro h; simpa using congr_arg (coeff R 1) h
 #align power_series.X_prime PowerSeries.X_prime
 
 /- warning: power_series.rescale_injective -> PowerSeries.rescale_injective is a dubious translation:
@@ -3351,9 +3203,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_of_lt_order PowerSeries.coeff_of_lt_orderₓ'. -/
 /-- The `n`th coefficient of a formal power series is `0` if `n` is strictly
 smaller than the order of the power series.-/
-theorem coeff_of_lt_order (n : ℕ) (h : ↑n < order φ) : coeff R n φ = 0 :=
-  by
-  contrapose! h
+theorem coeff_of_lt_order (n : ℕ) (h : ↑n < order φ) : coeff R n φ = 0 := by contrapose! h;
   exact order_le _ h
 #align power_series.coeff_of_lt_order PowerSeries.coeff_of_lt_order
 
@@ -3368,12 +3218,8 @@ Case conversion may be inaccurate. Consider using '#align power_series.order_eq_
 theorem order_eq_top {φ : PowerSeries R} : φ.order = ⊤ ↔ φ = 0 :=
   by
   constructor
-  · intro h
-    ext n
-    rw [(coeff R n).map_zero, coeff_of_lt_order]
-    simp [h]
-  · rintro rfl
-    exact order_zero
+  · intro h; ext n; rw [(coeff R n).map_zero, coeff_of_lt_order]; simp [h]
+  · rintro rfl; exact order_zero
 #align power_series.order_eq_top PowerSeries.order_eq_top
 
 /- warning: power_series.nat_le_order -> PowerSeries.nat_le_order is a dubious translation:
@@ -3403,12 +3249,9 @@ the `i`th coefficient is `0` for all `i < n`.-/
 theorem le_order (φ : PowerSeries R) (n : PartENat) (h : ∀ i : ℕ, ↑i < n → coeff R i φ = 0) :
     n ≤ order φ := by
   induction n using PartENat.casesOn
-  · show _ ≤ _
-    rw [top_le_iff, order_eq_top]
-    ext i
-    exact h _ (PartENat.natCast_lt_top i)
-  · apply nat_le_order
-    simpa only [PartENat.coe_lt_coe] using h
+  · show _ ≤ _; rw [top_le_iff, order_eq_top]
+    ext i; exact h _ (PartENat.natCast_lt_top i)
+  · apply nat_le_order; simpa only [PartENat.coe_lt_coe] using h
 #align power_series.le_order PowerSeries.le_order
 
 /- warning: power_series.order_eq_nat -> PowerSeries.order_eq_nat is a dubious translation:
@@ -3433,16 +3276,11 @@ theorem order_eq {φ : PowerSeries R} {n : PartENat} :
     order φ = n ↔ (∀ i : ℕ, ↑i = n → coeff R i φ ≠ 0) ∧ ∀ i : ℕ, ↑i < n → coeff R i φ = 0 :=
   by
   induction n using PartENat.casesOn
-  · rw [order_eq_top]
-    constructor
-    · rintro rfl
-      constructor <;> intros
-      · exfalso
-        exact PartENat.natCast_ne_top ‹_› ‹_›
+  · rw [order_eq_top]; constructor
+    · rintro rfl; constructor <;> intros
+      · exfalso; exact PartENat.natCast_ne_top ‹_› ‹_›
       · exact (coeff _ _).map_zero
-    · rintro ⟨h₁, h₂⟩
-      ext i
-      exact h₂ i (PartENat.natCast_lt_top i)
+    · rintro ⟨h₁, h₂⟩; ext i; exact h₂ i (PartENat.natCast_lt_top i)
   · simpa [PartENat.natCast_inj] using order_eq_nat
 #align power_series.order_eq PowerSeries.order_eq
 
@@ -3463,14 +3301,9 @@ theorem le_order_add (φ ψ : PowerSeries R) : min (order φ) (order ψ) ≤ ord
 private theorem order_add_of_order_eq.aux (φ ψ : PowerSeries R) (h : order φ ≠ order ψ)
     (H : order φ < order ψ) : order (φ + ψ) ≤ order φ ⊓ order ψ :=
   by
-  suffices order (φ + ψ) = order φ by
-    rw [le_inf_iff, this]
-    exact ⟨le_rfl, le_of_lt H⟩
-  · rw [order_eq]
-    constructor
-    · intro i hi
-      rw [← hi] at H
-      rw [(coeff _ _).map_add, coeff_of_lt_order i H, add_zero]
+  suffices order (φ + ψ) = order φ by rw [le_inf_iff, this]; exact ⟨le_rfl, le_of_lt H⟩
+  · rw [order_eq]; constructor
+    · intro i hi; rw [← hi] at H; rw [(coeff _ _).map_add, coeff_of_lt_order i H, add_zero]
       exact (order_eq_nat.1 hi.symm).1
     · intro i hi
       rw [(coeff _ _).map_add, coeff_of_lt_order i hi, coeff_of_lt_order i (lt_trans hi H),
@@ -3530,13 +3363,9 @@ theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
   by
   split_ifs with h
   · rw [h, order_eq_top, LinearMap.map_zero]
-  · rw [order_eq]
-    constructor <;> intro i hi
-    · rw [PartENat.natCast_inj] at hi
-      rwa [hi, coeff_monomial_same]
-    · rw [PartENat.coe_lt_coe] at hi
-      rw [coeff_monomial, if_neg]
-      exact ne_of_lt hi
+  · rw [order_eq]; constructor <;> intro i hi
+    · rw [PartENat.natCast_inj] at hi; rwa [hi, coeff_monomial_same]
+    · rw [PartENat.coe_lt_coe] at hi; rw [coeff_monomial, if_neg]; exact ne_of_lt hi
 #align power_series.order_monomial PowerSeries.order_monomial
 
 /- warning: power_series.order_monomial_of_ne_zero -> PowerSeries.order_monomial_of_ne_zero is a dubious translation:
@@ -3677,10 +3506,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align power_series.order_X_pow PowerSeries.order_X_powₓ'. -/
 /-- The order of the formal power series `X^n` is `n`.-/
 @[simp]
-theorem order_X_pow (n : ℕ) : order ((X : PowerSeries R) ^ n) = n :=
-  by
-  rw [X_pow_eq, order_monomial_of_ne_zero]
-  exact one_ne_zero
+theorem order_X_pow (n : ℕ) : order ((X : PowerSeries R) ^ n) = n := by
+  rw [X_pow_eq, order_monomial_of_ne_zero]; exact one_ne_zero
 #align power_series.order_X_pow PowerSeries.order_X_pow
 
 end OrderZeroNeOne
@@ -3743,9 +3570,7 @@ theorem coeff_coe (n) : PowerSeries.coeff R n φ = coeff φ n :=
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_monomial Polynomial.coe_monomialₓ'. -/
 @[simp, norm_cast]
 theorem coe_monomial (n : ℕ) (a : R) :
-    (monomial n a : PowerSeries R) = PowerSeries.monomial R n a :=
-  by
-  ext
+    (monomial n a : PowerSeries R) = PowerSeries.monomial R n a := by ext;
   simp [coeff_coe, PowerSeries.coeff_monomial, Polynomial.coeff_monomial, eq_comm]
 #align polynomial.coe_monomial Polynomial.coe_monomial
 
@@ -3780,10 +3605,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ψ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (PowerSeries.{u1} R) (Polynomial.ToPowerSeries.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) φ ψ)) (HAdd.hAdd.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHAdd.{u1} (PowerSeries.{u1} R) (Distrib.toAdd.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ) (Polynomial.ToPowerSeries.{u1} R _inst_1 ψ))
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_add Polynomial.coe_addₓ'. -/
 @[simp, norm_cast]
-theorem coe_add : ((φ + ψ : R[X]) : PowerSeries R) = φ + ψ :=
-  by
-  ext
-  simp
+theorem coe_add : ((φ + ψ : R[X]) : PowerSeries R) = φ + ψ := by ext; simp
 #align polynomial.coe_add Polynomial.coe_add
 
 /- warning: polynomial.coe_mul -> Polynomial.coe_mul is a dubious translation:
@@ -3853,9 +3675,7 @@ theorem constantCoeff_coe : PowerSeries.constantCoeff R φ = φ.coeff 0 :=
 variable (R)
 
 #print Polynomial.coe_injective /-
-theorem coe_injective : Function.Injective (coe : R[X] → PowerSeries R) := fun x y h =>
-  by
-  ext
+theorem coe_injective : Function.Injective (coe : R[X] → PowerSeries R) := fun x y h => by ext;
   simp_rw [← coeff_coe, h]
 #align polynomial.coe_injective Polynomial.coe_injective
 -/

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

@@ -175,10 +175,7 @@ theorem monomial_def [DecidableEq σ] (n : σ →₀ ℕ) : monomial R n = Linea
 #align mv_power_series.monomial_def MvPowerSeries.monomial_def
 
 /- warning: mv_power_series.coeff_monomial -> MvPowerSeries.coeff_monomial is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_monomial MvPowerSeries.coeff_monomialₓ'. -/
 -- unify the `decidable` arguments
 theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
@@ -188,10 +185,7 @@ theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
 #align mv_power_series.coeff_monomial MvPowerSeries.coeff_monomial
 
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_monomial_same MvPowerSeries.coeff_monomial_sameₓ'. -/
 @[simp]
 theorem coeff_monomial_same (n : σ →₀ ℕ) (a : R) : coeff R n (monomial R n a) = a :=
@@ -199,20 +193,14 @@ theorem coeff_monomial_same (n : σ →₀ ℕ) (a : R) : coeff R n (monomial R
 #align mv_power_series.coeff_monomial_same MvPowerSeries.coeff_monomial_same
 
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_monomial_ne MvPowerSeries.coeff_monomial_neₓ'. -/
 theorem coeff_monomial_ne {m n : σ →₀ ℕ} (h : m ≠ n) (a : R) : coeff R m (monomial R n a) = 0 :=
   LinearMap.stdBasis_ne R _ _ _ h a
 #align mv_power_series.coeff_monomial_ne MvPowerSeries.coeff_monomial_ne
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.eq_of_coeff_monomial_ne_zero MvPowerSeries.eq_of_coeff_monomial_ne_zeroₓ'. -/
 theorem eq_of_coeff_monomial_ne_zero {m n : σ →₀ ℕ} {a : R} (h : coeff R m (monomial R n a) ≠ 0) :
     m = n :=
@@ -247,10 +235,7 @@ instance : One (MvPowerSeries σ R) :=
   ⟨monomial R (0 : σ →₀ ℕ) 1⟩
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_one MvPowerSeries.coeff_oneₓ'. -/
 theorem coeff_one [DecidableEq σ] : coeff R n (1 : MvPowerSeries σ R) = if n = 0 then 1 else 0 :=
   coeff_monomial _ _ _
@@ -287,10 +272,7 @@ instance : Mul (MvPowerSeries σ R) :=
   ⟨fun φ ψ n => ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ⟩
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_mul MvPowerSeries.coeff_mulₓ'. -/
 theorem coeff_mul :
     coeff R n (φ * ψ) = ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ :=
@@ -318,10 +300,7 @@ protected theorem mul_zero : φ * 0 = 0 :=
 #align mv_power_series.mul_zero MvPowerSeries.mul_zero
 
 /- warning: mv_power_series.coeff_monomial_mul -> MvPowerSeries.coeff_monomial_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_monomial_mul MvPowerSeries.coeff_monomial_mulₓ'. -/
 theorem coeff_monomial_mul (a : R) :
     coeff R m (monomial R n a * φ) = if n ≤ m then a * coeff R (m - n) φ else 0 :=
@@ -335,10 +314,7 @@ theorem coeff_monomial_mul (a : R) :
 #align mv_power_series.coeff_monomial_mul MvPowerSeries.coeff_monomial_mul
 
 /- warning: mv_power_series.coeff_mul_monomial -> MvPowerSeries.coeff_mul_monomial is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_mul_monomial MvPowerSeries.coeff_mul_monomialₓ'. -/
 theorem coeff_mul_monomial (a : R) :
     coeff R m (φ * monomial R n a) = if n ≤ m then coeff R (m - n) φ * a else 0 :=
@@ -352,10 +328,7 @@ theorem coeff_mul_monomial (a : R) :
 #align mv_power_series.coeff_mul_monomial MvPowerSeries.coeff_mul_monomial
 
 /- warning: mv_power_series.coeff_add_monomial_mul -> MvPowerSeries.coeff_add_monomial_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_add_monomial_mul MvPowerSeries.coeff_add_monomial_mulₓ'. -/
 theorem coeff_add_monomial_mul (a : R) : coeff R (m + n) (monomial R m a * φ) = a * coeff R n φ :=
   by
@@ -364,10 +337,7 @@ theorem coeff_add_monomial_mul (a : R) : coeff R (m + n) (monomial R m a * φ) =
 #align mv_power_series.coeff_add_monomial_mul MvPowerSeries.coeff_add_monomial_mul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_add_mul_monomial MvPowerSeries.coeff_add_mul_monomialₓ'. -/
 theorem coeff_add_mul_monomial (a : R) : coeff R (m + n) (φ * monomial R n a) = coeff R m φ * a :=
   by
@@ -376,10 +346,7 @@ theorem coeff_add_mul_monomial (a : R) : coeff R (m + n) (φ * monomial R n a) =
 #align mv_power_series.coeff_add_mul_monomial MvPowerSeries.coeff_add_mul_monomial
 
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.commute_monomial MvPowerSeries.commute_monomialₓ'. -/
 @[simp]
 theorem commute_monomial {a : R} {n} : Commute φ (monomial R n a) ↔ ∀ m, Commute (coeff R m φ) a :=
@@ -493,10 +460,7 @@ section Semiring
 variable [Semiring R]
 
 /- warning: mv_power_series.monomial_mul_monomial -> MvPowerSeries.monomial_mul_monomial is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.monomial_mul_monomial MvPowerSeries.monomial_mul_monomialₓ'. -/
 theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
     monomial R m a * monomial R n b = monomial R (m + n) (a * b) :=
@@ -553,10 +517,7 @@ theorem monomial_zero_eq_C_apply (a : R) : monomial R (0 : σ →₀ ℕ) a = C
 #align mv_power_series.monomial_zero_eq_C_apply MvPowerSeries.monomial_zero_eq_C_apply
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_C MvPowerSeries.coeff_Cₓ'. -/
 theorem coeff_C [DecidableEq σ] (n : σ →₀ ℕ) (a : R) :
     coeff R n (C σ R a) = if n = 0 then a else 0 :=
@@ -564,10 +525,7 @@ theorem coeff_C [DecidableEq σ] (n : σ →₀ ℕ) (a : R) :
 #align mv_power_series.coeff_C MvPowerSeries.coeff_C
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_C MvPowerSeries.coeff_zero_Cₓ'. -/
 theorem coeff_zero_C (a : R) : coeff R (0 : σ →₀ ℕ) (C σ R a) = a :=
   coeff_monomial_same 0 a
@@ -660,10 +618,7 @@ theorem X_pow_eq (s : σ) (n : ℕ) : (X s : MvPowerSeries σ R) ^ n = monomial
 #align mv_power_series.X_pow_eq MvPowerSeries.X_pow_eq
 
 /- warning: mv_power_series.coeff_X_pow -> MvPowerSeries.coeff_X_pow is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_X_pow MvPowerSeries.coeff_X_powₓ'. -/
 theorem coeff_X_pow [DecidableEq σ] (m : σ →₀ ℕ) (s : σ) (n : ℕ) :
     coeff R m ((X s : MvPowerSeries σ R) ^ n) = if m = single s n then 1 else 0 := by
@@ -671,10 +626,7 @@ theorem coeff_X_pow [DecidableEq σ] (m : σ →₀ ℕ) (s : σ) (n : ℕ) :
 #align mv_power_series.coeff_X_pow MvPowerSeries.coeff_X_pow
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_mul_C MvPowerSeries.coeff_mul_Cₓ'. -/
 @[simp]
 theorem coeff_mul_C (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
@@ -682,10 +634,7 @@ theorem coeff_mul_C (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
 #align mv_power_series.coeff_mul_C MvPowerSeries.coeff_mul_C
 
 /- warning: mv_power_series.coeff_C_mul -> MvPowerSeries.coeff_C_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_C_mul MvPowerSeries.coeff_C_mulₓ'. -/
 @[simp]
 theorem coeff_C_mul (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
@@ -820,10 +769,7 @@ theorem isUnit_constantCoeff (φ : MvPowerSeries σ R) (h : IsUnit φ) :
 #align mv_power_series.is_unit_constant_coeff MvPowerSeries.isUnit_constantCoeff
 
 /- warning: mv_power_series.coeff_smul -> MvPowerSeries.coeff_smul is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_smul MvPowerSeries.coeff_smulₓ'. -/
 @[simp]
 theorem coeff_smul (f : MvPowerSeries σ R) (n) (a : R) : coeff _ n (a • f) = a * coeff _ n f :=
@@ -917,10 +863,7 @@ theorem map_comp : map σ (g.comp f) = (map σ g).comp (map σ f) :=
 #align mv_power_series.map_comp MvPowerSeries.map_comp
 
 /- warning: mv_power_series.coeff_map -> MvPowerSeries.coeff_map is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_map MvPowerSeries.coeff_mapₓ'. -/
 @[simp]
 theorem coeff_map (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) : coeff S n (map σ f φ) = f (coeff R n φ) :=
@@ -928,10 +871,7 @@ theorem coeff_map (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) : coeff S n (map
 #align mv_power_series.coeff_map MvPowerSeries.coeff_map
 
 /- warning: mv_power_series.constant_coeff_map -> MvPowerSeries.constantCoeff_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.constant_coeff_map MvPowerSeries.constantCoeff_mapₓ'. -/
 @[simp]
 theorem constantCoeff_map (φ : MvPowerSeries σ R) :
@@ -940,10 +880,7 @@ theorem constantCoeff_map (φ : MvPowerSeries σ R) :
 #align mv_power_series.constant_coeff_map MvPowerSeries.constantCoeff_map
 
 /- warning: mv_power_series.map_monomial -> MvPowerSeries.map_monomial is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.map_monomial MvPowerSeries.map_monomialₓ'. -/
 @[simp]
 theorem map_monomial (n : σ →₀ ℕ) (a : R) : map σ f (monomial R n a) = monomial S n (f a) :=
@@ -953,10 +890,7 @@ theorem map_monomial (n : σ →₀ ℕ) (a : R) : map σ f (monomial R n a) = m
 #align mv_power_series.map_monomial MvPowerSeries.map_monomial
 
 /- warning: mv_power_series.map_C -> MvPowerSeries.map_C is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.map_C MvPowerSeries.map_Cₓ'. -/
 @[simp]
 theorem map_C (a : R) : map σ f (C σ R a) = C σ S (f a) :=
@@ -1001,10 +935,7 @@ theorem c_eq_algebraMap : C σ R = algebraMap R (MvPowerSeries σ R) :=
 #align mv_power_series.C_eq_algebra_map MvPowerSeries.c_eq_algebraMap
 
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.algebra_map_apply MvPowerSeries.algebraMap_applyₓ'. -/
 theorem algebraMap_apply {r : R} : algebraMap R (MvPowerSeries σ A) r = C σ A (algebraMap R A r) :=
   by
@@ -1037,10 +968,7 @@ def truncFun (φ : MvPowerSeries σ R) : MvPolynomial σ R :=
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_trunc_fun MvPowerSeries.coeff_truncFunₓ'. -/
 theorem coeff_truncFun (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
     (truncFun n φ).coeff m = if m < n then coeff R m φ else 0 := by
@@ -1068,20 +996,14 @@ def trunc : MvPowerSeries σ R →+ MvPolynomial σ R
 variable {R}
 
 /- warning: mv_power_series.coeff_trunc -> MvPowerSeries.coeff_trunc is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_trunc MvPowerSeries.coeff_truncₓ'. -/
 theorem coeff_trunc (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
     (trunc R n φ).coeff m = if m < n then coeff R m φ else 0 := by simp [Trunc, coeff_trunc_fun]
 #align mv_power_series.coeff_trunc MvPowerSeries.coeff_trunc
 
 /- warning: mv_power_series.trunc_one -> MvPowerSeries.trunc_one is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.trunc_one MvPowerSeries.trunc_oneₓ'. -/
 @[simp]
 theorem trunc_one (hnn : n ≠ 0) : trunc R n 1 = 1 :=
@@ -1102,10 +1024,7 @@ theorem trunc_one (hnn : n ≠ 0) : trunc R n 1 = 1 :=
 #align mv_power_series.trunc_one MvPowerSeries.trunc_one
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.trunc_C MvPowerSeries.trunc_cₓ'. -/
 @[simp]
 theorem trunc_c (hnn : n ≠ 0) (a : R) : trunc R n (C σ R a) = MvPolynomial.C a :=
@@ -1225,10 +1144,7 @@ protected noncomputable def inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerS
 -/
 
 /- warning: mv_power_series.coeff_inv_aux -> MvPowerSeries.coeff_inv_aux is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_inv_aux MvPowerSeries.coeff_inv_auxₓ'. -/
 theorem coeff_inv_aux [DecidableEq σ] (n : σ →₀ ℕ) (a : R) (φ : MvPowerSeries σ R) :
     coeff R n (inv.aux a φ) =
@@ -1254,10 +1170,7 @@ def invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) : MvPowerSeries σ R :=
 #align mv_power_series.inv_of_unit MvPowerSeries.invOfUnit
 
 /- warning: mv_power_series.coeff_inv_of_unit -> MvPowerSeries.coeff_invOfUnit is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_inv_of_unit MvPowerSeries.coeff_invOfUnitₓ'. -/
 theorem coeff_invOfUnit [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (u : Rˣ) :
     coeff R n (invOfUnit φ u) =
@@ -1379,10 +1292,7 @@ instance : Inv (MvPowerSeries σ k) :=
   ⟨MvPowerSeries.inv⟩
 
 /- warning: mv_power_series.coeff_inv -> MvPowerSeries.coeff_inv is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_inv MvPowerSeries.coeff_invₓ'. -/
 theorem coeff_inv [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ k) :
     coeff k n φ⁻¹ =
@@ -1394,10 +1304,7 @@ theorem coeff_inv [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ k)
 #align mv_power_series.coeff_inv MvPowerSeries.coeff_inv
 
 /- warning: mv_power_series.constant_coeff_inv -> MvPowerSeries.constantCoeff_inv is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.constant_coeff_inv MvPowerSeries.constantCoeff_invₓ'. -/
 @[simp]
 theorem constantCoeff_inv (φ : MvPowerSeries σ k) :
@@ -1430,10 +1337,7 @@ theorem zero_inv : (0 : MvPowerSeries σ k)⁻¹ = 0 := by rw [inv_eq_zero, cons
 #align mv_power_series.zero_inv MvPowerSeries.zero_inv
 
 /- warning: mv_power_series.inv_of_unit_eq -> MvPowerSeries.invOfUnit_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.inv_of_unit_eq MvPowerSeries.invOfUnit_eqₓ'. -/
 @[simp]
 theorem invOfUnit_eq (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
@@ -1536,10 +1440,7 @@ instance : InvOneClass (MvPowerSeries σ k) :=
       simp }
 
 /- warning: mv_power_series.C_inv -> MvPowerSeries.C_inv is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.C_inv MvPowerSeries.C_invₓ'. -/
 @[simp]
 theorem C_inv (r : k) : (C σ k r)⁻¹ = C σ k r⁻¹ :=
@@ -1610,10 +1511,7 @@ theorem coeff_coe (n : σ →₀ ℕ) : MvPowerSeries.coeff R n ↑φ = coeff n
 #align mv_polynomial.coeff_coe MvPolynomial.coeff_coe
 
 /- warning: mv_polynomial.coe_monomial -> MvPolynomial.coe_monomial is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_monomial MvPolynomial.coe_monomialₓ'. -/
 @[simp, norm_cast]
 theorem coe_monomial (n : σ →₀ ℕ) (a : R) :
@@ -1669,10 +1567,7 @@ theorem coe_mul : ((φ * ψ : MvPolynomial σ R) : MvPowerSeries σ R) = φ * ψ
 #align mv_polynomial.coe_mul MvPolynomial.coe_mul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_C MvPolynomial.coe_Cₓ'. -/
 @[simp, norm_cast]
 theorem coe_C (a : R) : ((C a : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.C σ R a :=
@@ -1823,10 +1718,7 @@ def coeToMvPowerSeries.algHom : MvPolynomial σ R →ₐ[R] MvPowerSeries σ A :
 #align mv_polynomial.coe_to_mv_power_series.alg_hom MvPolynomial.coeToMvPowerSeries.algHom
 
 /- warning: mv_polynomial.coe_to_mv_power_series.alg_hom_apply -> MvPolynomial.coeToMvPowerSeries.algHom_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_to_mv_power_series.alg_hom_apply MvPolynomial.coeToMvPowerSeries.algHom_applyₓ'. -/
 @[simp]
 theorem coeToMvPowerSeries.algHom_apply :
@@ -1865,10 +1757,7 @@ instance algebraMvPowerSeries : Algebra (MvPowerSeries σ R) (MvPowerSeries σ A
 variable (A)
 
 /- warning: mv_power_series.algebra_map_apply' -> MvPowerSeries.algebraMap_apply' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.algebra_map_apply' MvPowerSeries.algebraMap_apply'ₓ'. -/
 theorem algebraMap_apply' (p : MvPolynomial σ R) :
     algebraMap (MvPolynomial σ R) (MvPowerSeries σ A) p = map σ (algebraMap R A) p :=
@@ -1876,10 +1765,7 @@ theorem algebraMap_apply' (p : MvPolynomial σ R) :
 #align mv_power_series.algebra_map_apply' MvPowerSeries.algebraMap_apply'
 
 /- warning: mv_power_series.algebra_map_apply'' -> MvPowerSeries.algebraMap_apply'' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_power_series.algebra_map_apply'' MvPowerSeries.algebraMap_apply''ₓ'. -/
 theorem algebraMap_apply'' :
     algebraMap (MvPowerSeries σ R) (MvPowerSeries σ A) f = map σ (algebraMap R A) f :=
@@ -2007,10 +1893,7 @@ theorem coeff_mk (n : ℕ) (f : ℕ → R) : coeff R n (mk f) = f n :=
 #align power_series.coeff_mk PowerSeries.coeff_mk
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_monomial PowerSeries.coeff_monomialₓ'. -/
 theorem coeff_monomial (m n : ℕ) (a : R) : coeff R m (monomial R n a) = if m = n then a else 0 :=
   calc
@@ -2030,10 +1913,7 @@ theorem monomial_eq_mk (n : ℕ) (a : R) : monomial R n a = mk fun m => if m = n
 #align power_series.monomial_eq_mk PowerSeries.monomial_eq_mk
 
 /- warning: power_series.coeff_monomial_same -> PowerSeries.coeff_monomial_same is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_monomial_same PowerSeries.coeff_monomial_sameₓ'. -/
 @[simp]
 theorem coeff_monomial_same (n : ℕ) (a : R) : coeff R n (monomial R n a) = a :=
@@ -2134,10 +2014,7 @@ theorem monomial_zero_eq_C_apply (a : R) : monomial R 0 a = C R a := by simp
 #align power_series.monomial_zero_eq_C_apply PowerSeries.monomial_zero_eq_C_apply
 
 /- warning: power_series.coeff_C -> PowerSeries.coeff_C is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_C PowerSeries.coeff_Cₓ'. -/
 theorem coeff_C (n : ℕ) (a : R) : coeff R n (C R a : PowerSeries R) = if n = 0 then a else 0 := by
   rw [← monomial_zero_eq_C_apply, coeff_monomial]
@@ -2259,10 +2136,7 @@ theorem coeff_zero_one : coeff R 0 (1 : PowerSeries R) = 1 :=
 #align power_series.coeff_zero_one PowerSeries.coeff_zero_one
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul PowerSeries.coeff_mulₓ'. -/
 theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
     coeff R n (φ * ψ) = ∑ p in Finset.Nat.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ :=
@@ -2286,10 +2160,7 @@ theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
 #align power_series.coeff_mul PowerSeries.coeff_mul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_C PowerSeries.coeff_mul_Cₓ'. -/
 @[simp]
 theorem coeff_mul_C (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (φ * C R a) = coeff R n φ * a :=
@@ -2297,10 +2168,7 @@ theorem coeff_mul_C (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (φ * C R
 #align power_series.coeff_mul_C PowerSeries.coeff_mul_C
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_C_mul PowerSeries.coeff_C_mulₓ'. -/
 @[simp]
 theorem coeff_C_mul (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (C R a * φ) = a * coeff R n φ :=
@@ -2308,10 +2176,7 @@ theorem coeff_C_mul (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (C R a *
 #align power_series.coeff_C_mul PowerSeries.coeff_C_mul
 
 /- warning: power_series.coeff_smul -> PowerSeries.coeff_smul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_smul PowerSeries.coeff_smulₓ'. -/
 @[simp]
 theorem coeff_smul {S : Type _} [Semiring S] [Module R S] (n : ℕ) (φ : PowerSeries S) (a : R) :
@@ -2332,10 +2197,7 @@ theorem smul_eq_C_mul (f : PowerSeries R) (a : R) : a • f = C R a * f :=
 #align power_series.smul_eq_C_mul PowerSeries.smul_eq_C_mul
 
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 Case conversion may be inaccurate. Consider using '#align power_series.coeff_succ_mul_X PowerSeries.coeff_succ_mul_Xₓ'. -/
 @[simp]
 theorem coeff_succ_mul_X (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (φ * X) = coeff R n φ :=
@@ -2346,10 +2208,7 @@ theorem coeff_succ_mul_X (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (φ *
 #align power_series.coeff_succ_mul_X PowerSeries.coeff_succ_mul_X
 
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 Case conversion may be inaccurate. Consider using '#align power_series.coeff_succ_X_mul PowerSeries.coeff_succ_X_mulₓ'. -/
 @[simp]
 theorem coeff_succ_X_mul (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (X * φ) = coeff R n φ :=
@@ -2433,10 +2292,7 @@ theorem coeff_zero_X_mul (φ : PowerSeries R) : coeff R 0 (X * φ) = 0 := by sim
 section
 
 /- warning: power_series.coeff_C_mul_X_pow -> PowerSeries.coeff_C_mul_X_pow is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align power_series.coeff_C_mul_X_pow PowerSeries.coeff_C_mul_X_powₓ'. -/
 theorem coeff_C_mul_X_pow (x : R) (k n : ℕ) :
     coeff R n (C R x * X ^ k : PowerSeries R) = if n = k then x else 0 := by
@@ -2444,10 +2300,7 @@ theorem coeff_C_mul_X_pow (x : R) (k n : ℕ) :
 #align power_series.coeff_C_mul_X_pow PowerSeries.coeff_C_mul_X_pow
 
 /- warning: power_series.coeff_mul_X_pow -> PowerSeries.coeff_mul_X_pow is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_X_powₓ'. -/
 @[simp]
 theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * X ^ n) = coeff R d p :=
@@ -2463,10 +2316,7 @@ theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * X
 #align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_X_pow
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow_mul PowerSeries.coeff_X_pow_mulₓ'. -/
 @[simp]
 theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (X ^ n * p) = coeff R d p :=
@@ -2483,10 +2333,7 @@ theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (X ^ n
 #align power_series.coeff_X_pow_mul PowerSeries.coeff_X_pow_mul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_X_pow' PowerSeries.coeff_mul_X_pow'ₓ'. -/
 theorem coeff_mul_X_pow' (p : PowerSeries R) (n d : ℕ) :
     coeff R d (p * X ^ n) = ite (n ≤ d) (coeff R (d - n) p) 0 :=
@@ -2499,10 +2346,7 @@ theorem coeff_mul_X_pow' (p : PowerSeries R) (n d : ℕ) :
 #align power_series.coeff_mul_X_pow' PowerSeries.coeff_mul_X_pow'
 
 /- warning: power_series.coeff_X_pow_mul' -> PowerSeries.coeff_X_pow_mul' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow_mul' PowerSeries.coeff_X_pow_mul'ₓ'. -/
 theorem coeff_X_pow_mul' (p : PowerSeries R) (n d : ℕ) :
     coeff R d (X ^ n * p) = ite (n ≤ d) (coeff R (d - n) p) 0 :=
@@ -2531,10 +2375,7 @@ theorem isUnit_constantCoeff (φ : PowerSeries R) (h : IsUnit φ) : IsUnit (cons
 #align power_series.is_unit_constant_coeff PowerSeries.isUnit_constantCoeff
 
 /- warning: power_series.eq_shift_mul_X_add_const -> PowerSeries.eq_shift_mul_X_add_const is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.eq_shift_mul_X_add_const PowerSeries.eq_shift_mul_X_add_constₓ'. -/
 /-- Split off the constant coefficient. -/
 theorem eq_shift_mul_X_add_const (φ : PowerSeries R) :
@@ -2550,10 +2391,7 @@ theorem eq_shift_mul_X_add_const (φ : PowerSeries R) :
 #align power_series.eq_shift_mul_X_add_const PowerSeries.eq_shift_mul_X_add_const
 
 /- warning: power_series.eq_X_mul_shift_add_const -> PowerSeries.eq_X_mul_shift_add_const is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.eq_X_mul_shift_add_const PowerSeries.eq_X_mul_shift_add_constₓ'. -/
 /-- Split off the constant coefficient. -/
 theorem eq_X_mul_shift_add_const (φ : PowerSeries R) :
@@ -2607,10 +2445,7 @@ theorem map_comp : map (g.comp f) = (map g).comp (map f) :=
 #align power_series.map_comp PowerSeries.map_comp
 
 /- warning: power_series.coeff_map -> PowerSeries.coeff_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_map PowerSeries.coeff_mapₓ'. -/
 @[simp]
 theorem coeff_map (n : ℕ) (φ : PowerSeries R) : coeff S n (map f φ) = f (coeff R n φ) :=
@@ -2618,10 +2453,7 @@ theorem coeff_map (n : ℕ) (φ : PowerSeries R) : coeff S n (map f φ) = f (coe
 #align power_series.coeff_map PowerSeries.coeff_map
 
 /- warning: power_series.map_C -> PowerSeries.map_C is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.map_C PowerSeries.map_Cₓ'. -/
 @[simp]
 theorem map_C (r : R) : map f (C _ r) = C _ (f r) :=
@@ -2718,10 +2550,7 @@ noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R
 #align power_series.rescale PowerSeries.rescale
 
 /- warning: power_series.coeff_rescale -> PowerSeries.coeff_rescale is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_rescale PowerSeries.coeff_rescaleₓ'. -/
 @[simp]
 theorem coeff_rescale (f : PowerSeries R) (a : R) (n : ℕ) :
@@ -2747,10 +2576,7 @@ theorem rescale_zero : rescale 0 = (C R).comp (constantCoeff R) :=
 #align power_series.rescale_zero PowerSeries.rescale_zero
 
 /- warning: power_series.rescale_zero_apply -> PowerSeries.rescale_zero_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.rescale_zero_apply PowerSeries.rescale_zero_applyₓ'. -/
 theorem rescale_zero_apply : rescale 0 X = C R (constantCoeff R X) := by simp
 #align power_series.rescale_zero_apply PowerSeries.rescale_zero_apply
@@ -2781,10 +2607,7 @@ theorem rescale_mk (f : ℕ → R) (a : R) : rescale a (mk f) = mk fun n : ℕ =
 #align power_series.rescale_mk PowerSeries.rescale_mk
 
 /- warning: power_series.rescale_rescale -> PowerSeries.rescale_rescale is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.rescale_rescale PowerSeries.rescale_rescaleₓ'. -/
 theorem rescale_rescale (f : PowerSeries R) (a b : R) :
     rescale b (rescale a f) = rescale (a * b) f :=
@@ -2905,10 +2728,7 @@ protected def inv.aux : R → PowerSeries R → PowerSeries R :=
 -/
 
 /- warning: power_series.coeff_inv_aux -> PowerSeries.coeff_inv_aux is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_inv_aux PowerSeries.coeff_inv_auxₓ'. -/
 theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
     coeff R n (inv.aux a φ) =
@@ -2966,10 +2786,7 @@ def invOfUnit (φ : PowerSeries R) (u : Rˣ) : PowerSeries R :=
 #align power_series.inv_of_unit PowerSeries.invOfUnit
 
 /- warning: power_series.coeff_inv_of_unit -> PowerSeries.coeff_invOfUnit is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_inv_of_unit PowerSeries.coeff_invOfUnitₓ'. -/
 theorem coeff_invOfUnit (n : ℕ) (φ : PowerSeries R) (u : Rˣ) :
     coeff R n (invOfUnit φ u) =
@@ -3005,10 +2822,7 @@ theorem mul_invOfUnit (φ : PowerSeries R) (u : Rˣ) (h : constantCoeff R φ = u
 #align power_series.mul_inv_of_unit PowerSeries.mul_invOfUnit
 
 /- warning: power_series.sub_const_eq_shift_mul_X -> PowerSeries.sub_const_eq_shift_mul_X is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.sub_const_eq_shift_mul_X PowerSeries.sub_const_eq_shift_mul_Xₓ'. -/
 /-- Two ways of removing the constant coefficient of a power series are the same. -/
 theorem sub_const_eq_shift_mul_X (φ : PowerSeries R) :
@@ -3017,10 +2831,7 @@ theorem sub_const_eq_shift_mul_X (φ : PowerSeries R) :
 #align power_series.sub_const_eq_shift_mul_X PowerSeries.sub_const_eq_shift_mul_X
 
 /- warning: power_series.sub_const_eq_X_mul_shift -> PowerSeries.sub_const_eq_X_mul_shift is a dubious translation:
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R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) φ)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.sub_const_eq_X_mul_shift PowerSeries.sub_const_eq_X_mul_shiftₓ'. -/
 theorem sub_const_eq_X_mul_shift (φ : PowerSeries R) :
     φ - C R (constantCoeff R φ) = X * PowerSeries.mk fun p => coeff R (p + 1) φ :=
@@ -3034,10 +2845,7 @@ section CommRing
 variable {A : Type _} [CommRing A]
 
 /- warning: power_series.rescale_X -> PowerSeries.rescale_X is a dubious translation:
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.rescale_X PowerSeries.rescale_Xₓ'. -/
 @[simp]
 theorem rescale_X (a : A) : rescale a X = C A a * X :=
@@ -3273,10 +3081,7 @@ theorem inv_eq_inv_aux (φ : PowerSeries k) : φ⁻¹ = inv.aux (constantCoeff k
 #align power_series.inv_eq_inv_aux PowerSeries.inv_eq_inv_aux
 
 /- warning: power_series.coeff_inv -> PowerSeries.coeff_inv is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_inv PowerSeries.coeff_invₓ'. -/
 theorem coeff_inv (n) (φ : PowerSeries k) :
     coeff k n φ⁻¹ =
@@ -3289,10 +3094,7 @@ theorem coeff_inv (n) (φ : PowerSeries k) :
 #align power_series.coeff_inv PowerSeries.coeff_inv
 
 /- warning: power_series.constant_coeff_inv -> PowerSeries.constantCoeff_inv is a dubious translation:
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k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} 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(Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ)) (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) φ))
+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.constant_coeff_inv PowerSeries.constantCoeff_invₓ'. -/
 @[simp]
 theorem constantCoeff_inv (φ : PowerSeries k) : constantCoeff k φ⁻¹ = (constantCoeff k φ)⁻¹ :=
@@ -3321,10 +3123,7 @@ theorem zero_inv : (0 : PowerSeries k)⁻¹ = 0 :=
 #align power_series.zero_inv PowerSeries.zero_inv
 
 /- warning: power_series.inv_of_unit_eq -> PowerSeries.invOfUnit_eq is a dubious translation:
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(Units.mk0.{u1} k (DivisionSemiring.toGroupWithZero.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} k) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toMul.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) φ) h)) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ)
+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.inv_of_unit_eq PowerSeries.invOfUnit_eqₓ'. -/
 @[simp]
 theorem invOfUnit_eq (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) :
@@ -3414,10 +3213,7 @@ instance : InvOneClass (PowerSeries k) :=
   MvPowerSeries.invOneClass
 
 /- warning: power_series.C_inv -> PowerSeries.C_inv is a dubious translation:
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(DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))))) (PowerSeries.C.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Inv.inv.{u1} k (Field.toInv.{u1} k _inst_1) r))
+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.C_inv PowerSeries.C_invₓ'. -/
 @[simp]
 theorem C_inv (r : k) : (C k r)⁻¹ = C k r⁻¹ :=
@@ -3616,10 +3412,7 @@ theorem le_order (φ : PowerSeries R) (n : PartENat) (h : ∀ i : ℕ, ↑i < n
 #align power_series.le_order PowerSeries.le_order
 
 /- warning: power_series.order_eq_nat -> PowerSeries.order_eq_nat is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.order_eq_nat PowerSeries.order_eq_natₓ'. -/
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
 and the `i`th coefficient is `0` for all `i < n`.-/
@@ -3632,10 +3425,7 @@ theorem order_eq_nat {φ : PowerSeries R} {n : ℕ} :
 #align power_series.order_eq_nat PowerSeries.order_eq_nat
 
 /- warning: power_series.order_eq -> PowerSeries.order_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.order_eq PowerSeries.order_eqₓ'. -/
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
 and the `i`th coefficient is `0` for all `i < n`.-/
@@ -3685,7 +3475,6 @@ private theorem order_add_of_order_eq.aux (φ ψ : PowerSeries R) (h : order φ
     · intro i hi
       rw [(coeff _ _).map_add, coeff_of_lt_order i hi, coeff_of_lt_order i (lt_trans hi H),
         zero_add]
-#align power_series.order_add_of_order_eq.aux power_series.order_add_of_order_eq.aux
 
 /- warning: power_series.order_add_of_order_eq -> PowerSeries.order_add_of_order_eq is a dubious translation:
 lean 3 declaration is
@@ -3783,10 +3572,7 @@ theorem coeff_mul_of_lt_order {φ ψ : PowerSeries R} {n : ℕ} (h : ↑n < ψ.o
 #align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_order
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_one_sub_of_lt_order PowerSeries.coeff_mul_one_sub_of_lt_orderₓ'. -/
 theorem coeff_mul_one_sub_of_lt_order {R : Type _} [CommRing R] {φ ψ : PowerSeries R} (n : ℕ)
     (h : ↑n < ψ.order) : coeff R n (φ * (1 - ψ)) = coeff R n φ := by
@@ -3794,10 +3580,7 @@ theorem coeff_mul_one_sub_of_lt_order {R : Type _} [CommRing R] {φ ψ : PowerSe
 #align power_series.coeff_mul_one_sub_of_lt_order PowerSeries.coeff_mul_one_sub_of_lt_order
 
 /- warning: power_series.coeff_mul_prod_one_sub_of_lt_order -> PowerSeries.coeff_mul_prod_one_sub_of_lt_order is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_prod_one_sub_of_lt_order PowerSeries.coeff_mul_prod_one_sub_of_lt_orderₓ'. -/
 theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type _} [CommRing R] (k : ℕ) (s : Finset ι)
     (φ : PowerSeries R) (f : ι → PowerSeries R) :
@@ -3956,10 +3739,7 @@ theorem coeff_coe (n) : PowerSeries.coeff R n φ = coeff φ n :=
 #align polynomial.coeff_coe Polynomial.coeff_coe
 
 /- warning: polynomial.coe_monomial -> Polynomial.coe_monomial is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_monomial Polynomial.coe_monomialₓ'. -/
 @[simp, norm_cast]
 theorem coe_monomial (n : ℕ) (a : R) :
@@ -4216,20 +3996,14 @@ instance (priority := 100) algebraPolynomial' {A : Type _} [CommSemiring A] [Alg
 variable (A)
 
 /- warning: power_series.algebra_map_apply' -> PowerSeries.algebraMap_apply' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.algebra_map_apply' PowerSeries.algebraMap_apply'ₓ'. -/
 theorem algebraMap_apply' (p : R[X]) : algebraMap R[X] (PowerSeries A) p = map (algebraMap R A) p :=
   rfl
 #align power_series.algebra_map_apply' PowerSeries.algebraMap_apply'
 
 /- warning: power_series.algebra_map_apply'' -> PowerSeries.algebraMap_apply'' is a dubious translation:
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(CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align power_series.algebra_map_apply'' PowerSeries.algebraMap_apply''ₓ'. -/
 theorem algebraMap_apply'' :
     algebraMap (PowerSeries R) (PowerSeries A) f = map (algebraMap R A) f :=

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

@@ -144,7 +144,7 @@ variable {R}
 lean 3 declaration is
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_inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R 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R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) ψ)) -> (Eq.{max (succ u1) (succ u2)} (MvPowerSeries.{u1, u2} σ R) φ ψ)
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : MvPowerSeries.{u2, u1} σ R} {ψ : MvPowerSeries.{u2, u1} σ R}, (forall (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) ψ)) -> (Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ R) φ ψ)
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : MvPowerSeries.{u2, u1} σ R} {ψ : MvPowerSeries.{u2, u1} σ R}, (forall (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) ψ)) -> (Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ R) φ ψ)
 Case conversion may be inaccurate. Consider using '#align mv_power_series.ext MvPowerSeries.extₓ'. -/
 /-- Two multivariate formal power series are equal if all their coefficients are equal.-/
 @[ext]
@@ -156,7 +156,7 @@ theorem ext {φ ψ} (h : ∀ n : σ →₀ ℕ, coeff R n φ = coeff R n ψ) : 
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {φ : MvPowerSeries.{u1, u2} σ R} {ψ : MvPowerSeries.{u1, u2} σ R}, Iff (Eq.{max (succ u1) (succ u2)} (MvPowerSeries.{u1, u2} σ R) φ ψ) (forall (n : Finsupp.{u1, 0} σ Nat Nat.hasZero), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) ψ))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : MvPowerSeries.{u2, u1} σ R} {ψ : MvPowerSeries.{u2, u1} σ R}, Iff (Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ R) φ ψ) (forall (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) ψ))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : MvPowerSeries.{u2, u1} σ R} {ψ : MvPowerSeries.{u2, u1} σ R}, Iff (Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ R) φ ψ) (forall (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) ψ))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.ext_iff MvPowerSeries.ext_iffₓ'. -/
 /-- Two multivariate formal power series are equal
  if and only if all their coefficients are equal.-/
@@ -178,7 +178,7 @@ theorem monomial_def [DecidableEq σ] (n : σ →₀ ℕ) : monomial R n = Linea
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (m : Finsupp.{u1, 0} σ Nat Nat.hasZero) (n : Finsupp.{u1, 0} σ Nat Nat.hasZero) (a : R), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) 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(MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.monomial.{u2, u1} σ R _inst_1 n) a)) (ite.{succ u1} R (Eq.{succ u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) m n) (Finsupp.decidableEq.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) m n) a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_monomial MvPowerSeries.coeff_monomialₓ'. -/
 -- unify the `decidable` arguments
 theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
@@ -191,7 +191,7 @@ theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
 lean 3 declaration is
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) => R -> (MvPowerSeries.{u1, u2} σ R)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPowerSeries.{u1, u2} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.monomial.{u1, u2} σ R _inst_1 n) a)) a
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_monomial_same MvPowerSeries.coeff_monomial_sameₓ'. -/
 @[simp]
 theorem coeff_monomial_same (n : σ →₀ ℕ) (a : R) : coeff R n (monomial R n a) = a :=
@@ -202,7 +202,7 @@ theorem coeff_monomial_same (n : σ →₀ ℕ) (a : R) : coeff R n (monomial R
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_monomial_ne MvPowerSeries.coeff_monomial_neₓ'. -/
 theorem coeff_monomial_ne {m n : σ →₀ ℕ} (h : m ≠ n) (a : R) : coeff R m (monomial R n a) = 0 :=
   LinearMap.stdBasis_ne R _ _ _ h a
@@ -212,7 +212,7 @@ theorem coeff_monomial_ne {m n : σ →₀ ℕ} (h : m ≠ n) (a : R) : coeff R
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.eq_of_coeff_monomial_ne_zero MvPowerSeries.eq_of_coeff_monomial_ne_zeroₓ'. -/
 theorem eq_of_coeff_monomial_ne_zero {m n : σ →₀ ℕ} {a : R} (h : coeff R m (monomial R n a) ≠ 0) :
     m = n :=
@@ -234,7 +234,7 @@ theorem coeff_comp_monomial (n : σ →₀ ℕ) : (coeff R n).comp (monomial R n
 lean 3 declaration is
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 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 0 (Zero.toOfNat0.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 0 (Zero.toOfNat0.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 0 (Zero.toOfNat0.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 0 (Zero.toOfNat0.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 0 (Zero.toOfNat0.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 0 (Zero.toOfNat0.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) _inst_1))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 0 (Zero.toOfNat0.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 0 (Zero.toOfNat0.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 0 (Zero.toOfNat0.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 0 (Zero.toOfNat0.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 0 (Zero.toOfNat0.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 0 (Zero.toOfNat0.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero MvPowerSeries.coeff_zeroₓ'. -/
 @[simp]
 theorem coeff_zero (n : σ →₀ ℕ) : coeff R n (0 : MvPowerSeries σ R) = 0 :=
@@ -250,7 +250,7 @@ instance : One (MvPowerSeries σ R) :=
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (n : Finsupp.{u1, 0} σ Nat Nat.hasZero) [_inst_2 : DecidableEq.{succ u1} σ], Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) (OfNat.ofNat.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) 1 (OfNat.mk.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) 1 (One.one.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.hasOne.{u1, u2} σ R _inst_1))))) (ite.{succ u2} R (Eq.{succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) n (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero))))) (Finsupp.decidableEq.{u1, 0} σ Nat Nat.hasZero (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => Nat.decidableEq a b) n (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) [_inst_2 : DecidableEq.{succ u2} σ], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) (Eq.{succ u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) n (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (Finsupp.decidableEq.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) n (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) _inst_1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) _inst_1)))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) [_inst_2 : DecidableEq.{succ u2} σ], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) (Eq.{succ u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) n (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (Finsupp.decidableEq.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) n (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) _inst_1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_one MvPowerSeries.coeff_oneₓ'. -/
 theorem coeff_one [DecidableEq σ] : coeff R n (1 : MvPowerSeries σ R) = if n = 0 then 1 else 0 :=
   coeff_monomial _ _ _
@@ -260,7 +260,7 @@ theorem coeff_one [DecidableEq σ] : coeff R n (1 : MvPowerSeries σ R) = if n =
 lean 3 declaration is
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 but is expected to have type
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+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (OfNat.ofNat.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) 1 (One.toOfNat1.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instOneMvPowerSeries.{u1, u2} σ R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) (fun (_x : MvPowerSeries.{u1, u2} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (OfNat.ofNat.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) 1 (One.toOfNat1.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instOneMvPowerSeries.{u1, u2} σ R _inst_1)))) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (OfNat.ofNat.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) 1 (One.toOfNat1.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instOneMvPowerSeries.{u1, u2} σ R _inst_1)))) 1 (One.toOfNat1.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (OfNat.ofNat.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) 1 (One.toOfNat1.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instOneMvPowerSeries.{u1, u2} σ R _inst_1)))) (Semiring.toOne.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (OfNat.ofNat.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) 1 (One.toOfNat1.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instOneMvPowerSeries.{u1, u2} σ R _inst_1)))) _inst_1)))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_one MvPowerSeries.coeff_zero_oneₓ'. -/
 theorem coeff_zero_one : coeff R (0 : σ →₀ ℕ) 1 = 1 :=
   coeff_monomial_same 0 1
@@ -270,7 +270,7 @@ theorem coeff_zero_one : coeff R (0 : σ →₀ ℕ) 1 = 1 :=
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R], Eq.{max (succ u1) (succ u2)} (MvPowerSeries.{u1, u2} σ R) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) => R -> (MvPowerSeries.{u1, u2} σ R)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPowerSeries.{u1, u2} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.monomial.{u1, u2} σ R _inst_1 (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))))) (OfNat.ofNat.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) 1 (OfNat.mk.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) 1 (One.one.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.hasOne.{u1, u2} σ R _inst_1))))
 but is expected to have type
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+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPowerSeries.{u2, u1} σ R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPowerSeries.{u2, u1} σ R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPowerSeries.{u2, u1} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.monomial.{u2, u1} σ R _inst_1 (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (OfNat.ofNat.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPowerSeries.{u2, u1} σ R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) 1 (One.toOfNat1.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPowerSeries.{u2, u1} σ R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.monomial_zero_one MvPowerSeries.monomial_zero_oneₓ'. -/
 theorem monomial_zero_one : monomial R (0 : σ →₀ ℕ) 1 = 1 :=
   rfl
@@ -290,7 +290,7 @@ instance : Mul (MvPowerSeries σ R) :=
 lean 3 declaration is
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(Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u2} σ R) (instHMul.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.hasMul.{u1, u2} σ R _inst_1)) φ ψ)) (Finset.sum.{u2, u1} R (Prod.{u1, u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.{u1, 0} σ Nat Nat.hasZero)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.antidiagonal.{u1} σ n) (fun (p : Prod.{u1, u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.{u1, 0} σ Nat Nat.hasZero)) => HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (Distrib.toHasMul.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (Prod.fst.{u1, u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.{u1, 0} σ Nat Nat.hasZero) p)) φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (Prod.snd.{u1, u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.{u1, 0} σ Nat Nat.hasZero) p)) ψ)))
 but is expected to have type
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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (Prod.snd.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) p)) ψ)))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_mul MvPowerSeries.coeff_mulₓ'. -/
 theorem coeff_mul :
     coeff R n (φ * ψ) = ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ :=
@@ -321,7 +321,7 @@ protected theorem mul_zero : φ * 0 = 0 :=
 lean 3 declaration is
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(MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_monomial_mul MvPowerSeries.coeff_monomial_mulₓ'. -/
 theorem coeff_monomial_mul (a : R) :
     coeff R m (monomial R n a * φ) = if n ≤ m then a * coeff R (m - n) φ else 0 :=
@@ -338,7 +338,7 @@ theorem coeff_monomial_mul (a : R) :
 lean 3 declaration is
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 but is expected to have type
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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) φ) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) φ) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) φ) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) φ) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_mul_monomial MvPowerSeries.coeff_mul_monomialₓ'. -/
 theorem coeff_mul_monomial (a : R) :
     coeff R m (φ * monomial R n a) = if n ≤ m then coeff R (m - n) φ * a else 0 :=
@@ -355,7 +355,7 @@ theorem coeff_mul_monomial (a : R) :
 lean 3 declaration is
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 but is expected to have type
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(MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPowerSeries.{u1, u2} σ R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u1 u2} R R R (MvPowerSeries.{u1, u2} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)))) a (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) (fun (_x : MvPowerSeries.{u1, u2} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) φ))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_add_monomial_mul MvPowerSeries.coeff_add_monomial_mulₓ'. -/
 theorem coeff_add_monomial_mul (a : R) : coeff R (m + n) (monomial R m a * φ) = a * coeff R n φ :=
   by
@@ -367,7 +367,7 @@ theorem coeff_add_monomial_mul (a : R) : coeff R (m + n) (monomial R m a * φ) =
 lean 3 declaration is
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 but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) (fun (_x : MvPowerSeries.{u1, u2} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 m) φ) a)
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_add_mul_monomial MvPowerSeries.coeff_add_mul_monomialₓ'. -/
 theorem coeff_add_mul_monomial (a : R) : coeff R (m + n) (φ * monomial R n a) = coeff R m φ * a :=
   by
@@ -379,7 +379,7 @@ theorem coeff_add_mul_monomial (a : R) : coeff R (m + n) (φ * monomial R n a) =
 lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 m) φ) a)
 but is expected to have type
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+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : MvPowerSeries.{u2, u1} σ R) {a : R} {n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)}, Iff (Commute.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1) φ (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPowerSeries.{u2, u1} σ R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (MvPowerSeries.{u2, u1} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.monomial.{u2, u1} σ R _inst_1 n) a)) (forall (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 m) φ) a)
 Case conversion may be inaccurate. Consider using '#align mv_power_series.commute_monomial MvPowerSeries.commute_monomialₓ'. -/
 @[simp]
 theorem commute_monomial {a : R} {n} : Commute φ (monomial R n a) ↔ ∀ m, Commute (coeff R m φ) a :=
@@ -388,7 +388,7 @@ theorem commute_monomial {a : R} {n} : Commute φ (monomial R n a) ↔ ∀ m, Co
   · have := h (m + n)
     rwa [coeff_add_mul_monomial, add_comm, coeff_add_monomial_mul] at this
   · rw [coeff_mul_monomial, coeff_monomial_mul]
-    split_ifs <;> [apply h, rfl]
+    split_ifs <;> [apply h;rfl]
 #align mv_power_series.commute_monomial MvPowerSeries.commute_monomial
 
 /- warning: mv_power_series.one_mul -> MvPowerSeries.one_mul is a dubious translation:
@@ -496,7 +496,7 @@ variable [Semiring R]
 lean 3 declaration is
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(MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPowerSeries.{u2, u1} σ R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPowerSeries.{u2, u1} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.monomial.{u2, u1} σ R _inst_1 (HAdd.hAdd.{u2, u2, u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (instHAdd.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) m 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)))) a b))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.monomial_mul_monomial MvPowerSeries.monomial_mul_monomialₓ'. -/
 theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
     monomial R m a * monomial R n b = monomial R (m + n) (a * b) :=
@@ -535,7 +535,7 @@ variable {σ} {R}
 lean 3 declaration is
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 but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPowerSeries.{u2, u1} σ R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPowerSeries.{u2, u1} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.monomial.{u2, u1} σ R _inst_1 (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))))) (MvPowerSeries.C.{u2, u1} σ R _inst_1))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.monomial_zero_eq_C MvPowerSeries.monomial_zero_eq_Cₓ'. -/
 @[simp]
 theorem monomial_zero_eq_C : ⇑(monomial R (0 : σ →₀ ℕ)) = C σ R :=
@@ -546,7 +546,7 @@ theorem monomial_zero_eq_C : ⇑(monomial R (0 : σ →₀ ℕ)) = C σ R :=
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (a : R), Eq.{max (succ u1) (succ u2)} (MvPowerSeries.{u1, u2} σ R) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) => R -> (MvPowerSeries.{u1, u2} σ R)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPowerSeries.{u1, u2} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.monomial.{u1, u2} σ R _inst_1 (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero))))) a) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) => R -> (MvPowerSeries.{u1, u2} σ R)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) (MvPowerSeries.C.{u1, u2} σ R _inst_1) a)
 but is expected to have type
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_inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))))) (MvPowerSeries.C.{u2, u1} σ R _inst_1) a)
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPowerSeries.{u2, u1} σ R) a) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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(Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.monomial.{u2, u1} σ R _inst_1 (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) a) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))))) (MvPowerSeries.C.{u2, u1} σ R _inst_1) a)
 Case conversion may be inaccurate. Consider using '#align mv_power_series.monomial_zero_eq_C_apply MvPowerSeries.monomial_zero_eq_C_applyₓ'. -/
 theorem monomial_zero_eq_C_apply (a : R) : monomial R (0 : σ →₀ ℕ) a = C σ R a :=
   rfl
@@ -556,7 +556,7 @@ theorem monomial_zero_eq_C_apply (a : R) : monomial R (0 : σ →₀ ℕ) a = C
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (n : Finsupp.{u1, 0} σ Nat Nat.hasZero) (a : R), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) => R -> (MvPowerSeries.{u1, u2} σ R)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) (MvPowerSeries.C.{u1, u2} σ R _inst_1) a)) (ite.{succ u2} R (Eq.{succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) n (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero))))) (Finsupp.decidableEq.{u1, 0} σ Nat Nat.hasZero (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => Nat.decidableEq a b) n (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero))))) a (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) a) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))))) (MvPowerSeries.C.{u2, u1} σ R _inst_1) a)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))))) (MvPowerSeries.C.{u2, u1} σ R _inst_1) a)) (ite.{succ u1} R (Eq.{succ u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) n (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (Finsupp.decidableEq.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) n (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) a) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))))) (MvPowerSeries.C.{u2, u1} σ R _inst_1) a)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))))) (MvPowerSeries.C.{u2, u1} σ R _inst_1) a)) (ite.{succ u1} R (Eq.{succ u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) n (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (Finsupp.decidableEq.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) n (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_C MvPowerSeries.coeff_Cₓ'. -/
 theorem coeff_C [DecidableEq σ] (n : σ →₀ ℕ) (a : R) :
     coeff R n (C σ R a) = if n = 0 then a else 0 :=
@@ -567,7 +567,7 @@ theorem coeff_C [DecidableEq σ] (n : σ →₀ ℕ) (a : R) :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (a : R), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero))))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) => R -> (MvPowerSeries.{u1, u2} σ R)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) (MvPowerSeries.C.{u1, u2} σ R _inst_1) a)) a
 but is expected to have type
-  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (a : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u1, u2} σ R) => R) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u2 u1} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u2} σ R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u1, u2} σ R) a) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u2} σ R _inst_1))) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u2} σ R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u2} σ R _inst_1))) R (MvPowerSeries.{u1, u2} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) 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+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (a : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u2 u1} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u2} σ R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u1, u2} σ R) a) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u2} σ R _inst_1))) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toMul.{u2} R 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_inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) (fun (_x : MvPowerSeries.{u1, u2} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max 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(Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u2 u1} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u2} σ R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u1, u2} σ R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u2} σ R _inst_1))) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u2} σ R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u2} σ R _inst_1))) R (MvPowerSeries.{u1, u2} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) 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 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_C MvPowerSeries.coeff_zero_Cₓ'. -/
 theorem coeff_zero_C (a : R) : coeff R (0 : σ →₀ ℕ) (C σ R a) = a :=
   coeff_monomial_same 0 a
@@ -584,7 +584,7 @@ def X (s : σ) : MvPowerSeries σ R :=
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (n : Finsupp.{u1, 0} σ Nat Nat.hasZero) (s : σ), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (ite.{succ u2} R (Eq.{succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) n (Finsupp.single.{u1, 0} σ Nat Nat.hasZero s (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Finsupp.decidableEq.{u1, 0} σ Nat Nat.hasZero (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => Nat.decidableEq a b) n (Finsupp.single.{u1, 0} σ Nat Nat.hasZero s (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (s : σ), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (Eq.{succ u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) n (Finsupp.single.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Finsupp.decidableEq.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) n (Finsupp.single.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) _inst_1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) _inst_1)))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (s : σ), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (Eq.{succ u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) n (Finsupp.single.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Finsupp.decidableEq.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) n (Finsupp.single.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) _inst_1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_X MvPowerSeries.coeff_Xₓ'. -/
 theorem coeff_X [DecidableEq σ] (n : σ →₀ ℕ) (s : σ) :
     coeff R n (X s : MvPowerSeries σ R) = if n = single s 1 then 1 else 0 :=
@@ -595,7 +595,7 @@ theorem coeff_X [DecidableEq σ] (n : σ →₀ ℕ) (s : σ) :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (s : σ) (t : σ), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (Finsupp.single.{u1, 0} σ Nat Nat.hasZero t (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (ite.{succ u2} R (Eq.{succ u1} σ t s) (_inst_2 t s) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))
 but is expected to have type
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+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (s : σ) (t : σ), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 (Finsupp.single.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) t (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (Eq.{succ u2} σ t s) (_inst_2 t s) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) _inst_1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s)) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_index_single_X MvPowerSeries.coeff_index_single_Xₓ'. -/
 theorem coeff_index_single_X [DecidableEq σ] (s t : σ) :
     coeff R (single t 1) (X s : MvPowerSeries σ R) = if t = s then 1 else 0 := by
@@ -606,7 +606,7 @@ theorem coeff_index_single_X [DecidableEq σ] (s t : σ) :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (s : σ), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (Finsupp.single.{u1, 0} σ Nat Nat.hasZero s (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))))
 but is expected to have type
-  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (s : σ), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) (fun (_x : MvPowerSeries.{u1, u2} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u1, u2} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (Finsupp.single.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) 1 (One.toOfNat1.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (Semiring.toOne.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) _inst_1)))
+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (s : σ), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) (fun (_x : MvPowerSeries.{u1, u2} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (Finsupp.single.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) 1 (One.toOfNat1.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (Semiring.toOne.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) _inst_1)))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_index_single_self_X MvPowerSeries.coeff_index_single_self_Xₓ'. -/
 @[simp]
 theorem coeff_index_single_self_X (s : σ) : coeff R (single s 1) (X s : MvPowerSeries σ R) = 1 :=
@@ -617,7 +617,7 @@ theorem coeff_index_single_self_X (s : σ) : coeff R (single s 1) (X s : MvPower
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (s : σ), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero))))) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))))
 but is expected to have type
-  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (s : σ), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) (fun (_x : MvPowerSeries.{u1, u2} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u1, u2} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) _inst_1))))
+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (s : σ), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) (fun (_x : MvPowerSeries.{u1, u2} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u1, u2} σ R) => R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_X MvPowerSeries.coeff_zero_Xₓ'. -/
 theorem coeff_zero_X (s : σ) : coeff R (0 : σ →₀ ℕ) (X s : MvPowerSeries σ R) = 0 :=
   by
@@ -640,7 +640,7 @@ theorem commute_X (φ : MvPowerSeries σ R) (s : σ) : Commute φ (X s) :=
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (s : σ), Eq.{max (succ u1) (succ u2)} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) => R -> (MvPowerSeries.{u1, u2} σ R)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPowerSeries.{u1, u2} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.monomial.{u1, u2} σ R _inst_1 (Finsupp.single.{u1, 0} σ Nat Nat.hasZero s (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (s : σ), Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPowerSeries.{u2, u1} σ R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPowerSeries.{u2, u1} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.monomial.{u2, u1} σ R _inst_1 (Finsupp.single.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (s : σ), Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPowerSeries.{u2, u1} σ R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPowerSeries.{u2, u1} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.monomial.{u2, u1} σ R _inst_1 (Finsupp.single.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.X_def MvPowerSeries.X_defₓ'. -/
 theorem X_def (s : σ) : X s = monomial R (single s 1) 1 :=
   rfl
@@ -650,7 +650,7 @@ theorem X_def (s : σ) : X s = monomial R (single s 1) 1 :=
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (s : σ) (n : Nat), Eq.{succ (max u1 u2)} (MvPowerSeries.{u1, u2} σ R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (MvPowerSeries.{u1, u2} σ R) Nat (MvPowerSeries.{u1, u2} σ R) (instHPow.{max u1 u2, 0} (MvPowerSeries.{u1, u2} σ R) Nat (Monoid.Pow.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MonoidWithZero.toMonoid.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (Semiring.toMonoidWithZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))))) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s) n) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) => R -> (MvPowerSeries.{u1, u2} σ R)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPowerSeries.{u1, u2} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.monomial.{u1, u2} σ R _inst_1 (Finsupp.single.{u1, 0} σ Nat Nat.hasZero s n)) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (s : σ) (n : Nat), Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPowerSeries.{u2, u1} σ R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPowerSeries.{u2, u1} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.monomial.{u2, u1} σ R _inst_1 (Finsupp.single.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s n)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (s : σ) (n : Nat), Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPowerSeries.{u2, u1} σ R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPowerSeries.{u2, u1} σ R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.monomial.{u2, u1} σ R _inst_1 (Finsupp.single.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s n)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.X_pow_eq MvPowerSeries.X_pow_eqₓ'. -/
 theorem X_pow_eq (s : σ) (n : ℕ) : (X s : MvPowerSeries σ R) ^ n = monomial R (single s n) 1 :=
   by
@@ -663,7 +663,7 @@ theorem X_pow_eq (s : σ) (n : ℕ) : (X s : MvPowerSeries σ R) ^ n = monomial
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (m : Finsupp.{u1, 0} σ Nat Nat.hasZero) (s : σ) (n : Nat), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 m) (HPow.hPow.{max u1 u2, 0, max u1 u2} (MvPowerSeries.{u1, u2} σ R) Nat (MvPowerSeries.{u1, u2} σ R) (instHPow.{max u1 u2, 0} (MvPowerSeries.{u1, u2} σ R) Nat (Monoid.Pow.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MonoidWithZero.toMonoid.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (Semiring.toMonoidWithZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))))) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s) n)) (ite.{succ u2} R (Eq.{succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) m (Finsupp.single.{u1, 0} σ Nat Nat.hasZero s n)) (Finsupp.decidableEq.{u1, 0} σ Nat Nat.hasZero (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => Nat.decidableEq a b) m (Finsupp.single.{u1, 0} σ Nat Nat.hasZero s n)) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (s : σ) (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 m) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) (Eq.{succ u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) m (Finsupp.single.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s n)) (Finsupp.decidableEq.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) m (Finsupp.single.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s n)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) _inst_1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) _inst_1)))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (s : σ) (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 m) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) (Eq.{succ u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) m (Finsupp.single.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s n)) (Finsupp.decidableEq.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) m (Finsupp.single.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s n)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) _inst_1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n)) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_X_pow MvPowerSeries.coeff_X_powₓ'. -/
 theorem coeff_X_pow [DecidableEq σ] (m : σ →₀ ℕ) (s : σ) (n : ℕ) :
     coeff R m ((X s : MvPowerSeries σ R) ^ n) = if m = single s n then 1 else 0 := by
@@ -674,7 +674,7 @@ theorem coeff_X_pow [DecidableEq σ] (m : σ →₀ ℕ) (s : σ) (n : ℕ) :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (n : Finsupp.{u1, 0} σ Nat Nat.hasZero) (φ : MvPowerSeries.{u1, u2} σ R) (a : R), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u2} σ R) (instHMul.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.hasMul.{u1, u2} σ R _inst_1)) φ (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) => R -> (MvPowerSeries.{u1, u2} σ R)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) (MvPowerSeries.C.{u1, u2} σ R _inst_1) a))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (Distrib.toHasMul.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) φ) a)
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (φ : MvPowerSeries.{u2, u1} σ R) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) a) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) φ (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (fun (a : R) => (fun 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(MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))))) (MvPowerSeries.C.{u2, u1} σ R _inst_1) a))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) _inst_1)))) (FunLike.coe.{max (succ 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) φ) a)
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_mul_C MvPowerSeries.coeff_mul_Cₓ'. -/
 @[simp]
 theorem coeff_mul_C (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
@@ -685,7 +685,7 @@ theorem coeff_mul_C (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (n : Finsupp.{u1, 0} σ Nat Nat.hasZero) (φ : MvPowerSeries.{u1, u2} σ R) (a : R), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u2} σ R) (instHMul.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.hasMul.{u1, u2} σ R _inst_1)) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, 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(succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) φ))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (φ : MvPowerSeries.{u2, u1} σ R) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) a) (MvPowerSeries.{u2, u1} σ R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) a) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) a) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPowerSeries.{u2, u1} σ R) a) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, 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u1} σ R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))))) (MvPowerSeries.C.{u2, u1} σ R _inst_1) a) φ)) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) φ))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_C_mul MvPowerSeries.coeff_C_mulₓ'. -/
 @[simp]
 theorem coeff_C_mul (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
@@ -696,7 +696,7 @@ theorem coeff_C_mul (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (φ : MvPowerSeries.{u1, u2} σ R) (s : σ), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero))))) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u2} σ R) (instHMul.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.hasMul.{u1, u2} σ R _inst_1)) φ (MvPowerSeries.X.{u1, u2} σ R _inst_1 s))) (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : MvPowerSeries.{u2, u1} σ R) (s : σ), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) φ (MvPowerSeries.X.{u2, u1} σ R _inst_1 s))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) φ (MvPowerSeries.X.{u2, u1} σ R _inst_1 s))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) φ (MvPowerSeries.X.{u2, u1} σ R _inst_1 s))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) φ (MvPowerSeries.X.{u2, u1} σ R _inst_1 s))) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) φ (MvPowerSeries.X.{u2, u1} σ R _inst_1 s))) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) φ (MvPowerSeries.X.{u2, u1} σ R _inst_1 s))) _inst_1))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : MvPowerSeries.{u2, u1} σ R) (s : σ), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) φ (MvPowerSeries.X.{u2, u1} σ R _inst_1 s))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) φ (MvPowerSeries.X.{u2, u1} σ R _inst_1 s))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) φ (MvPowerSeries.X.{u2, u1} σ R _inst_1 s))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) φ (MvPowerSeries.X.{u2, u1} σ R _inst_1 s))) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) φ (MvPowerSeries.X.{u2, u1} σ R _inst_1 s))) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) φ (MvPowerSeries.X.{u2, u1} σ R _inst_1 s))) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_mul_X MvPowerSeries.coeff_zero_mul_Xₓ'. -/
 theorem coeff_zero_mul_X (φ : MvPowerSeries σ R) (s : σ) : coeff R (0 : σ →₀ ℕ) (φ * X s) = 0 :=
   by
@@ -708,7 +708,7 @@ theorem coeff_zero_mul_X (φ : MvPowerSeries σ R) (s : σ) : coeff R (0 : σ 
 lean 3 declaration is
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 but is expected to have type
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+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : MvPowerSeries.{u2, u1} σ R) (s : σ), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) φ)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) φ)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) φ)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) φ)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) φ)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R _inst_1)) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) φ)) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_X_mul MvPowerSeries.coeff_zero_X_mulₓ'. -/
 theorem coeff_zero_X_mul (φ : MvPowerSeries σ R) (s : σ) : coeff R (0 : σ →₀ ℕ) (X s * φ) = 0 := by
   rw [← (φ.commute_X s).Eq, coeff_zero_mul_X]
@@ -737,7 +737,7 @@ variable {σ} {R}
 lean 3 declaration is
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 but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPowerSeries.{u2, u1} σ R) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{max u2 u1, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MvPowerSeries.constantCoeff.{u2, u1} σ R _inst_1))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : MvPowerSeries.{u2, u1} σ R), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPowerSeries.{u2, u1} σ R) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{max u2 u1, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MvPowerSeries.constantCoeff.{u2, u1} σ R _inst_1))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_eq_constant_coeff MvPowerSeries.coeff_zero_eq_constantCoeffₓ'. -/
 @[simp]
 theorem coeff_zero_eq_constantCoeff : ⇑(coeff R (0 : σ →₀ ℕ)) = constantCoeff σ R :=
@@ -748,7 +748,7 @@ theorem coeff_zero_eq_constantCoeff : ⇑(coeff R (0 : σ →₀ ℕ)) = constan
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (φ : MvPowerSeries.{u1, u2} σ R), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero))))) φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (RingHom.{max u1 u2, u2} (MvPowerSeries.{u1, u2} σ R) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (fun (_x : RingHom.{max u1 u2, u2} (MvPowerSeries.{u1, u2} σ R) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (RingHom.hasCoeToFun.{max u1 u2, u2} (MvPowerSeries.{u1, u2} σ R) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.constantCoeff.{u1, u2} σ R _inst_1) φ)
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : MvPowerSeries.{u2, u1} σ R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPowerSeries.{u2, u1} σ R) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{max u2 u1, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MvPowerSeries.constantCoeff.{u2, u1} σ R _inst_1) φ)
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : MvPowerSeries.{u2, u1} σ R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPowerSeries.{u2, u1} σ R) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{max u2 u1, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MvPowerSeries.constantCoeff.{u2, u1} σ R _inst_1) φ)
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_eq_constant_coeff_apply MvPowerSeries.coeff_zero_eq_constantCoeff_applyₓ'. -/
 theorem coeff_zero_eq_constantCoeff_apply (φ : MvPowerSeries σ R) :
     coeff R (0 : σ →₀ ℕ) φ = constantCoeff σ R φ :=
@@ -823,7 +823,7 @@ theorem isUnit_constantCoeff (φ : MvPowerSeries σ R) (h : IsUnit φ) :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (f : MvPowerSeries.{u1, u2} σ R) (n : Finsupp.{u1, 0} σ Nat Nat.hasZero) (a : R), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) (SMul.smul.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (SMulZeroClass.toHasSmul.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (AddZeroClass.toHasZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (AddCommMonoid.toAddMonoid.{max u1 u2} 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(NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) a (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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 but is expected to have type
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(MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) (HSMul.hSMul.{u1, max u2 u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHSMul.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (SMulZeroClass.toSMul.{u1, max u2 u1} R 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(MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))))))) a f)) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) f) R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) f))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : MvPowerSeries.{u2, u1} σ R) (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (HSMul.hSMul.{u1, max u2 u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHSMul.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (SMulZeroClass.toSMul.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (SMulWithZero.toSMulZeroClass.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{u1} R _inst_1) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Module.toMulActionWithZero.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))))))) a f)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) (HSMul.hSMul.{u1, max u2 u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHSMul.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (SMulZeroClass.toSMul.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (SMulWithZero.toSMulZeroClass.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{u1} R _inst_1) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Module.toMulActionWithZero.{u1, max u2 u1} R (MvPowerSeries.{u2, u1} σ R) _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))))))) a f)) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) f) R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 n) f))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_smul MvPowerSeries.coeff_smulₓ'. -/
 @[simp]
 theorem coeff_smul (f : MvPowerSeries σ R) (n) (a : R) : coeff _ n (a • f) = a * coeff _ n f :=
@@ -920,7 +920,7 @@ theorem map_comp : map σ (g.comp f) = (map σ g).comp (map σ f) :=
 lean 3 declaration is
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) (Semiring.toModule.{u3} S _inst_2)) (Semiring.toModule.{u3} S _inst_2)) (fun (_x : LinearMap.{u3, u3, max u1 u3, u3} S S _inst_2 _inst_2 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (MvPowerSeries.{u1, u3} σ S) S (MvPowerSeries.addCommMonoid.{u1, u3} σ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) (MvPowerSeries.module.{u1, u3, u3} σ S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) (Semiring.toModule.{u3} S _inst_2)) (Semiring.toModule.{u3} S _inst_2)) => (MvPowerSeries.{u1, u3} σ S) -> S) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u3} S S (MvPowerSeries.{u1, u3} σ S) S _inst_2 _inst_2 (MvPowerSeries.addCommMonoid.{u1, u3} σ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) (MvPowerSeries.module.{u1, u3, u3} σ S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) (Semiring.toModule.{u3} S _inst_2)) (Semiring.toModule.{u3} S _inst_2) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) (MvPowerSeries.coeff.{u1, u3} σ S _inst_2 n) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ S) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPowerSeries.{u1, u3} σ S) (MvPowerSeries.semiring.{u1, u3} σ S _inst_2))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ S) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPowerSeries.{u1, u3} σ S) (MvPowerSeries.semiring.{u1, u3} σ S _inst_2))) => (MvPowerSeries.{u1, u2} σ R) -> (MvPowerSeries.{u1, u3} σ S)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ S) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPowerSeries.{u1, u3} σ S) (MvPowerSeries.semiring.{u1, u3} σ S _inst_2))) (MvPowerSeries.map.{u1, u2, u3} σ R S _inst_1 _inst_2 f) φ)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (fun (_x : RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S _inst_2)) f (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 n) φ))
 but is expected to have type
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(MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u3, u1, u1} σ S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (Semiring.toModule.{u1} S _inst_2)) (Semiring.toModule.{u1} S _inst_2)) (MvPowerSeries.{u3, u1} σ S) (fun (_x : MvPowerSeries.{u3, u1} σ S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u3, u1} σ S) => S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u1, u1} S S (MvPowerSeries.{u3, u1} σ S) S _inst_2 _inst_2 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u3, u1} σ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) 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u2} R R (MvPowerSeries.{u3, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u3, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u3, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u3, u2} σ R _inst_1 n) φ))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_map MvPowerSeries.coeff_mapₓ'. -/
 @[simp]
 theorem coeff_map (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) : coeff S n (map σ f φ) = f (coeff R n φ) :=
@@ -943,7 +943,7 @@ theorem constantCoeff_map (φ : MvPowerSeries σ R) :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S] (f : RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S _inst_2)) (n : Finsupp.{u1, 0} σ Nat Nat.hasZero) (a : R), Eq.{max (succ u1) (succ u3)} (MvPowerSeries.{u1, u3} σ S) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ S) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPowerSeries.{u1, u3} σ S) (MvPowerSeries.semiring.{u1, u3} σ S _inst_2))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ S) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPowerSeries.{u1, u3} σ S) (MvPowerSeries.semiring.{u1, u3} σ S _inst_2))) => (MvPowerSeries.{u1, u2} σ R) -> (MvPowerSeries.{u1, u3} σ S)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ S) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPowerSeries.{u1, u3} σ S) (MvPowerSeries.semiring.{u1, u3} σ S _inst_2))) (MvPowerSeries.map.{u1, u2, u3} σ R S _inst_1 _inst_2 f) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R 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(NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f a))
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(MvPowerSeries.{u3, u2} σ S) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ S) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u3 u1) u2, max u3 u1, max u3 u2} (RingHom.{max u1 u3, max u2 u3} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.{u3, u2} σ S) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ S) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ S _inst_2))) (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.{u3, u2} σ S) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u1} σ R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ S) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ S _inst_2)) (RingHom.instRingHomClassRingHom.{max u3 u1, max u3 u2} 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_inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.monomial.{u3, u1} σ R _inst_1 n) a)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u3} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (MvPowerSeries.{u3, u2} σ S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u3, u2} σ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u3, u2, u2} σ S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : S) => MvPowerSeries.{u3, u2} σ S) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u3 u2} S S S (MvPowerSeries.{u3, u2} σ S) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u3, u2} σ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u3, u2, u2} σ S S _inst_2 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(NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f a))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.map_monomial MvPowerSeries.map_monomialₓ'. -/
 @[simp]
 theorem map_monomial (n : σ →₀ ℕ) (a : R) : map σ f (monomial R n a) = monomial S n (f a) :=
@@ -1040,7 +1040,7 @@ def truncFun (φ : MvPowerSeries σ R) : MvPolynomial σ R :=
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (n : Finsupp.{u1, 0} σ Nat Nat.hasZero) (m : Finsupp.{u1, 0} σ Nat Nat.hasZero) (φ : MvPowerSeries.{u1, u2} σ R), Eq.{succ u2} R (MvPolynomial.coeff.{u2, u1} R σ _inst_1 m (MvPowerSeries.truncFun.{u1, u2} σ R _inst_1 n φ)) (ite.{succ u2} R (LT.lt.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Preorder.toHasLt.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.preorder.{u1, 0} σ Nat Nat.hasZero (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n) (And.decidable (LE.le.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.hasLe.{u1, 0} σ Nat Nat.hasZero (Preorder.toHasLe.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n) (Not (LE.le.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.hasLe.{u1, 0} σ Nat Nat.hasZero (Preorder.toHasLe.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) n m)) (Finsupp.decidableLE.{u1, 0} σ Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring) (fun (a : Nat) (b : Nat) => Nat.decidableLe a b) m n) (Not.decidable (LE.le.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.hasLe.{u1, 0} σ Nat Nat.hasZero (Preorder.toHasLe.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) n m) (Finsupp.decidableLE.{u1, 0} σ Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring) (fun (a : Nat) (b : Nat) => Nat.decidableLe a b) n m))) (coeFn.{max (succ (max u1 u2)) (succ 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(CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.module.{u1, u2, u2} σ R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.module.{u1, u2, u2} σ R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.coeff.{u1, u2} σ R (CommSemiring.toSemiring.{u2} R _inst_1) m) φ) (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (φ : MvPowerSeries.{u2, u1} σ R), Eq.{succ u1} R (MvPolynomial.coeff.{u1, u2} R σ _inst_1 m (MvPowerSeries.truncFun.{u2, u1} σ R _inst_1 n φ)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (LT.lt.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Preorder.toLT.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.preorder.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) m n) (Classical.propDecidable (LT.lt.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Preorder.toLT.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.preorder.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) m n)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.coeff.{u2, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1) m) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) _inst_1)))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (φ : MvPowerSeries.{u2, u1} σ R), Eq.{succ u1} R (MvPolynomial.coeff.{u1, u2} R σ _inst_1 m (MvPowerSeries.truncFun.{u2, u1} σ R _inst_1 n φ)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (LT.lt.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Preorder.toLT.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.preorder.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) m n) (Classical.propDecidable (LT.lt.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Preorder.toLT.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.preorder.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) m n)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.coeff.{u2, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1) m) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_trunc_fun MvPowerSeries.coeff_truncFunₓ'. -/
 theorem coeff_truncFun (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
     (truncFun n φ).coeff m = if m < n then coeff R m φ else 0 := by
@@ -1071,7 +1071,7 @@ variable {R}
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (n : Finsupp.{u1, 0} σ Nat Nat.hasZero) (m : Finsupp.{u1, 0} σ Nat Nat.hasZero) (φ : MvPowerSeries.{u1, u2} σ R), Eq.{succ u2} R (MvPolynomial.coeff.{u2, u1} R σ _inst_1 m (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AddMonoidHom.{max u1 u2, max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.addMonoid.{u1, u2} σ R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))))) (fun (_x : AddMonoidHom.{max u1 u2, max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.addMonoid.{u1, u2} σ R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))))) => (MvPowerSeries.{u1, u2} σ R) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (AddMonoidHom.hasCoeToFun.{max u1 u2, max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.addMonoid.{u1, u2} σ R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))))) (MvPowerSeries.trunc.{u1, u2} σ R _inst_1 n) φ)) (ite.{succ u2} R (LT.lt.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Preorder.toHasLt.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.preorder.{u1, 0} σ Nat Nat.hasZero (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n) (And.decidable (LE.le.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.hasLe.{u1, 0} σ Nat Nat.hasZero (Preorder.toHasLe.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n) (Not (LE.le.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.hasLe.{u1, 0} σ Nat Nat.hasZero (Preorder.toHasLe.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) n m)) (Finsupp.decidableLE.{u1, 0} σ Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring) (fun (a : Nat) (b : Nat) => Nat.decidableLe a b) m n) (Not.decidable (LE.le.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.hasLe.{u1, 0} σ Nat Nat.hasZero (Preorder.toHasLe.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) n m) (Finsupp.decidableLE.{u1, 0} σ Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring) (fun (a : Nat) (b : Nat) => Nat.decidableLe a b) n m))) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.module.{u1, u2, u2} σ R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.module.{u1, u2, u2} σ R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.module.{u1, u2, u2} σ R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.coeff.{u1, u2} σ R (CommSemiring.toSemiring.{u2} R _inst_1) m) φ) (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))))
 but is expected to have type
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(AddMonoidWithOne.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))))) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : MvPowerSeries.{u2, u1} σ R) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (AddHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (AddMonoidHom.{max u1 u2, max u1 u2} (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instAddMonoidMvPowerSeries.{u2, u1} σ R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))))) (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.{u2, u1} σ R _inst_1) (AddZeroClass.toAdd.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instAddMonoidMvPowerSeries.{u2, u1} σ R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (AddZeroClass.toAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, max u2 u1, max u2 u1} (AddMonoidHom.{max u1 u2, max u1 u2} (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instAddMonoidMvPowerSeries.{u2, u1} σ R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))))) (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instAddMonoidMvPowerSeries.{u2, u1} σ R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (AddMonoidHom.addMonoidHomClass.{max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instAddMonoidMvPowerSeries.{u2, u1} σ R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))))))) (MvPowerSeries.trunc.{u2, u1} σ R _inst_1 n) φ)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (LT.lt.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Preorder.toLT.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.preorder.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) m n) (Classical.propDecidable (LT.lt.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Preorder.toLT.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.preorder.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) m n)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.coeff.{u2, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1) m) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) _inst_1)))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (φ : MvPowerSeries.{u2, u1} σ R), Eq.{succ u1} R (MvPolynomial.coeff.{u1, u2} R σ _inst_1 m (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (AddMonoidHom.{max u1 u2, max u1 u2} (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instAddMonoidMvPowerSeries.{u2, u1} σ R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))))) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : MvPowerSeries.{u2, u1} σ R) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (AddHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (AddMonoidHom.{max u1 u2, max u1 u2} (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instAddMonoidMvPowerSeries.{u2, u1} σ R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))))) (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.{u2, u1} σ R _inst_1) (AddZeroClass.toAdd.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instAddMonoidMvPowerSeries.{u2, u1} σ R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (AddZeroClass.toAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, max u2 u1, max u2 u1} (AddMonoidHom.{max u1 u2, max u1 u2} (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instAddMonoidMvPowerSeries.{u2, u1} σ R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))))) (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instAddMonoidMvPowerSeries.{u2, u1} σ R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (AddMonoidHom.addMonoidHomClass.{max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instAddMonoidMvPowerSeries.{u2, u1} σ R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoidWithOne.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))))))) (MvPowerSeries.trunc.{u2, u1} σ R _inst_1 n) φ)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (LT.lt.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Preorder.toLT.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.preorder.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) m n) (Classical.propDecidable (LT.lt.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Preorder.toLT.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.preorder.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) m n)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.coeff.{u2, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1) m) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_trunc MvPowerSeries.coeff_truncₓ'. -/
 theorem coeff_trunc (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
     (trunc R n φ).coeff m = if m < n then coeff R m φ else 0 := by simp [Trunc, coeff_trunc_fun]
@@ -1126,7 +1126,7 @@ variable [Semiring R]
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {s : σ} {n : Nat} {φ : MvPowerSeries.{u1, u2} σ R}, Iff (Dvd.Dvd.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (semigroupDvd.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (SemigroupWithZero.toSemigroup.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (NonUnitalSemiring.toSemigroupWithZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonUnitalSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (MvPowerSeries.{u1, u2} σ R) Nat (MvPowerSeries.{u1, u2} σ R) (instHPow.{max u1 u2, 0} (MvPowerSeries.{u1, u2} σ R) Nat (Monoid.Pow.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MonoidWithZero.toMonoid.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (Semiring.toMonoidWithZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))))) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s) n) φ) (forall (m : Finsupp.{u1, 0} σ Nat Nat.hasZero), (LT.lt.{0} Nat Nat.hasLt (coeFn.{succ u1, succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u1, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u1, 0} σ Nat Nat.hasZero) m s) n) -> (Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 m) φ) (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))))))
 but is expected to have type
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+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {s : σ} {n : Nat} {φ : MvPowerSeries.{u2, u1} σ R}, Iff (Dvd.dvd.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (semigroupDvd.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (SemigroupWithZero.toSemigroup.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonUnitalSemiring.toSemigroupWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonUnitalSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPowerSeries.{u2, u1} σ R) Nat (MvPowerSeries.{u2, u1} σ R) (instHPow.{max u2 u1, 0} (MvPowerSeries.{u2, u1} σ R) Nat (Monoid.Pow.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MonoidWithZero.toMonoid.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toMonoidWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) n) φ) (forall (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), (LT.lt.{0} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) s) instLTNat (FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (_x : σ) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) _x) (Finsupp.funLike.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) m s) n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 m) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.X_pow_dvd_iff MvPowerSeries.X_pow_dvd_iffₓ'. -/
 theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
     (X s : MvPowerSeries σ R) ^ n ∣ φ ↔ ∀ m : σ →₀ ℕ, m s < n → coeff R m φ = 0 :=
@@ -1188,7 +1188,7 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {s : σ} {φ : MvPowerSeries.{u1, u2} σ R}, Iff (Dvd.Dvd.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (semigroupDvd.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (SemigroupWithZero.toSemigroup.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (NonUnitalSemiring.toSemigroupWithZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonUnitalSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))))) (MvPowerSeries.X.{u1, u2} σ R _inst_1 s) φ) (forall (m : Finsupp.{u1, 0} σ Nat Nat.hasZero), (Eq.{1} Nat (coeFn.{succ u1, succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u1, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u1, 0} σ Nat Nat.hasZero) m s) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R _inst_1 _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MvPowerSeries.coeff.{u1, u2} σ R _inst_1 m) φ) (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))))))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {s : σ} {φ : MvPowerSeries.{u2, u1} σ R}, Iff (Dvd.dvd.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (semigroupDvd.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (SemigroupWithZero.toSemigroup.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonUnitalSemiring.toSemigroupWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonUnitalSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) φ) (forall (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), (Eq.{1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) s) (FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (_x : σ) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) _x) (Finsupp.funLike.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) m s) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) s) 0 (instOfNatNat 0))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 m) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) _inst_1))))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {s : σ} {φ : MvPowerSeries.{u2, u1} σ R}, Iff (Dvd.dvd.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (semigroupDvd.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (SemigroupWithZero.toSemigroup.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonUnitalSemiring.toSemigroupWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonUnitalSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) φ) (forall (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), (Eq.{1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) s) (FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (_x : σ) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) _x) (Finsupp.funLike.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) m s) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) s) 0 (instOfNatNat 0))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 m) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.X_dvd_iff MvPowerSeries.X_dvd_iffₓ'. -/
 theorem X_dvd_iff {s : σ} {φ : MvPowerSeries σ R} :
     (X s : MvPowerSeries σ R) ∣ φ ↔ ∀ m : σ →₀ ℕ, m s = 0 → coeff R m φ = 0 :=
@@ -1228,7 +1228,7 @@ protected noncomputable def inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerS
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Ring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (n : Finsupp.{u1, 0} σ Nat Nat.hasZero) (a : R) (φ : MvPowerSeries.{u1, u2} σ R), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.module.{u1, u2, u2} σ R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.module.{u1, u2, u2} σ R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.module.{u1, u2, u2} σ R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.coeff.{u1, u2} σ R (Ring.toSemiring.{u2} R _inst_1) n) (MvPowerSeries.inv.aux.{u1, u2} σ R _inst_1 a φ)) (ite.{succ u2} R (Eq.{succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) n (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero))))) (Finsupp.decidableEq.{u1, 0} σ Nat Nat.hasZero (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => Nat.decidableEq a b) n (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_inv_aux MvPowerSeries.coeff_inv_auxₓ'. -/
 theorem coeff_inv_aux [DecidableEq σ] (n : σ →₀ ℕ) (a : R) (φ : MvPowerSeries σ R) :
     coeff R n (inv.aux a φ) =
@@ -1257,7 +1257,7 @@ def invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) : MvPowerSeries σ R :=
 lean 3 declaration is
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 but is expected to have type
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(Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Inv.inv.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.instInv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) u)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : 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(Ring.toSemiring.{u1} R _inst_1)))) u))) (Finset.sum.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (Prod.{u2, u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) _inst_1)))) (Finsupp.antidiagonal.{u2} σ n) (fun (x : 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(LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) x) n) (Classical.propDecidable (LT.lt.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Preorder.toLT.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.preorder.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Prod.snd.{u2, u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) x) n)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) ((fun 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(LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) x) n) (Classical.propDecidable (LT.lt.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Preorder.toLT.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.preorder.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Prod.snd.{u2, u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) x) n)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) ((fun 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R 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(LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) x)) (MvPowerSeries.invOfUnit.{u2, u1} σ R _inst_1 φ u))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) φ) _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_inv_of_unit MvPowerSeries.coeff_invOfUnitₓ'. -/
 theorem coeff_invOfUnit [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (u : Rˣ) :
     coeff R n (invOfUnit φ u) =
@@ -1331,7 +1331,7 @@ instance [LocalRing R] : LocalRing (MvPowerSeries σ R) :=
     by
     intro φ
     rcases LocalRing.isUnit_or_isUnit_one_sub_self (constant_coeff σ R φ) with (⟨u, h⟩ | ⟨u, h⟩) <;>
-        [left, right] <;>
+        [left;right] <;>
       · refine' isUnit_of_mul_eq_one _ _ (mul_inv_of_unit _ u _)
         simpa using h.symm
 
@@ -1382,7 +1382,7 @@ instance : Inv (MvPowerSeries σ k) :=
 lean 3 declaration is
   forall {σ : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u2} k] [_inst_2 : DecidableEq.{succ u1} σ] (n : Finsupp.{u1, 0} σ Nat Nat.hasZero) (φ : MvPowerSeries.{u1, u2} σ k), Eq.{succ u2} k (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} k k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (MvPowerSeries.{u1, u2} σ k) k (MvPowerSeries.addCommMonoid.{u1, u2} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (MvPowerSeries.module.{u1, u2, u2} σ k k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} k k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (MvPowerSeries.{u1, u2} σ k) k (MvPowerSeries.addCommMonoid.{u1, u2} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (MvPowerSeries.module.{u1, u2, u2} σ k k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) => (MvPowerSeries.{u1, u2} σ k) -> k) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} k k (MvPowerSeries.{u1, u2} σ k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (MvPowerSeries.module.{u1, u2, u2} σ k k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (MvPowerSeries.coeff.{u1, u2} σ k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) n) (Inv.inv.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (MvPowerSeries.hasInv.{u1, u2} σ k _inst_1) φ)) (ite.{succ u2} k (Eq.{succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) n (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero))))) (Finsupp.decidableEq.{u1, 0} σ Nat Nat.hasZero (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => Nat.decidableEq a b) n (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero))))) (Inv.inv.{u2} k (DivInvMonoid.toHasInv.{u2} k (DivisionRing.toDivInvMonoid.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (RingHom.{max u1 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Nat.hasZero) (Finsupp.{u1, 0} σ Nat Nat.hasZero) x)))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (Distrib.toHasMul.{u2} k (Ring.toDistrib.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} k k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (MvPowerSeries.{u1, u2} σ k) k (MvPowerSeries.addCommMonoid.{u1, u2} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))) 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_inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (MvPowerSeries.module.{u1, u2, u2} σ k k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (MvPowerSeries.coeff.{u1, u2} σ k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (Prod.fst.{u1, u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.{u1, 0} σ Nat Nat.hasZero) x)) φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} k k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (MvPowerSeries.{u1, u2} σ k) k (MvPowerSeries.addCommMonoid.{u1, u2} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))) 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(Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (MvPowerSeries.{u1, u2} σ k) k (MvPowerSeries.addCommMonoid.{u1, u2} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (MvPowerSeries.module.{u1, u2, u2} σ k k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) => (MvPowerSeries.{u1, u2} σ k) -> k) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} k k (MvPowerSeries.{u1, u2} σ k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (MvPowerSeries.module.{u1, u2, u2} σ k k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (MvPowerSeries.coeff.{u1, u2} σ k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (Prod.snd.{u1, u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.{u1, 0} σ Nat Nat.hasZero) x)) (Inv.inv.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (MvPowerSeries.hasInv.{u1, u2} σ k _inst_1) φ))) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))))))))))
 but is expected to have type
-  forall {σ : Type.{u2}} {k : Type.{u1}} [_inst_1 : Field.{u1} k] [_inst_2 : DecidableEq.{succ u2} σ] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (φ : MvPowerSeries.{u2, u1} σ k), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) (Inv.inv.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instInvMvPowerSeries.{u2, u1} σ k _inst_1) φ)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (MvPowerSeries.{u2, u1} σ k) k 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(LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.preorder.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Prod.snd.{u2, u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) x) n)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) (Inv.inv.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instInvMvPowerSeries.{u2, u1} σ k _inst_1) φ)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) _inst_1)))))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k 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(Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (MvPowerSeries.{u2, u1} σ k) (fun (_x : MvPowerSeries.{u2, u1} σ k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} k k (MvPowerSeries.{u2, u1} σ k) k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.coeff.{u2, u1} σ k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Prod.fst.{u2, u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) x)) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) 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(Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (MvPowerSeries.{u2, u1} σ k) (fun (_x : MvPowerSeries.{u2, u1} σ k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} k k (MvPowerSeries.{u2, u1} σ k) k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.coeff.{u2, u1} σ k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Prod.snd.{u2, u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) x)) (Inv.inv.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instInvMvPowerSeries.{u2, u1} σ k _inst_1) φ))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) φ) _inst_1))))))))))
+  forall {σ : Type.{u2}} {k : Type.{u1}} [_inst_1 : Field.{u1} k] [_inst_2 : DecidableEq.{succ u2} σ] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (φ : MvPowerSeries.{u2, u1} σ k), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ k) => k) (Inv.inv.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instInvMvPowerSeries.{u2, u1} σ k _inst_1) φ)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (MvPowerSeries.{u2, u1} σ k) k (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (MvPowerSeries.{u2, u1} σ k) (fun (_x : MvPowerSeries.{u2, u1} σ k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ k) => k) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} k k (MvPowerSeries.{u2, u1} σ k) k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k 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(Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (MvPowerSeries.{u2, u1} σ k) k (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (MvPowerSeries.{u2, u1} σ k) (fun (_x : MvPowerSeries.{u2, u1} σ k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ k) => k) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} k k (MvPowerSeries.{u2, u1} σ k) k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.coeff.{u2, u1} σ k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Prod.fst.{u2, u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) x)) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) 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(Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (MvPowerSeries.{u2, u1} σ k) (fun (_x : MvPowerSeries.{u2, u1} σ k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ k) => k) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} k k (MvPowerSeries.{u2, u1} σ k) k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.coeff.{u2, u1} σ k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Prod.snd.{u2, u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) x)) (Inv.inv.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instInvMvPowerSeries.{u2, u1} σ k _inst_1) φ))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ k) => k) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ k) => k) φ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ k) => k) φ) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ k) => k) φ) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ k) => k) φ) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ k) => k) φ) _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_inv MvPowerSeries.coeff_invₓ'. -/
 theorem coeff_inv [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ k) :
     coeff k n φ⁻¹ =
@@ -1602,7 +1602,7 @@ theorem coe_def : (φ : MvPowerSeries σ R) = fun n => coeff n φ :=
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{u1, u2} σ R _inst_1) (n : Finsupp.{u1, 0} σ Nat Nat.hasZero), Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearMap.{u2, u2, max u1 u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.module.{u1, u2, u2} σ R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : LinearMap.{u2, u2, max u1 u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPowerSeries.{u1, u2} σ R) R (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.module.{u1, u2, u2} σ R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => (MvPowerSeries.{u1, u2} σ R) -> R) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u2} R R (MvPowerSeries.{u1, u2} σ R) R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.module.{u1, u2, u2} σ R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.coeff.{u1, u2} σ R (CommSemiring.toSemiring.{u2} R _inst_1) n) ((fun (a : Sort.{max (succ u1) (succ u2)}) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{max (succ u1) (succ u2), max (succ u1) (succ u2)} a b] => self.0) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u2} σ R) (HasLiftT.mk.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u2} σ R) (CoeTCₓ.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u2} σ R) (coeBase.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u2} σ R) (MvPolynomial.coeToMvPowerSeries.{u1, u2} σ R _inst_1)))) φ)) (MvPolynomial.coeff.{u2, u1} R σ _inst_1 n φ)
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : MvPolynomial.{u2, u1} σ R _inst_1) (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) (MvPolynomial.toMvPowerSeries.{u2, u1} σ R _inst_1 φ)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.coeff.{u2, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1) n) (MvPolynomial.toMvPowerSeries.{u2, u1} σ R _inst_1 φ)) (MvPolynomial.coeff.{u1, u2} R σ _inst_1 n φ)
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : MvPolynomial.{u2, u1} σ R _inst_1) (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) (MvPolynomial.toMvPowerSeries.{u2, u1} σ R _inst_1 φ)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.coeff.{u2, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1) n) (MvPolynomial.toMvPowerSeries.{u2, u1} σ R _inst_1 φ)) (MvPolynomial.coeff.{u1, u2} R σ _inst_1 n φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coeff_coe MvPolynomial.coeff_coeₓ'. -/
 @[simp, norm_cast]
 theorem coeff_coe (n : σ →₀ ℕ) : MvPowerSeries.coeff R n ↑φ = coeff n φ :=
@@ -1613,7 +1613,7 @@ theorem coeff_coe (n : σ →₀ ℕ) : MvPowerSeries.coeff R n ↑φ = coeff n
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (n : Finsupp.{u1, 0} σ Nat Nat.hasZero) (a : R), Eq.{max (succ u1) (succ u2)} (MvPowerSeries.{u1, u2} σ R) ((fun (a : Sort.{max (succ u1) (succ u2)}) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{max (succ u1) (succ u2), max (succ u1) (succ u2)} a b] => self.0) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u2} σ R) (HasLiftT.mk.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u2} σ R) (CoeTCₓ.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u2} σ R) (coeBase.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u2} σ R) (MvPolynomial.coeToMvPowerSeries.{u1, u2} σ R _inst_1)))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPolynomial.monomial.{u2, u1} R σ _inst_1 n) a)) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPowerSeries.module.{u1, u2, u2} σ R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPowerSeries.{u1, u2} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPowerSeries.module.{u1, u2, u2} σ R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => R -> (MvPowerSeries.{u1, u2} σ R)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPowerSeries.{u1, u2} σ R) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPowerSeries.module.{u1, u2, u2} σ R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPowerSeries.monomial.{u1, u2} σ R (CommSemiring.toSemiring.{u2} R _inst_1) n) a)
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.toMvPowerSeries.{u2, u1} σ R _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 n) a)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPowerSeries.{u2, u1} σ R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPowerSeries.{u2, u1} σ R) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.monomial.{u2, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1) n) a)
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ R) (MvPolynomial.toMvPowerSeries.{u2, u1} σ R _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 n) a)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPowerSeries.{u2, u1} σ R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPowerSeries.{u2, u1} σ R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPowerSeries.{u2, u1} σ R) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPowerSeries.monomial.{u2, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1) n) a)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_monomial MvPolynomial.coe_monomialₓ'. -/
 @[simp, norm_cast]
 theorem coe_monomial (n : σ →₀ ℕ) (a : R) :
@@ -1826,7 +1826,7 @@ def coeToMvPowerSeries.algHom : MvPolynomial σ R →ₐ[R] MvPowerSeries σ A :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{u1, u2} σ R _inst_1) (A : Type.{u3}) [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)], Eq.{max (succ u1) (succ u3)} (MvPowerSeries.{u1, u3} σ A) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (AlgHom.{u2, max u1 u2, max u1 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u3} σ A) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPowerSeries.semiring.{u1, u3} σ A (CommSemiring.toSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPowerSeries.algebra.{u1, u2, u3} σ R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u3} σ A) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPowerSeries.semiring.{u1, u3} σ A (CommSemiring.toSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPowerSeries.algebra.{u1, u2, u3} σ R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPowerSeries.{u1, u3} σ A)) ([anonymous].{u2, max u1 u2, max u1 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u3} σ A) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPowerSeries.semiring.{u1, u3} σ A (CommSemiring.toSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPowerSeries.algebra.{u1, u2, u3} σ R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (MvPolynomial.coeToMvPowerSeries.algHom.{u1, u2, u3} σ R _inst_1 A _inst_2 _inst_3) φ) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ A) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPowerSeries.{u1, u3} σ A) (MvPowerSeries.semiring.{u1, u3} σ A (CommSemiring.toSemiring.{u3} A _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ A) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPowerSeries.{u1, u3} σ A) (MvPowerSeries.semiring.{u1, u3} σ A (CommSemiring.toSemiring.{u3} A _inst_2)))) => (MvPowerSeries.{u1, u2} σ R) -> (MvPowerSeries.{u1, u3} σ A)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ A) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPowerSeries.{u1, u3} σ A) (MvPowerSeries.semiring.{u1, u3} σ A (CommSemiring.toSemiring.{u3} A _inst_2)))) (MvPowerSeries.map.{u1, u2, u3} σ R A (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A _inst_2) (algebraMap.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) ((fun (a : Sort.{max (succ u1) (succ u2)}) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{max (succ u1) (succ u2), max (succ u1) (succ u2)} a b] => self.0) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u2} σ R) (HasLiftT.mk.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u2} σ R) (CoeTCₓ.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u2} σ R) (coeBase.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u2} σ R) (MvPolynomial.coeToMvPowerSeries.{u1, u2} σ R _inst_1)))) φ))
 but is expected to have type
-  forall {σ : Type.{u3}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : MvPolynomial.{u3, u1} σ R _inst_1) (A : Type.{u2}) [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)], Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u3, u1} σ R _inst_1) => MvPowerSeries.{u3, u2} σ A) φ) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u1) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, max u1 u3, max u2 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPowerSeries.{u3, u2} σ A) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u3, u1, u2} σ R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (MvPolynomial.{u3, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u3, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u3, u1} σ R _inst_1) => MvPowerSeries.{u3, u2} σ A) _x) (SMulHomClass.toFunLike.{max (max u2 u1) u3, u1, max u1 u3, max u2 u3} (AlgHom.{u1, max u1 u3, max u2 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPowerSeries.{u3, u2} σ A) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u3, u1, u2} σ R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPowerSeries.{u3, u2} σ A) (SMulZeroClass.toSMul.{u1, max u1 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(Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u2 u3} R (MvPowerSeries.{u3, u2} σ A) (AddMonoid.toZero.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u3} R (MvPowerSeries.{u3, u2} σ A) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} R (MvPowerSeries.{u3, u2} σ A) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)))))) (Module.toDistribMulAction.{u1, max u2 u3} R (MvPowerSeries.{u3, u2} σ A) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u1, max u2 u3} R (MvPowerSeries.{u3, u2} σ A) _inst_1 (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)) (MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u3, u1, u2} σ R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u3, u1, max u1 u3, max u2 u3} (AlgHom.{u1, max u1 u3, max u2 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPowerSeries.{u3, u2} σ A) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u3, u1, u2} σ R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPowerSeries.{u3, u2} σ A) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u3} R (MvPowerSeries.{u3, u2} σ A) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) 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(MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u3, u1, u2} σ R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPowerSeries.{u3, u2} σ A) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, max u1 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u3, u1, u2} σ R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (AlgHom.{u1, max u1 u3, max u2 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPowerSeries.{u3, u2} σ A) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u3, u1, u2} σ R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (AlgHom.algHomClass.{u1, max u1 u3, max u2 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPowerSeries.{u3, u2} σ A) _inst_1 (CommSemiring.toSemiring.{max u3 u1} 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(CommSemiring.toSemiring.{u2} A _inst_2)))) (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{max u3 u1, max u3 u2} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MvPowerSeries.map.{u3, u1, u2} σ R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A 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+  forall {σ : Type.{u3}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : MvPolynomial.{u3, u1} σ R _inst_1) (A : Type.{u2}) [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)], Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u1} σ R _inst_1) => MvPowerSeries.{u3, u2} σ A) φ) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u1) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, max u1 u3, max u2 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPowerSeries.{u3, u2} σ A) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u3, u1, u2} σ R 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(MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u3, u1, u2} σ R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPowerSeries.{u3, u2} σ A) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, max u1 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u3} R (MvPowerSeries.{u3, u2} σ A) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u1, max u2 u3} R (MvPowerSeries.{u3, u2} σ A) _inst_1 (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)) (MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u3, u1, u2} σ R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u3, max u2 u3, max (max u2 u1) u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPowerSeries.{u3, u2} σ A) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u3, u1, u2} σ R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (AlgHom.{u1, max u1 u3, max u2 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPowerSeries.{u3, u2} σ A) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u3, u1, u2} σ R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (AlgHom.algHomClass.{u1, max u1 u3, max u2 u3} R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPowerSeries.{u3, u2} σ A) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u3, u1, u2} σ R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (MvPolynomial.coeToMvPowerSeries.algHom.{u3, u1, u2} σ R _inst_1 A _inst_2 _inst_3) φ) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u1), max (succ u3) (succ u2)} (RingHom.{max u1 u3, max u2 u3} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)))) (MvPowerSeries.{u3, u1} σ R) (fun (_x : MvPowerSeries.{u3, u1} σ R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPowerSeries.{u3, u1} σ R) => MvPowerSeries.{u3, u2} σ A) _x) (MulHomClass.toFunLike.{max (max u3 u1) u2, max u3 u1, max u3 u2} (RingHom.{max u1 u3, max u2 u3} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)))) (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.{u3, u2} σ A) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (MvPowerSeries.{u3, u2} σ A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u3 u1) u2, max u3 u1, max u3 u2} (RingHom.{max u1 u3, max u2 u3} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)))) (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.{u3, u2} σ A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u3 u1) u2, max u3 u1, max u3 u2} (RingHom.{max u1 u3, max u2 u3} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2)))) (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{max u3 u1, max u3 u2} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.{u3, u2} σ A) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPowerSeries.{u3, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u1} σ R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MvPowerSeries.map.{u3, u1, u2} σ R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A _inst_2) (algebraMap.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (MvPolynomial.toMvPowerSeries.{u3, u1} σ R _inst_1 φ))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_to_mv_power_series.alg_hom_apply MvPolynomial.coeToMvPowerSeries.algHom_applyₓ'. -/
 @[simp]
 theorem coeToMvPowerSeries.algHom_apply :
@@ -1967,7 +1967,7 @@ theorem coeff_def {s : Unit →₀ ℕ} {n : ℕ} (h : s () = n) : coeff R n = M
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {ψ : PowerSeries.{u1} R}, (forall (n : Nat), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) ψ)) -> (Eq.{succ u1} (PowerSeries.{u1} R) φ ψ)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {ψ : PowerSeries.{u1} R}, (forall (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) ψ)) -> (Eq.{succ u1} (PowerSeries.{u1} R) φ ψ)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {ψ : PowerSeries.{u1} R}, (forall (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) ψ)) -> (Eq.{succ u1} (PowerSeries.{u1} R) φ ψ)
 Case conversion may be inaccurate. Consider using '#align power_series.ext PowerSeries.extₓ'. -/
 /-- Two formal power series are equal if all their coefficients are equal.-/
 @[ext]
@@ -1982,7 +1982,7 @@ theorem ext {φ ψ : PowerSeries R} (h : ∀ n, coeff R n φ = coeff R n ψ) : 
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {ψ : PowerSeries.{u1} R}, Iff (Eq.{succ u1} (PowerSeries.{u1} R) φ ψ) (forall (n : Nat), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) ψ))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {ψ : PowerSeries.{u1} R}, Iff (Eq.{succ u1} (PowerSeries.{u1} R) φ ψ) (forall (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) ψ))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {ψ : PowerSeries.{u1} R}, Iff (Eq.{succ u1} (PowerSeries.{u1} R) φ ψ) (forall (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) ψ))
 Case conversion may be inaccurate. Consider using '#align power_series.ext_iff PowerSeries.ext_iffₓ'. -/
 /-- Two formal power series are equal if all their coefficients are equal.-/
 theorem ext_iff {φ ψ : PowerSeries R} : φ = ψ ↔ ∀ n, coeff R n φ = coeff R n ψ :=
@@ -1999,7 +1999,7 @@ def mk {R} (f : ℕ → R) : PowerSeries R := fun s => f (s ())
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (f : Nat -> R), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (PowerSeries.mk.{u1} R f)) (f n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (f : Nat -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.mk.{u1} R 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (PowerSeries.mk.{u1} R f)) (f n)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (f : Nat -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.mk.{u1} R 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (PowerSeries.mk.{u1} R f)) (f n)
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mk PowerSeries.coeff_mkₓ'. -/
 @[simp]
 theorem coeff_mk (n : ℕ) (f : ℕ → R) : coeff R n (mk f) = f n :=
@@ -2010,7 +2010,7 @@ theorem coeff_mk (n : ℕ) (f : ℕ → R) : coeff R n (mk f) = f n :=
 lean 3 declaration is
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 m) (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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) => R -> (PowerSeries.{u1} R)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) (ite.{succ u1} R (Eq.{1} Nat m n) (Nat.decidableEq m n) a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
 but is expected to have type
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(PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 m) (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 (PowerSeries.{u1} R) 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_inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) (FunLike.coe.{succ u1, succ 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(PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 m) (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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) (ite.{succ u1} R (Eq.{1} Nat m n) (instDecidableEqNat m n) a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_monomial PowerSeries.coeff_monomialₓ'. -/
 theorem coeff_monomial (m n : ℕ) (a : R) : coeff R m (monomial R n a) = if m = n then a else 0 :=
   calc
@@ -2023,7 +2023,7 @@ theorem coeff_monomial (m n : ℕ) (a : R) : coeff R m (monomial R n a) = if m =
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R), Eq.{succ u1} (PowerSeries.{u1} 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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) => R -> (PowerSeries.{u1} R)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a) (PowerSeries.mk.{u1} R (fun (m : Nat) => ite.{succ u1} R (Eq.{1} Nat m n) (Nat.decidableEq m n) a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => PowerSeries.{u1} R) a) (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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a) (PowerSeries.mk.{u1} R (fun (m : Nat) => ite.{succ u1} R (Eq.{1} Nat m n) (instDecidableEqNat m n) a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) a) (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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a) (PowerSeries.mk.{u1} R (fun (m : Nat) => ite.{succ u1} R (Eq.{1} Nat m n) (instDecidableEqNat m n) a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align power_series.monomial_eq_mk PowerSeries.monomial_eq_mkₓ'. -/
 theorem monomial_eq_mk (n : ℕ) (a : R) : monomial R n a = mk fun m => if m = n then a else 0 :=
   ext fun m => by rw [coeff_monomial, coeff_mk]
@@ -2033,7 +2033,7 @@ theorem monomial_eq_mk (n : ℕ) (a : R) : monomial R n a = mk fun m => if m = n
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) => R -> (PowerSeries.{u1} R)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) a
 but is expected to have type
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(PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) a
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} 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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) (FunLike.coe.{succ u1, succ 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(PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) a
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_monomial_same PowerSeries.coeff_monomial_sameₓ'. -/
 @[simp]
 theorem coeff_monomial_same (n : ℕ) (a : R) : coeff R n (monomial R n a) = a :=
@@ -2094,7 +2094,7 @@ theorem commute_X (φ : PowerSeries R) : Commute φ X :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((PowerSeries.{u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.constantCoeff.{u1} R _inst_1))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (forall (ᾰ : PowerSeries.{u1} R), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (forall (ᾰ : PowerSeries.{u1} R), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_eq_constant_coeff PowerSeries.coeff_zero_eq_constantCoeffₓ'. -/
 @[simp]
 theorem coeff_zero_eq_constantCoeff : ⇑(coeff R 0) = constantCoeff R :=
@@ -2107,7 +2107,7 @@ theorem coeff_zero_eq_constantCoeff : ⇑(coeff R 0) = constantCoeff R :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) φ) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) φ) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) φ) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_eq_constant_coeff_apply PowerSeries.coeff_zero_eq_constantCoeff_applyₓ'. -/
 theorem coeff_zero_eq_constantCoeff_apply (φ : PowerSeries R) : coeff R 0 φ = constantCoeff R φ :=
   by rw [coeff_zero_eq_constant_coeff] <;> rfl
@@ -2117,7 +2117,7 @@ theorem coeff_zero_eq_constantCoeff_apply (φ : PowerSeries R) : coeff R 0 φ =
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (R -> (PowerSeries.{u1} 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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) => R -> (PowerSeries.{u1} R)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) => R -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (PowerSeries.C.{u1} R _inst_1))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (forall (ᾰ : R), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => PowerSeries.{u1} R) 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)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (forall (ᾰ : R), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) 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)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1))
 Case conversion may be inaccurate. Consider using '#align power_series.monomial_zero_eq_C PowerSeries.monomial_zero_eq_Cₓ'. -/
 @[simp]
 theorem monomial_zero_eq_C : ⇑(monomial R 0) = C R := by
@@ -2128,7 +2128,7 @@ theorem monomial_zero_eq_C : ⇑(monomial R 0) = C R := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), Eq.{succ u1} (PowerSeries.{u1} 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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) => R -> (PowerSeries.{u1} R)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) a) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) => R -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (PowerSeries.C.{u1} R _inst_1) a)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => PowerSeries.{u1} R) a) (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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) a) (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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a)
 Case conversion may be inaccurate. Consider using '#align power_series.monomial_zero_eq_C_apply PowerSeries.monomial_zero_eq_C_applyₓ'. -/
 theorem monomial_zero_eq_C_apply (a : R) : monomial R 0 a = C R a := by simp
 #align power_series.monomial_zero_eq_C_apply PowerSeries.monomial_zero_eq_C_apply
@@ -2137,7 +2137,7 @@ theorem monomial_zero_eq_C_apply (a : R) : monomial R 0 a = C R a := by simp
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) => R -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (PowerSeries.C.{u1} R _inst_1) a)) (ite.{succ u1} R (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Nat.decidableEq n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a)) (ite.{succ u1} R (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (instDecidableEqNat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a)) (ite.{succ u1} R (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (instDecidableEqNat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_C PowerSeries.coeff_Cₓ'. -/
 theorem coeff_C (n : ℕ) (a : R) : coeff R n (C R a : PowerSeries R) = if n = 0 then a else 0 := by
   rw [← monomial_zero_eq_C_apply, coeff_monomial]
@@ -2147,7 +2147,7 @@ theorem coeff_C (n : ℕ) (a : R) : coeff R n (C R a : PowerSeries R) = if n = 0
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) => R -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (PowerSeries.C.{u1} R _inst_1) a)) a
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a)) a
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a)) a
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_C PowerSeries.coeff_zero_Cₓ'. -/
 @[simp]
 theorem coeff_zero_C (a : R) : coeff R 0 (C R a) = a := by
@@ -2158,7 +2158,7 @@ theorem coeff_zero_C (a : R) : coeff R 0 (C R a) = a := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (PowerSeries.{u1} R) (PowerSeries.X.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) => R -> (PowerSeries.{u1} R)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (PowerSeries.{u1} R) (PowerSeries.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)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (PowerSeries.{u1} R) (PowerSeries.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)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align power_series.X_eq PowerSeries.X_eqₓ'. -/
 theorem X_eq : (X : PowerSeries R) = monomial R 1 1 :=
   rfl
@@ -2168,7 +2168,7 @@ theorem X_eq : (X : PowerSeries R) = monomial R 1 1 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (PowerSeries.X.{u1} R _inst_1)) (ite.{succ u1} R (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Nat.decidableEq n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (PowerSeries.X.{u1} R _inst_1)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (instDecidableEqNat n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) _inst_1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) _inst_1)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (PowerSeries.X.{u1} R _inst_1)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (instDecidableEqNat n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) _inst_1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_X PowerSeries.coeff_Xₓ'. -/
 theorem coeff_X (n : ℕ) : coeff R n (X : PowerSeries R) = if n = 1 then 1 else 0 := by
   rw [X_eq, coeff_monomial]
@@ -2178,7 +2178,7 @@ theorem coeff_X (n : ℕ) : coeff R n (X : PowerSeries R) = if n = 1 then 1 else
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (PowerSeries.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (PowerSeries.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (PowerSeries.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_X PowerSeries.coeff_zero_Xₓ'. -/
 @[simp]
 theorem coeff_zero_X : coeff R 0 (X : PowerSeries R) = 0 := by
@@ -2189,7 +2189,7 @@ theorem coeff_zero_X : coeff R 0 (X : PowerSeries R) = 0 := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (PowerSeries.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (PowerSeries.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (PowerSeries.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) _inst_1)))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_one_X PowerSeries.coeff_one_Xₓ'. -/
 @[simp]
 theorem coeff_one_X : coeff R 1 (X : PowerSeries R) = 1 := by rw [coeff_X, if_pos rfl]
@@ -2210,7 +2210,7 @@ theorem X_ne_zero [Nontrivial R] : (X : PowerSeries R) ≠ 0 := fun H => by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} (PowerSeries.{u1} R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) => R -> (PowerSeries.{u1} R)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} (PowerSeries.{u1} R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} (PowerSeries.{u1} R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align power_series.X_pow_eq PowerSeries.X_pow_eqₓ'. -/
 theorem X_pow_eq (n : ℕ) : (X : PowerSeries R) ^ n = monomial R n 1 :=
   MvPowerSeries.X_pow_eq _ n
@@ -2220,7 +2220,7 @@ theorem X_pow_eq (n : ℕ) : (X : PowerSeries R) ^ n = monomial R n 1 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (m : Nat) (n : Nat), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 m) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (ite.{succ u1} R (Eq.{1} Nat m n) (Nat.decidableEq m n) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
 but is expected to have type
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(Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 m) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (Eq.{1} Nat m n) (instDecidableEqNat m n) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) _inst_1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) _inst_1)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (m : Nat) (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 m) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (Eq.{1} Nat m n) (instDecidableEqNat m n) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) _inst_1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow PowerSeries.coeff_X_powₓ'. -/
 theorem coeff_X_pow (m n : ℕ) : coeff R m ((X : PowerSeries R) ^ n) = if m = n then 1 else 0 := by
   rw [X_pow_eq, coeff_monomial]
@@ -2230,7 +2230,7 @@ theorem coeff_X_pow (m n : ℕ) : coeff R m ((X : PowerSeries R) ^ n) = if m = n
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) _inst_1)))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow_self PowerSeries.coeff_X_pow_selfₓ'. -/
 @[simp]
 theorem coeff_X_pow_self (n : ℕ) : coeff R n ((X : PowerSeries R) ^ n) = 1 := by
@@ -2241,7 +2241,7 @@ theorem coeff_X_pow_self (n : ℕ) : coeff R n ((X : PowerSeries R) ^ n) = 1 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (OfNat.mk.{u1} (PowerSeries.{u1} R) 1 (One.one.{u1} (PowerSeries.{u1} R) (AddMonoidWithOne.toOne.{u1} (PowerSeries.{u1} R) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))))))) (ite.{succ u1} R (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Nat.decidableEq n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (instDecidableEqNat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) _inst_1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_one PowerSeries.coeff_oneₓ'. -/
 @[simp]
 theorem coeff_one (n : ℕ) : coeff R n (1 : PowerSeries R) = if n = 0 then 1 else 0 :=
@@ -2252,7 +2252,7 @@ theorem coeff_one (n : ℕ) : coeff R n (1 : PowerSeries R) = if n = 0 then 1 el
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (OfNat.mk.{u1} (PowerSeries.{u1} R) 1 (One.one.{u1} (PowerSeries.{u1} R) (AddMonoidWithOne.toOne.{u1} (PowerSeries.{u1} R) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) _inst_1)))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_one PowerSeries.coeff_zero_oneₓ'. -/
 theorem coeff_zero_one : coeff R 0 (1 : PowerSeries R) = 1 :=
   coeff_zero_C 1
@@ -2262,7 +2262,7 @@ theorem coeff_zero_one : coeff R 0 (1 : PowerSeries R) = 1 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) φ ψ)) (Finset.sum.{u1, 0} R (Prod.{0, 0} Nat Nat) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finset.Nat.antidiagonal n) (fun (p : Prod.{0, 0} Nat Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (Prod.fst.{0, 0} Nat Nat p)) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (Prod.snd.{0, 0} Nat Nat p)) ψ)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) (Finset.sum.{u1, 0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Prod.{0, 0} Nat Nat) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1))) (Finset.Nat.antidiagonal n) (fun (p : Prod.{0, 0} Nat Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) ψ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (Prod.fst.{0, 0} Nat Nat p)) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (Prod.snd.{0, 0} Nat Nat p)) ψ)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) (Finset.sum.{u1, 0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Prod.{0, 0} Nat Nat) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1))) (Finset.Nat.antidiagonal n) (fun (p : Prod.{0, 0} Nat Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) ψ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (Prod.fst.{0, 0} Nat Nat p)) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (Prod.snd.{0, 0} Nat Nat p)) ψ)))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul PowerSeries.coeff_mulₓ'. -/
 theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
     coeff R n (φ * ψ) = ∑ p in Finset.Nat.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ :=
@@ -2289,7 +2289,7 @@ theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R) (a : R), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) φ (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) => R -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (PowerSeries.C.{u1} R _inst_1) a))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) a)
 but is expected to have type
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(RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a))) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) a)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a))) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) a)
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_C PowerSeries.coeff_mul_Cₓ'. -/
 @[simp]
 theorem coeff_mul_C (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (φ * C R a) = coeff R n φ * a :=
@@ -2300,7 +2300,7 @@ theorem coeff_mul_C (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (φ * C R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R) (a : R), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) => R -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (PowerSeries.C.{u1} R _inst_1) a) φ)) (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))))) a (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (PowerSeries.{u1} R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a) φ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a) φ)) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (PowerSeries.{u1} R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a) φ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (PowerSeries.{u1} R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) a) φ)) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_C_mul PowerSeries.coeff_C_mulₓ'. -/
 @[simp]
 theorem coeff_C_mul (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (C R a * φ) = a * coeff R n φ :=
@@ -2311,7 +2311,7 @@ theorem coeff_C_mul (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (C R a *
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] [_inst_3 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] (n : Nat) (φ : PowerSeries.{u2} S) (a : R), Eq.{succ u2} S (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (PowerSeries.{u2} S) S (PowerSeries.addCommMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.module.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2)) (fun (_x : LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (PowerSeries.{u2} S) S (PowerSeries.addCommMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.module.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2)) => (PowerSeries.{u2} S) -> S) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S (PowerSeries.{u2} S) S _inst_2 _inst_2 (PowerSeries.addCommMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.module.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.coeff.{u2} S _inst_2 n) (SMul.smul.{u1, u2} R (PowerSeries.{u2} S) (SMulZeroClass.toHasSmul.{u1, u2} R (PowerSeries.{u2} S) (AddZeroClass.toHasZero.{u2} (PowerSeries.{u2} S) (AddMonoid.toAddZeroClass.{u2} (PowerSeries.{u2} S) (AddCommMonoid.toAddMonoid.{u2} (PowerSeries.{u2} S) (PowerSeries.addCommMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R (PowerSeries.{u2} S) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} (PowerSeries.{u2} S) (AddMonoid.toAddZeroClass.{u2} (PowerSeries.{u2} S) (AddCommMonoid.toAddMonoid.{u2} (PowerSeries.{u2} S) (PowerSeries.addCommMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R (PowerSeries.{u2} S) (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} (PowerSeries.{u2} S) (AddMonoid.toAddZeroClass.{u2} (PowerSeries.{u2} S) (AddCommMonoid.toAddMonoid.{u2} (PowerSeries.{u2} S) (PowerSeries.addCommMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R (PowerSeries.{u2} S) _inst_1 (PowerSeries.addCommMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (PowerSeries.module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_3))))) a φ)) (SMul.smul.{u1, u2} R S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_3)))) a (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (PowerSeries.{u2} S) S (PowerSeries.addCommMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.module.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2)) (fun (_x : LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (PowerSeries.{u2} S) S (PowerSeries.addCommMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.module.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2)) => (PowerSeries.{u2} S) -> S) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S (PowerSeries.{u2} S) S _inst_2 _inst_2 (PowerSeries.addCommMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.module.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.coeff.{u2} S _inst_2 n) φ))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] [_inst_3 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] (n : Nat) (φ : PowerSeries.{u2} S) (a : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) (HSMul.hSMul.{u1, u2, u2} R (PowerSeries.{u2} S) (PowerSeries.{u2} S) (instHSMul.{u1, u2} R (PowerSeries.{u2} S) (SMulZeroClass.toSMul.{u1, u2} R (PowerSeries.{u2} S) (PowerSeries.instZeroPowerSeries.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (SMulWithZero.toSMulZeroClass.{u1, u2} R (PowerSeries.{u2} S) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (PowerSeries.instZeroPowerSeries.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R (PowerSeries.{u2} S) (Semiring.toMonoidWithZero.{u1} R _inst_1) (PowerSeries.instZeroPowerSeries.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Module.toMulActionWithZero.{u1, u2} R (PowerSeries.{u2} S) _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_3)))))) a φ)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (PowerSeries.{u2} S) S (PowerSeries.instAddCommMonoidPowerSeries.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2)) (PowerSeries.{u2} S) (fun (_x : PowerSeries.{u2} S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S (PowerSeries.{u2} S) S _inst_2 _inst_2 (PowerSeries.instAddCommMonoidPowerSeries.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.coeff.{u2} S _inst_2 n) (HSMul.hSMul.{u1, u2, u2} R (PowerSeries.{u2} S) (PowerSeries.{u2} S) (instHSMul.{u1, u2} R (PowerSeries.{u2} S) (SMulZeroClass.toSMul.{u1, u2} R (PowerSeries.{u2} S) (PowerSeries.instZeroPowerSeries.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (SMulWithZero.toSMulZeroClass.{u1, u2} R (PowerSeries.{u2} S) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (PowerSeries.instZeroPowerSeries.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R (PowerSeries.{u2} S) (Semiring.toMonoidWithZero.{u1} R _inst_1) (PowerSeries.instZeroPowerSeries.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Module.toMulActionWithZero.{u1, u2} R (PowerSeries.{u2} S) _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_3)))))) a φ)) (HSMul.hSMul.{u1, u2, u2} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) (instHSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) (SMulZeroClass.toSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) _inst_2)) (Module.toMulActionWithZero.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) φ) _inst_2))) _inst_3))))) a (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (PowerSeries.{u2} S) S (PowerSeries.instAddCommMonoidPowerSeries.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2)) (PowerSeries.{u2} S) (fun (_x : PowerSeries.{u2} S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} S) => S) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S (PowerSeries.{u2} S) S _inst_2 _inst_2 (PowerSeries.instAddCommMonoidPowerSeries.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.coeff.{u2} S _inst_2 n) φ))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] [_inst_3 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] (n : Nat) (φ : PowerSeries.{u2} S) (a : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) (HSMul.hSMul.{u1, u2, u2} R (PowerSeries.{u2} S) (PowerSeries.{u2} S) (instHSMul.{u1, u2} R (PowerSeries.{u2} S) (SMulZeroClass.toSMul.{u1, u2} R (PowerSeries.{u2} S) (PowerSeries.instZeroPowerSeries.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (SMulWithZero.toSMulZeroClass.{u1, u2} R (PowerSeries.{u2} S) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (PowerSeries.instZeroPowerSeries.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R (PowerSeries.{u2} S) (Semiring.toMonoidWithZero.{u1} R _inst_1) (PowerSeries.instZeroPowerSeries.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Module.toMulActionWithZero.{u1, u2} R (PowerSeries.{u2} S) _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_3)))))) a φ)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (PowerSeries.{u2} S) S (PowerSeries.instAddCommMonoidPowerSeries.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2)) (PowerSeries.{u2} S) (fun (_x : PowerSeries.{u2} S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S (PowerSeries.{u2} S) S _inst_2 _inst_2 (PowerSeries.instAddCommMonoidPowerSeries.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.coeff.{u2} S _inst_2 n) (HSMul.hSMul.{u1, u2, u2} R (PowerSeries.{u2} S) (PowerSeries.{u2} S) (instHSMul.{u1, u2} R (PowerSeries.{u2} S) (SMulZeroClass.toSMul.{u1, u2} R (PowerSeries.{u2} S) (PowerSeries.instZeroPowerSeries.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (SMulWithZero.toSMulZeroClass.{u1, u2} R (PowerSeries.{u2} S) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (PowerSeries.instZeroPowerSeries.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R (PowerSeries.{u2} S) (Semiring.toMonoidWithZero.{u1} R _inst_1) (PowerSeries.instZeroPowerSeries.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Module.toMulActionWithZero.{u1, u2} R (PowerSeries.{u2} S) _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_3)))))) a φ)) (HSMul.hSMul.{u1, u2, u2} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) (instHSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) (SMulZeroClass.toSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) _inst_2)) (Module.toMulActionWithZero.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) φ) _inst_2))) _inst_3))))) a (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (PowerSeries.{u2} S) S (PowerSeries.instAddCommMonoidPowerSeries.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2)) (PowerSeries.{u2} S) (fun (_x : PowerSeries.{u2} S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} S) => S) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S (PowerSeries.{u2} S) S _inst_2 _inst_2 (PowerSeries.instAddCommMonoidPowerSeries.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.coeff.{u2} S _inst_2 n) φ))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_smul PowerSeries.coeff_smulₓ'. -/
 @[simp]
 theorem coeff_smul {S : Type _} [Semiring S] [Module R S] (n : ℕ) (φ : PowerSeries S) (a : R) :
@@ -2335,7 +2335,7 @@ theorem smul_eq_C_mul (f : PowerSeries R) (a : R) : a • f = C R a * f :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) φ (PowerSeries.X.{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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ (PowerSeries.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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ (PowerSeries.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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ (PowerSeries.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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ (PowerSeries.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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ)
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_succ_mul_X PowerSeries.coeff_succ_mul_Xₓ'. -/
 @[simp]
 theorem coeff_succ_mul_X (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (φ * X) = coeff R n φ :=
@@ -2349,7 +2349,7 @@ theorem coeff_succ_mul_X (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (φ *
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) (PowerSeries.X.{u1} R _inst_1) φ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ)
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_succ_X_mul PowerSeries.coeff_succ_X_mulₓ'. -/
 @[simp]
 theorem coeff_succ_X_mul (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (X * φ) = coeff R n φ :=
@@ -2414,7 +2414,7 @@ theorem constantCoeff_X : constantCoeff R X = 0 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) φ (PowerSeries.X.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))
 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ (PowerSeries.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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ (PowerSeries.X.{u1} R _inst_1))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ (PowerSeries.X.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ (PowerSeries.X.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ (PowerSeries.X.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ (PowerSeries.X.{u1} R _inst_1))) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_mul_X PowerSeries.coeff_zero_mul_Xₓ'. -/
 theorem coeff_zero_mul_X (φ : PowerSeries R) : coeff R 0 (φ * X) = 0 := by simp
 #align power_series.coeff_zero_mul_X PowerSeries.coeff_zero_mul_X
@@ -2423,7 +2423,7 @@ theorem coeff_zero_mul_X (φ : PowerSeries R) : coeff R 0 (φ * X) = 0 := by sim
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) (PowerSeries.X.{u1} R _inst_1) φ)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_X_mul PowerSeries.coeff_zero_X_mulₓ'. -/
 theorem coeff_zero_X_mul (φ : PowerSeries R) : coeff R 0 (X * φ) = 0 := by simp
 #align power_series.coeff_zero_X_mul PowerSeries.coeff_zero_X_mul
@@ -2436,7 +2436,7 @@ section
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : R) (k : Nat) (n : Nat), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) => R -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (PowerSeries.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) k))) (ite.{succ u1} R (Eq.{1} Nat n k) (Nat.decidableEq n k) x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
 but is expected to have type
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(Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (PowerSeries.{u1} R) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) k))) (ite.{succ u1} R (Eq.{1} Nat n k) (instDecidableEqNat n k) x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : R) (k : Nat) (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (PowerSeries.{u1} R) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (PowerSeries.{u1} R) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) x) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) k))) (ite.{succ u1} R (Eq.{1} Nat n k) (instDecidableEqNat n k) x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_C_mul_X_pow PowerSeries.coeff_C_mul_X_powₓ'. -/
 theorem coeff_C_mul_X_pow (x : R) (k n : ℕ) :
     coeff R n (C R x * X ^ k : PowerSeries R) = if n = k then x else 0 := by
@@ -2447,7 +2447,7 @@ theorem coeff_C_mul_X_pow (x : R) (k n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : PowerSeries.{u1} R) (n : Nat) (d : Nat), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d n)) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) p (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 d) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : PowerSeries.{u1} R) (n : Nat) (d : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) p (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d n)) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) p (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 d) p)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : PowerSeries.{u1} R) (n : Nat) (d : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) p (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d n)) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) p (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 d) p)
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_X_powₓ'. -/
 @[simp]
 theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * X ^ n) = coeff R d p :=
@@ -2466,7 +2466,7 @@ theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * X
 lean 3 declaration is
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(instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) p)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 d) p)
 but is expected to have type
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(PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d n)) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 d) p)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : PowerSeries.{u1} R) (n : Nat) (d : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d n)) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 d) p)
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow_mul PowerSeries.coeff_X_pow_mulₓ'. -/
 @[simp]
 theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (X ^ n * p) = coeff R d p :=
@@ -2486,7 +2486,7 @@ theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (X ^ n
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : PowerSeries.{u1} R) (n : Nat) (d : Nat), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 d) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) p (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n))) (ite.{succ u1} R (LE.le.{0} Nat Nat.hasLe n d) (Nat.decidableLe n d) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) d n)) p) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
 but is expected to have type
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(PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 d) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) p (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n))) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) p) (LE.le.{0} Nat instLENat n d) (Nat.decLe n d) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) d n)) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) p) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) p) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) p) _inst_1)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : PowerSeries.{u1} R) (n : Nat) (d : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) p (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 d) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) p (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n))) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) p) (LE.le.{0} Nat instLENat n d) (Nat.decLe n d) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) d n)) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) p) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) p) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) p) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_X_pow' PowerSeries.coeff_mul_X_pow'ₓ'. -/
 theorem coeff_mul_X_pow' (p : PowerSeries R) (n d : ℕ) :
     coeff R d (p * X ^ n) = ite (n ≤ d) (coeff R (d - n) p) 0 :=
@@ -2502,7 +2502,7 @@ theorem coeff_mul_X_pow' (p : PowerSeries R) (n d : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : PowerSeries.{u1} R) (n : Nat) (d : Nat), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 d) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) p)) (ite.{succ u1} R (LE.le.{0} Nat Nat.hasLe n d) (Nat.decidableLe n d) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) d n)) p) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : PowerSeries.{u1} R) (n : Nat) (d : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 d) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) p)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) p) (LE.le.{0} Nat instLENat n d) (Nat.decLe n d) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) d n)) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) p) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) p) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) p) _inst_1)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : PowerSeries.{u1} R) (n : Nat) (d : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 d) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) p)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) p) (LE.le.{0} Nat instLENat n d) (Nat.decLe n d) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) d n)) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) p) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) p) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) p) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow_mul' PowerSeries.coeff_X_pow_mul'ₓ'. -/
 theorem coeff_X_pow_mul' (p : PowerSeries R) (n d : ℕ) :
     coeff R d (X ^ n * p) = ite (n ≤ d) (coeff R (d - n) p) 0 :=
@@ -2534,7 +2534,7 @@ theorem isUnit_constantCoeff (φ : PowerSeries R) (h : IsUnit φ) : IsUnit (cons
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} (PowerSeries.{u1} R) φ (HAdd.hAdd.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHAdd.{u1} (PowerSeries.{u1} R) (Distrib.toHasAdd.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) (PowerSeries.mk.{u1} R (fun (p : Nat) => 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) p (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) φ)) (PowerSeries.X.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) => R -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (PowerSeries.C.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} (PowerSeries.{u1} R) φ (HAdd.hAdd.{u1, u1, u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (a : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)) (PowerSeries.{u1} R) (instHAdd.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (Distrib.toAdd.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.instSemiringPowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (instHMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.instSemiringPowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1))))) (PowerSeries.mk.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (fun (p : Nat) => 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) φ)) (PowerSeries.X.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} (PowerSeries.{u1} R) φ (HAdd.hAdd.{u1, u1, u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (a : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)) (PowerSeries.{u1} R) (instHAdd.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (Distrib.toAdd.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.instSemiringPowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (instHMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.instSemiringPowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1))))) (PowerSeries.mk.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (fun (p : Nat) => 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) φ)) (PowerSeries.X.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)))
 Case conversion may be inaccurate. Consider using '#align power_series.eq_shift_mul_X_add_const PowerSeries.eq_shift_mul_X_add_constₓ'. -/
 /-- Split off the constant coefficient. -/
 theorem eq_shift_mul_X_add_const (φ : PowerSeries R) :
@@ -2553,7 +2553,7 @@ theorem eq_shift_mul_X_add_const (φ : PowerSeries R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} (PowerSeries.{u1} R) φ (HAdd.hAdd.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHAdd.{u1} (PowerSeries.{u1} R) (Distrib.toHasAdd.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) (PowerSeries.X.{u1} R _inst_1) (PowerSeries.mk.{u1} R (fun (p : Nat) => 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) p (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) φ))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) => R -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))) (PowerSeries.C.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} (PowerSeries.{u1} R) φ (HAdd.hAdd.{u1, u1, u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (a : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)) (PowerSeries.{u1} R) (instHAdd.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (Distrib.toAdd.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.instSemiringPowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (instHMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.instSemiringPowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1))))) (PowerSeries.X.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1) (PowerSeries.mk.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (fun (p : Nat) => 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) φ))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} (PowerSeries.{u1} R) φ (HAdd.hAdd.{u1, u1, u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (a : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)) (PowerSeries.{u1} R) (instHAdd.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (Distrib.toAdd.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.instSemiringPowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (instHMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.instSemiringPowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1))))) (PowerSeries.X.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1) (PowerSeries.mk.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (fun (p : Nat) => 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) φ))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) (PowerSeries.C.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)))
 Case conversion may be inaccurate. Consider using '#align power_series.eq_X_mul_shift_add_const PowerSeries.eq_X_mul_shift_add_constₓ'. -/
 /-- Split off the constant coefficient. -/
 theorem eq_X_mul_shift_add_const (φ : PowerSeries R) :
@@ -2610,7 +2610,7 @@ theorem map_comp : map (g.comp f) = (map g).comp (map f) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat) (φ : PowerSeries.{u1} R), Eq.{succ u2} S (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (PowerSeries.{u2} S) S (PowerSeries.addCommMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.module.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2)) (fun (_x : LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (PowerSeries.{u2} S) S (PowerSeries.addCommMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.module.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2)) => (PowerSeries.{u2} S) -> S) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S (PowerSeries.{u2} S) S _inst_2 _inst_2 (PowerSeries.addCommMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.module.{u2, u2} S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (Semiring.toModule.{u2} S _inst_2) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (PowerSeries.coeff.{u2} S _inst_2 n) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.semiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.semiring.{u2} S _inst_2))) => (PowerSeries.{u1} R) -> (PowerSeries.{u2} S)) (RingHom.hasCoeToFun.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.semiring.{u2} S _inst_2))) (PowerSeries.map.{u1, u2} R _inst_1 S _inst_2 f) φ)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (n : Nat) (φ : PowerSeries.{u2} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} S) => S) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (PowerSeries.{u2} R) (PowerSeries.{u1} S) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} R) (PowerSeries.instSemiringPowerSeries.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_2))) (PowerSeries.{u2} R) (fun (a : PowerSeries.{u2} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u2} R) => PowerSeries.{u1} S) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (PowerSeries.{u2} R) (PowerSeries.{u1} S) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} R) (PowerSeries.instSemiringPowerSeries.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_2))) (PowerSeries.{u2} R) (PowerSeries.{u1} S) (NonUnitalNonAssocSemiring.toMul.{u2} (PowerSeries.{u2} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (PowerSeries.{u2} R) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} R) (PowerSeries.instSemiringPowerSeries.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (PowerSeries.{u2} R) (PowerSeries.{u1} S) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} R) (PowerSeries.instSemiringPowerSeries.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_2))) (PowerSeries.{u2} R) (PowerSeries.{u1} S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (PowerSeries.{u2} R) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} R) (PowerSeries.instSemiringPowerSeries.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (PowerSeries.{u2} R) (PowerSeries.{u1} S) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} R) (PowerSeries.instSemiringPowerSeries.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_2))) (PowerSeries.{u2} R) (PowerSeries.{u1} S) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} R) (PowerSeries.instSemiringPowerSeries.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} 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S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} (PowerSeries.{u2} R) (PowerSeries.{u1} S) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} R) (PowerSeries.instSemiringPowerSeries.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_2)))))) (PowerSeries.map.{u2, u1} R _inst_1 S _inst_2 f) φ)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (PowerSeries.{u2} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1)) (PowerSeries.{u2} R) (fun (_x : PowerSeries.{u2} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} R R (PowerSeries.{u2} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Semiring.toModule.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (PowerSeries.coeff.{u2} R _inst_1 n) φ))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_map PowerSeries.coeff_mapₓ'. -/
 @[simp]
 theorem coeff_map (n : ℕ) (φ : PowerSeries R) : coeff S n (map f φ) = f (coeff R n φ) :=
@@ -2648,7 +2648,7 @@ end Map
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {φ : PowerSeries.{u1} R}, Iff (Dvd.Dvd.{u1} (PowerSeries.{u1} R) (semigroupDvd.{u1} (PowerSeries.{u1} R) (SemigroupWithZero.toSemigroup.{u1} (PowerSeries.{u1} R) (NonUnitalSemiring.toSemigroupWithZero.{u1} (PowerSeries.{u1} R) (Semiring.toNonUnitalSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) φ) (forall (m : Nat), (LT.lt.{0} Nat Nat.hasLt m n) -> (Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 m) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {φ : PowerSeries.{u1} R}, Iff (Dvd.dvd.{u1} (PowerSeries.{u1} R) (semigroupDvd.{u1} (PowerSeries.{u1} R) (SemigroupWithZero.toSemigroup.{u1} (PowerSeries.{u1} R) (NonUnitalSemiring.toSemigroupWithZero.{u1} (PowerSeries.{u1} R) (Semiring.toNonUnitalSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) φ) (forall (m : Nat), (LT.lt.{0} Nat instLTNat m n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 m) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {φ : PowerSeries.{u1} R}, Iff (Dvd.dvd.{u1} (PowerSeries.{u1} R) (semigroupDvd.{u1} (PowerSeries.{u1} R) (SemigroupWithZero.toSemigroup.{u1} (PowerSeries.{u1} R) (NonUnitalSemiring.toSemigroupWithZero.{u1} (PowerSeries.{u1} R) (Semiring.toNonUnitalSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) φ) (forall (m : Nat), (LT.lt.{0} Nat instLTNat m n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 m) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align power_series.X_pow_dvd_iff PowerSeries.X_pow_dvd_iffₓ'. -/
 theorem X_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
     (X : PowerSeries R) ^ n ∣ φ ↔ ∀ m, m < n → coeff R m φ = 0 :=
@@ -2721,7 +2721,7 @@ noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : PowerSeries.{u1} R) (a : R) (n : Nat), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (PowerSeries.{u1} R) -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.rescale.{u1} R _inst_1 a) f)) (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 (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) a n) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) f))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : PowerSeries.{u1} R) (a : R) (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (fun (a : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u1} R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (PowerSeries.rescale.{u1} R _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (PowerSeries.rescale.{u1} R _inst_1 a) f)) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) f) R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) a n) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) f))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : PowerSeries.{u1} R) (a : R) (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (fun (a : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u1} R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (PowerSeries.rescale.{u1} R _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (PowerSeries.rescale.{u1} R _inst_1 a) f)) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) f) R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) a n) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) f))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_rescale PowerSeries.coeff_rescaleₓ'. -/
 @[simp]
 theorem coeff_rescale (f : PowerSeries R) (a : R) (n : ℕ) :
@@ -2819,7 +2819,7 @@ def trunc (n : ℕ) (φ : PowerSeries R) : R[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (m : Nat) (n : Nat) (φ : PowerSeries.{u1} R), Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.trunc.{u1} R _inst_1 n φ) m) (ite.{succ u1} R (LT.lt.{0} Nat Nat.hasLt m n) (Nat.decidableLt m n) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) m) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (m : Nat) (n : Nat) (φ : PowerSeries.{u1} R), Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.trunc.{u1} R _inst_1 n φ) m) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (LT.lt.{0} Nat instLTNat m n) (Nat.decLt m n) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) m) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (m : Nat) (n : Nat) (φ : PowerSeries.{u1} R), Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.trunc.{u1} R _inst_1 n φ) m) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (LT.lt.{0} Nat instLTNat m n) (Nat.decLt m n) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) m) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_trunc PowerSeries.coeff_truncₓ'. -/
 theorem coeff_trunc (m) (n) (φ : PowerSeries R) :
     (trunc n φ).coeff m = if m < n then coeff R m φ else 0 := by
@@ -2908,7 +2908,7 @@ protected def inv.aux : R → PowerSeries R → PowerSeries R :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (n : Nat) (a : R) (φ : PowerSeries.{u1} R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) n) (PowerSeries.inv.aux.{u1} R _inst_1 a φ)) (ite.{succ u1} R (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Nat.decidableEq n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) a (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) a) (Finset.sum.{u1, 0} R (Prod.{0, 0} Nat Nat) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Finset.Nat.antidiagonal n) (fun (x : Prod.{0, 0} Nat Nat) => ite.{succ u1} R (LT.lt.{0} Nat Nat.hasLt (Prod.snd.{0, 0} Nat Nat x) n) (Nat.decidableLt (Prod.snd.{0, 0} Nat Nat x) n) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Prod.fst.{0, 0} Nat Nat x)) φ) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Prod.snd.{0, 0} Nat Nat x)) (PowerSeries.inv.aux.{u1} R _inst_1 a φ))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (n : Nat) (a : R) (φ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.inv.aux.{u1} R _inst_1 a φ)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) n) (PowerSeries.inv.aux.{u1} R _inst_1 a φ)) (ite.{succ u1} R (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (instDecidableEqNat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) a (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a) (Finset.sum.{u1, 0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Prod.{0, 0} Nat Nat) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))) (Finset.Nat.antidiagonal n) (fun (x : Prod.{0, 0} Nat Nat) => ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (LT.lt.{0} Nat instLTNat (Prod.snd.{0, 0} Nat Nat x) n) (Nat.decLt (Prod.snd.{0, 0} Nat Nat x) n) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.inv.aux.{u1} R _inst_1 a φ)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Prod.fst.{0, 0} Nat Nat x)) φ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Prod.snd.{0, 0} Nat Nat x)) (PowerSeries.inv.aux.{u1} R _inst_1 a φ))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (n : Nat) (a : R) (φ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.inv.aux.{u1} R _inst_1 a φ)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) n) (PowerSeries.inv.aux.{u1} R _inst_1 a φ)) (ite.{succ u1} R (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (instDecidableEqNat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) a (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) 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R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Prod.fst.{0, 0} Nat Nat x)) φ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Prod.snd.{0, 0} Nat Nat x)) (PowerSeries.inv.aux.{u1} R _inst_1 a φ))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_inv_aux PowerSeries.coeff_inv_auxₓ'. -/
 theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
     coeff R n (inv.aux a φ) =
@@ -2969,7 +2969,7 @@ def invOfUnit (φ : PowerSeries R) (u : Rˣ) : PowerSeries R :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R) (u : Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} 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 but is expected to have type
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(PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) 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R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Prod.snd.{0, 0} Nat Nat x)) (PowerSeries.invOfUnit.{u1} R _inst_1 φ u))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R) (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.invOfUnit.{u1} R _inst_1 φ u)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) n) (PowerSeries.invOfUnit.{u1} R _inst_1 φ u)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (instDecidableEqNat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Inv.inv.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.instInv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) u)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Inv.inv.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.instInv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) u))) (Finset.sum.{u1, 0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Prod.{0, 0} Nat Nat) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))) (Finset.Nat.antidiagonal n) (fun (x : Prod.{0, 0} Nat Nat) => ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (LT.lt.{0} Nat instLTNat (Prod.snd.{0, 0} Nat Nat x) n) (Nat.decLt (Prod.snd.{0, 0} Nat Nat x) n) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (PowerSeries.invOfUnit.{u1} R _inst_1 φ u)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Prod.fst.{0, 0} Nat Nat x)) φ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Prod.snd.{0, 0} Nat Nat x)) (PowerSeries.invOfUnit.{u1} R _inst_1 φ u))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_inv_of_unit PowerSeries.coeff_invOfUnitₓ'. -/
 theorem coeff_invOfUnit (n : ℕ) (φ : PowerSeries R) (u : Rˣ) :
     coeff R n (invOfUnit φ u) =
@@ -3008,7 +3008,7 @@ theorem mul_invOfUnit (φ : PowerSeries R) (u : Rˣ) (h : constantCoeff R φ = u
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} (PowerSeries.{u1} R) (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (SubNegMonoid.toHasSub.{u1} (PowerSeries.{u1} R) (AddGroup.toSubNegMonoid.{u1} (PowerSeries.{u1} R) (PowerSeries.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))))) φ (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => R -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> R) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.constantCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1)) φ))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (Ring.toDistrib.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R _inst_1)))) (PowerSeries.mk.{u1} R (fun (p : Nat) => coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) p (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) φ)) (PowerSeries.X.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} (PowerSeries.{u1} R) (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (a : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (PowerSeries.constantCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1)) φ)) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (Ring.toSub.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R _inst_1))) φ (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (PowerSeries.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (PowerSeries.constantCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1)) φ))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.instRingPowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1))))) (PowerSeries.mk.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (fun (p : Nat) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) φ)) (PowerSeries.X.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} (PowerSeries.{u1} R) (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (a : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (PowerSeries.constantCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1)) φ)) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (Ring.toSub.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R _inst_1))) φ (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (PowerSeries.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (PowerSeries.constantCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1)) φ))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.instRingPowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1))))) (PowerSeries.mk.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (fun (p : Nat) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) φ)) (PowerSeries.X.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))
 Case conversion may be inaccurate. Consider using '#align power_series.sub_const_eq_shift_mul_X PowerSeries.sub_const_eq_shift_mul_Xₓ'. -/
 /-- Two ways of removing the constant coefficient of a power series are the same. -/
 theorem sub_const_eq_shift_mul_X (φ : PowerSeries R) :
@@ -3020,7 +3020,7 @@ theorem sub_const_eq_shift_mul_X (φ : PowerSeries R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} (PowerSeries.{u1} R) (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (SubNegMonoid.toHasSub.{u1} (PowerSeries.{u1} R) (AddGroup.toSubNegMonoid.{u1} (PowerSeries.{u1} R) (PowerSeries.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))))) φ (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => R -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> R) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.constantCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1)) φ))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (Ring.toDistrib.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R _inst_1)))) (PowerSeries.X.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PowerSeries.mk.{u1} R (fun (p : Nat) => coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) p (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) φ)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} (PowerSeries.{u1} R) (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (a : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (PowerSeries.constantCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1)) φ)) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (Ring.toSub.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R _inst_1))) φ (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (PowerSeries.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (PowerSeries.constantCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1)) φ))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.instRingPowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1))))) (PowerSeries.X.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)) (PowerSeries.mk.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (fun (p : Nat) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) φ)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} (PowerSeries.{u1} R) (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (a : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (PowerSeries.constantCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1)) φ)) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (Ring.toSub.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R _inst_1))) φ (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (PowerSeries.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (PowerSeries.constantCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1)) φ))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.instRingPowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1))))) (PowerSeries.X.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)) (PowerSeries.mk.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (fun (p : Nat) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) φ)))
 Case conversion may be inaccurate. Consider using '#align power_series.sub_const_eq_X_mul_shift PowerSeries.sub_const_eq_X_mul_shiftₓ'. -/
 theorem sub_const_eq_X_mul_shift (φ : PowerSeries R) :
     φ - C R (constantCoeff R φ) = X * PowerSeries.mk fun p => coeff R (p + 1) φ :=
@@ -3276,7 +3276,7 @@ theorem inv_eq_inv_aux (φ : PowerSeries k) : φ⁻¹ = inv.aux (constantCoeff k
 lean 3 declaration is
   forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] (n : Nat) (φ : PowerSeries.{u1} k), Eq.{succ u1} k (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) => (PowerSeries.{u1} k) -> k) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} k k (PowerSeries.{u1} k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.coeff.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) n) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) φ)) (ite.{succ u1} k (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Nat.decidableEq n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) => 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(DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) => (PowerSeries.{u1} k) -> k) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.coeff.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Prod.fst.{0, 0} Nat Nat x)) φ) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (RingHom.id.{u1} k 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) => (PowerSeries.{u1} k) -> k) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} k k (PowerSeries.{u1} k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.coeff.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Prod.snd.{0, 0} Nat Nat x)) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) φ))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))))))))
 but is expected to have type
-  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] (n : Nat) (φ : PowerSeries.{u1} k), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} k) => k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} k) => k) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} k k (PowerSeries.{u1} k) k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k 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(PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} k) => k) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} k k (PowerSeries.{u1} k) k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.coeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Prod.fst.{0, 0} Nat Nat x)) φ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} k) => k) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} k k (PowerSeries.{u1} k) k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.coeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Prod.snd.{0, 0} Nat Nat x)) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} k) => k) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} k) => k) φ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} k) => k) φ) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} k) => k) φ) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} k) => k) φ) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} k) => k) φ) _inst_1))))))))))
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] (n : Nat) (φ : PowerSeries.{u1} k), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} k k (PowerSeries.{u1} k) k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.coeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) n) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (instDecidableEqNat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} k) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toMul.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) φ)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) _inst_1)))))) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) _inst_1))) (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} k) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toMul.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) φ))) (Finset.sum.{u1, 0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (Prod.{0, 0} Nat Nat) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) _inst_1)))))) (Finset.Nat.antidiagonal n) (fun (x : Prod.{0, 0} Nat Nat) => ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (LT.lt.{0} Nat instLTNat (Prod.snd.{0, 0} Nat Nat x) n) (Nat.decLt (Prod.snd.{0, 0} Nat Nat x) n) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} k k (PowerSeries.{u1} k) k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.coeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Prod.fst.{0, 0} Nat Nat x)) φ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} k k (PowerSeries.{u1} k) k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.coeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Prod.snd.{0, 0} Nat Nat x)) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} k) => k) φ) _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_inv PowerSeries.coeff_invₓ'. -/
 theorem coeff_inv (n) (φ : PowerSeries k) :
     coeff k n φ⁻¹ =
@@ -3468,7 +3468,7 @@ variable [Semiring R] {φ : PowerSeries R}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R}, Iff (Exists.{1} Nat (fun (n : Nat) => Ne.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) (Ne.{succ u1} (PowerSeries.{u1} R) φ (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (OfNat.mk.{u1} (PowerSeries.{u1} R) 0 (Zero.zero.{u1} (PowerSeries.{u1} R) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R}, Iff (Exists.{1} Nat (fun (n : Nat) => Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) (Ne.{succ u1} (PowerSeries.{u1} R) φ (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (Zero.toOfNat0.{u1} (PowerSeries.{u1} R) (PowerSeries.instZeroPowerSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R}, Iff (Exists.{1} Nat (fun (n : Nat) => Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) (Ne.{succ u1} (PowerSeries.{u1} R) φ (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (Zero.toOfNat0.{u1} (PowerSeries.{u1} R) (PowerSeries.instZeroPowerSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align power_series.exists_coeff_ne_zero_iff_ne_zero PowerSeries.exists_coeff_ne_zero_iff_ne_zeroₓ'. -/
 theorem exists_coeff_ne_zero_iff_ne_zero : (∃ n : ℕ, coeff R n φ ≠ 0) ↔ φ ≠ 0 :=
   by
@@ -3519,7 +3519,7 @@ theorem order_finite_iff_ne_zero : (order φ).Dom ↔ φ ≠ 0 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} (h : Part.Dom.{0} Nat (PowerSeries.order.{u1} R _inst_1 φ)), Ne.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (Part.get.{0} Nat (PowerSeries.order.{u1} R _inst_1 φ) h)) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} (h : Part.Dom.{0} Nat (PowerSeries.order.{u1} R _inst_1 φ)), Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (Part.get.{0} Nat (PowerSeries.order.{u1} R _inst_1 φ) h)) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} (h : Part.Dom.{0} Nat (PowerSeries.order.{u1} R _inst_1 φ)), Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (Part.get.{0} Nat (PowerSeries.order.{u1} R _inst_1 φ) h)) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_order PowerSeries.coeff_orderₓ'. -/
 /-- If the order of a formal power series is finite,
 then the coefficient indexed by the order is nonzero.-/
@@ -3534,7 +3534,7 @@ theorem coeff_order (h : (order φ).Dom) : coeff R (φ.order.get h) φ ≠ 0 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} (n : Nat), (Ne.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (LE.le.{0} PartENat PartENat.hasLe (PowerSeries.order.{u1} R _inst_1 φ) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} (n : Nat), (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1))))) -> (LE.le.{0} PartENat PartENat.instLEPartENat (PowerSeries.order.{u1} R _inst_1 φ) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} (n : Nat), (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1))))) -> (LE.le.{0} PartENat PartENat.instLEPartENat (PowerSeries.order.{u1} R _inst_1 φ) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n))
 Case conversion may be inaccurate. Consider using '#align power_series.order_le PowerSeries.order_leₓ'. -/
 /-- If the `n`th coefficient of a formal power series is nonzero,
 then the order of the power series is less than or equal to `n`.-/
@@ -3551,7 +3551,7 @@ theorem order_le (n : ℕ) (h : coeff R n φ ≠ 0) : order φ ≤ n :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} (n : Nat), (LT.lt.{0} PartENat (Preorder.toHasLt.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) n) (PowerSeries.order.{u1} R _inst_1 φ)) -> (Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} (n : Nat), (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n) (PowerSeries.order.{u1} R _inst_1 φ)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} (n : Nat), (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n) (PowerSeries.order.{u1} R _inst_1 φ)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_of_lt_order PowerSeries.coeff_of_lt_orderₓ'. -/
 /-- The `n`th coefficient of a formal power series is `0` if `n` is strictly
 smaller than the order of the power series.-/
@@ -3584,7 +3584,7 @@ theorem order_eq_top {φ : PowerSeries R} : φ.order = ⊤ ↔ φ = 0 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R) (n : Nat), (forall (i : Nat), (LT.lt.{0} Nat Nat.hasLt i n) -> (Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) -> (LE.le.{0} PartENat PartENat.hasLe ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) n) (PowerSeries.order.{u1} R _inst_1 φ))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R) (n : Nat), (forall (i : Nat), (LT.lt.{0} Nat instLTNat i n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) -> (LE.le.{0} PartENat PartENat.instLEPartENat (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n) (PowerSeries.order.{u1} R _inst_1 φ))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R) (n : Nat), (forall (i : Nat), (LT.lt.{0} Nat instLTNat i n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) -> (LE.le.{0} PartENat PartENat.instLEPartENat (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n) (PowerSeries.order.{u1} R _inst_1 φ))
 Case conversion may be inaccurate. Consider using '#align power_series.nat_le_order PowerSeries.nat_le_orderₓ'. -/
 /-- The order of a formal power series is at least `n` if
 the `i`th coefficient is `0` for all `i < n`.-/
@@ -3600,7 +3600,7 @@ theorem nat_le_order (φ : PowerSeries R) (n : ℕ) (h : ∀ i < n, coeff R i φ
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R) (n : PartENat), (forall (i : Nat), (LT.lt.{0} PartENat (Preorder.toHasLt.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) i) n) -> (Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) -> (LE.le.{0} PartENat PartENat.hasLe n (PowerSeries.order.{u1} R _inst_1 φ))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R) (n : PartENat), (forall (i : Nat), (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) i) n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) -> (LE.le.{0} PartENat PartENat.instLEPartENat n (PowerSeries.order.{u1} R _inst_1 φ))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R) (n : PartENat), (forall (i : Nat), (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) i) n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) -> (LE.le.{0} PartENat PartENat.instLEPartENat n (PowerSeries.order.{u1} R _inst_1 φ))
 Case conversion may be inaccurate. Consider using '#align power_series.le_order PowerSeries.le_orderₓ'. -/
 /-- The order of a formal power series is at least `n` if
 the `i`th coefficient is `0` for all `i < n`.-/
@@ -3619,7 +3619,7 @@ theorem le_order (φ : PowerSeries R) (n : PartENat) (h : ∀ i : ℕ, ↑i < n
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {n : Nat}, Iff (Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 φ) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) n)) (And (Ne.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (forall (i : Nat), (LT.lt.{0} Nat Nat.hasLt i n) -> (Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {n : Nat}, Iff (Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 φ) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n)) (And (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1))))) (forall (i : Nat), (LT.lt.{0} Nat instLTNat i n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {n : Nat}, Iff (Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 φ) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n)) (And (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1))))) (forall (i : Nat), (LT.lt.{0} Nat instLTNat i n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align power_series.order_eq_nat PowerSeries.order_eq_natₓ'. -/
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
 and the `i`th coefficient is `0` for all `i < n`.-/
@@ -3635,7 +3635,7 @@ theorem order_eq_nat {φ : PowerSeries R} {n : ℕ} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {n : PartENat}, Iff (Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 φ) n) (And (forall (i : Nat), (Eq.{1} PartENat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) i) n) -> (Ne.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) (forall (i : Nat), (LT.lt.{0} PartENat (Preorder.toHasLt.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) i) n) -> (Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {n : PartENat}, Iff (Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 φ) n) (And (forall (i : Nat), (Eq.{1} PartENat (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) i) n) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) (forall (i : Nat), (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) i) n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {n : PartENat}, Iff (Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 φ) n) (And (forall (i : Nat), (Eq.{1} PartENat (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) i) n) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) (forall (i : Nat), (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) i) n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) φ) _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align power_series.order_eq PowerSeries.order_eqₓ'. -/
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
 and the `i`th coefficient is `0` for all `i < n`.-/
@@ -3733,7 +3733,7 @@ theorem order_mul_ge (φ ψ : PowerSeries R) : order φ + order ψ ≤ order (φ
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R) [_inst_2 : Decidable (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))], Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) => R -> (PowerSeries.{u1} R)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) (ite.{1} PartENat (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) _inst_2 (Top.top.{0} PartENat PartENat.hasTop) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R) [_inst_2 : Decidable (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))], Eq.{1} PartENat (PowerSeries.order.{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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) (ite.{1} PartENat (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) _inst_2 (Top.top.{0} PartENat PartENat.instTopPartENat) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R) [_inst_2 : Decidable (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))], Eq.{1} PartENat (PowerSeries.order.{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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) (ite.{1} PartENat (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) _inst_2 (Top.top.{0} PartENat PartENat.instTopPartENat) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n))
 Case conversion may be inaccurate. Consider using '#align power_series.order_monomial PowerSeries.order_monomialₓ'. -/
 /-- The order of the monomial `a*X^n` is infinite if `a = 0` and `n` otherwise.-/
 theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
@@ -3754,7 +3754,7 @@ theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) => R -> (PowerSeries.{u1} R)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} PartENat (PowerSeries.order.{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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} PartENat (PowerSeries.order.{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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n))
 Case conversion may be inaccurate. Consider using '#align power_series.order_monomial_of_ne_zero PowerSeries.order_monomial_of_ne_zeroₓ'. -/
 /-- The order of the monomial `a*X^n` is `n` if `a ≠ 0`.-/
 theorem order_monomial_of_ne_zero (n : ℕ) (a : R) (h : a ≠ 0) : order (monomial R n a) = n := by
@@ -3765,7 +3765,7 @@ theorem order_monomial_of_ne_zero (n : ℕ) (a : R) (h : a ≠ 0) : order (monom
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {ψ : PowerSeries.{u1} R} {n : Nat}, (LT.lt.{0} PartENat (Preorder.toHasLt.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) n) (PowerSeries.order.{u1} R _inst_1 ψ)) -> (Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) φ ψ)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {ψ : PowerSeries.{u1} R} {n : Nat}, (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n) (PowerSeries.order.{u1} R _inst_1 ψ)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) _inst_1)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} {ψ : PowerSeries.{u1} R} {n : Nat}, (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n) (PowerSeries.order.{u1} R _inst_1 ψ)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ)) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_orderₓ'. -/
 /-- If `n` is strictly smaller than the order of `ψ`, then the `n`th coefficient of its product
 with any other power series is `0`. -/
@@ -3786,7 +3786,7 @@ theorem coeff_mul_of_lt_order {φ ψ : PowerSeries R} {n : ℕ} (h : ↑n < ψ.o
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_2 : CommRing.{u1} R] {φ : PowerSeries.{u1} R} {ψ : PowerSeries.{u1} R} (n : Nat), (LT.lt.{0} PartENat (Preorder.toHasLt.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) n) (PowerSeries.order.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) ψ)) -> (Eq.{succ u1} R (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (Ring.toDistrib.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) φ (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (SubNegMonoid.toHasSub.{u1} (PowerSeries.{u1} R) (AddGroup.toSubNegMonoid.{u1} (PowerSeries.{u1} R) (PowerSeries.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_2)))))))) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (OfNat.mk.{u1} (PowerSeries.{u1} R) 1 (One.one.{u1} (PowerSeries.{u1} R) (AddMonoidWithOne.toOne.{u1} (PowerSeries.{u1} R) (AddGroupWithOne.toAddMonoidWithOne.{u1} (PowerSeries.{u1} R) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (PowerSeries.{u1} R) (Ring.toAddCommGroupWithOne.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R (CommRing.toRing.{u1} R _inst_2))))))))) ψ))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) n) φ))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_2 : CommRing.{u1} R] {φ : PowerSeries.{u1} R} {ψ : PowerSeries.{u1} R} (n : Nat), (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n) (PowerSeries.order.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) ψ)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} R) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} R) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) φ (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (Ring.toSub.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) ψ))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} R) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} R) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) φ (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (Ring.toSub.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) ψ))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) n) φ))
+  forall {R : Type.{u1}} [_inst_2 : CommRing.{u1} R] {φ : PowerSeries.{u1} R} {ψ : PowerSeries.{u1} R} (n : Nat), (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n) (PowerSeries.order.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) ψ)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} R) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} R) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) φ (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (Ring.toSub.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) ψ))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} R) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} R) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) φ (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (Ring.toSub.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) ψ))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) n) φ))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_one_sub_of_lt_order PowerSeries.coeff_mul_one_sub_of_lt_orderₓ'. -/
 theorem coeff_mul_one_sub_of_lt_order {R : Type _} [CommRing R] {φ ψ : PowerSeries R} (n : ℕ)
     (h : ↑n < ψ.order) : coeff R n (φ * (1 - ψ)) = coeff R n φ := by
@@ -3797,7 +3797,7 @@ theorem coeff_mul_one_sub_of_lt_order {R : Type _} [CommRing R] {φ ψ : PowerSe
 lean 3 declaration is
   forall {R : Type.{u1}} {ι : Type.{u2}} [_inst_2 : CommRing.{u1} R] (k : Nat) (s : Finset.{u2} ι) (φ : PowerSeries.{u1} R) (f : ι -> (PowerSeries.{u1} R)), (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (LT.lt.{0} PartENat (Preorder.toHasLt.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) k) (PowerSeries.order.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (f i)))) -> (Eq.{succ u1} R (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) k) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (Ring.toDistrib.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) φ (Finset.prod.{u1, u2} (PowerSeries.{u1} R) ι (CommRing.toCommMonoid.{u1} (PowerSeries.{u1} R) (PowerSeries.commRing.{u1} R _inst_2)) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (SubNegMonoid.toHasSub.{u1} (PowerSeries.{u1} R) (AddGroup.toSubNegMonoid.{u1} (PowerSeries.{u1} R) (PowerSeries.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_2)))))))) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (OfNat.mk.{u1} (PowerSeries.{u1} R) 1 (One.one.{u1} (PowerSeries.{u1} R) (AddMonoidWithOne.toOne.{u1} (PowerSeries.{u1} R) (AddGroupWithOne.toAddMonoidWithOne.{u1} (PowerSeries.{u1} R) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (PowerSeries.{u1} R) (Ring.toAddCommGroupWithOne.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R (CommRing.toRing.{u1} R _inst_2))))))))) (f i))))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) k) φ))
 but is expected to have type
-  forall {R : Type.{u2}} {ι : Type.{u1}} [_inst_2 : CommRing.{u2} R] (k : Nat) (s : Finset.{u1} ι) (φ : PowerSeries.{u2} R) (f : ι -> (PowerSeries.{u2} R)), (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) k) (PowerSeries.order.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (f i)))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} R) => R) (HMul.hMul.{u2, u2, u2} (PowerSeries.{u2} R) (PowerSeries.{u2} R) (PowerSeries.{u2} R) (instHMul.{u2} (PowerSeries.{u2} R) (NonUnitalNonAssocRing.toMul.{u2} (PowerSeries.{u2} R) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (PowerSeries.{u2} R) (Ring.toNonAssocRing.{u2} (PowerSeries.{u2} R) (PowerSeries.instRingPowerSeries.{u2} R (CommRing.toRing.{u2} R _inst_2)))))) φ (Finset.prod.{u2, u1} (PowerSeries.{u2} R) ι (CommRing.toCommMonoid.{u2} (PowerSeries.{u2} R) (PowerSeries.instCommRingPowerSeries.{u2} R _inst_2)) s (fun (i : ι) => HSub.hSub.{u2, u2, u2} (PowerSeries.{u2} R) (PowerSeries.{u2} R) (PowerSeries.{u2} R) (instHSub.{u2} (PowerSeries.{u2} R) (Ring.toSub.{u2} (PowerSeries.{u2} R) (PowerSeries.instRingPowerSeries.{u2} R (CommRing.toRing.{u2} R _inst_2)))) (OfNat.ofNat.{u2} (PowerSeries.{u2} R) 1 (One.toOfNat1.{u2} (PowerSeries.{u2} R) (Semiring.toOne.{u2} (PowerSeries.{u2} R) (PowerSeries.instSemiringPowerSeries.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (f i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (PowerSeries.{u2} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (PowerSeries.{u2} R) (fun (_x : PowerSeries.{u2} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} R R (PowerSeries.{u2} R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (PowerSeries.instAddCommMonoidPowerSeries.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.coeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) k) (HMul.hMul.{u2, u2, u2} (PowerSeries.{u2} R) (PowerSeries.{u2} R) (PowerSeries.{u2} R) (instHMul.{u2} (PowerSeries.{u2} R) (NonUnitalNonAssocRing.toMul.{u2} (PowerSeries.{u2} R) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (PowerSeries.{u2} R) (Ring.toNonAssocRing.{u2} (PowerSeries.{u2} R) (PowerSeries.instRingPowerSeries.{u2} R (CommRing.toRing.{u2} R _inst_2)))))) φ (Finset.prod.{u2, u1} (PowerSeries.{u2} R) ι (CommRing.toCommMonoid.{u2} (PowerSeries.{u2} R) (PowerSeries.instCommRingPowerSeries.{u2} R _inst_2)) s (fun (i : ι) => HSub.hSub.{u2, u2, u2} (PowerSeries.{u2} R) (PowerSeries.{u2} R) (PowerSeries.{u2} R) (instHSub.{u2} (PowerSeries.{u2} R) (Ring.toSub.{u2} (PowerSeries.{u2} R) (PowerSeries.instRingPowerSeries.{u2} R (CommRing.toRing.{u2} R _inst_2)))) (OfNat.ofNat.{u2} (PowerSeries.{u2} R) 1 (One.toOfNat1.{u2} (PowerSeries.{u2} R) (Semiring.toOne.{u2} (PowerSeries.{u2} R) (PowerSeries.instSemiringPowerSeries.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (f i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (PowerSeries.{u2} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (PowerSeries.{u2} R) (fun (_x : PowerSeries.{u2} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} R R (PowerSeries.{u2} R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (PowerSeries.instAddCommMonoidPowerSeries.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.coeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) k) φ))
+  forall {R : Type.{u2}} {ι : Type.{u1}} [_inst_2 : CommRing.{u2} R] (k : Nat) (s : Finset.{u1} ι) (φ : PowerSeries.{u2} R) (f : ι -> (PowerSeries.{u2} R)), (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) k) (PowerSeries.order.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (f i)))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} R) => R) (HMul.hMul.{u2, u2, u2} (PowerSeries.{u2} R) (PowerSeries.{u2} R) (PowerSeries.{u2} R) (instHMul.{u2} (PowerSeries.{u2} R) (NonUnitalNonAssocRing.toMul.{u2} (PowerSeries.{u2} R) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (PowerSeries.{u2} R) (Ring.toNonAssocRing.{u2} (PowerSeries.{u2} R) (PowerSeries.instRingPowerSeries.{u2} R (CommRing.toRing.{u2} R _inst_2)))))) φ (Finset.prod.{u2, u1} (PowerSeries.{u2} R) ι (CommRing.toCommMonoid.{u2} (PowerSeries.{u2} R) (PowerSeries.instCommRingPowerSeries.{u2} R _inst_2)) s (fun (i : ι) => HSub.hSub.{u2, u2, u2} (PowerSeries.{u2} R) (PowerSeries.{u2} R) (PowerSeries.{u2} R) (instHSub.{u2} (PowerSeries.{u2} R) (Ring.toSub.{u2} (PowerSeries.{u2} R) (PowerSeries.instRingPowerSeries.{u2} R (CommRing.toRing.{u2} R _inst_2)))) (OfNat.ofNat.{u2} (PowerSeries.{u2} R) 1 (One.toOfNat1.{u2} (PowerSeries.{u2} R) (Semiring.toOne.{u2} (PowerSeries.{u2} R) (PowerSeries.instSemiringPowerSeries.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (f i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (PowerSeries.{u2} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (PowerSeries.{u2} R) (fun (_x : PowerSeries.{u2} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} R R (PowerSeries.{u2} R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (PowerSeries.instAddCommMonoidPowerSeries.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.coeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) k) (HMul.hMul.{u2, u2, u2} (PowerSeries.{u2} R) (PowerSeries.{u2} R) (PowerSeries.{u2} R) (instHMul.{u2} (PowerSeries.{u2} R) (NonUnitalNonAssocRing.toMul.{u2} (PowerSeries.{u2} R) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (PowerSeries.{u2} R) (Ring.toNonAssocRing.{u2} (PowerSeries.{u2} R) (PowerSeries.instRingPowerSeries.{u2} R (CommRing.toRing.{u2} R _inst_2)))))) φ (Finset.prod.{u2, u1} (PowerSeries.{u2} R) ι (CommRing.toCommMonoid.{u2} (PowerSeries.{u2} R) (PowerSeries.instCommRingPowerSeries.{u2} R _inst_2)) s (fun (i : ι) => HSub.hSub.{u2, u2, u2} (PowerSeries.{u2} R) (PowerSeries.{u2} R) (PowerSeries.{u2} R) (instHSub.{u2} (PowerSeries.{u2} R) (Ring.toSub.{u2} (PowerSeries.{u2} R) (PowerSeries.instRingPowerSeries.{u2} R (CommRing.toRing.{u2} R _inst_2)))) (OfNat.ofNat.{u2} (PowerSeries.{u2} R) 1 (One.toOfNat1.{u2} (PowerSeries.{u2} R) (Semiring.toOne.{u2} (PowerSeries.{u2} R) (PowerSeries.instSemiringPowerSeries.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (f i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (PowerSeries.{u2} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (PowerSeries.{u2} R) (fun (_x : PowerSeries.{u2} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u2} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} R R (PowerSeries.{u2} R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (PowerSeries.instAddCommMonoidPowerSeries.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.coeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) k) φ))
 Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_prod_one_sub_of_lt_order PowerSeries.coeff_mul_prod_one_sub_of_lt_orderₓ'. -/
 theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type _} [CommRing R] (k : ℕ) (s : Finset ι)
     (φ : PowerSeries R) (f : ι → PowerSeries R) :
@@ -3948,7 +3948,7 @@ theorem coe_def : (φ : PowerSeries R) = PowerSeries.mk (coeff φ) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (n : Nat), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (coeBase.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Polynomial.coeToPowerSeries.{u1} R _inst_1)))) φ)) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) φ n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ)) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) φ n)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ)) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) φ n)
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_coe Polynomial.coeff_coeₓ'. -/
 @[simp, norm_cast]
 theorem coeff_coe (n) : PowerSeries.coeff R n φ = coeff φ n :=
@@ -3959,7 +3959,7 @@ theorem coeff_coe (n) : PowerSeries.coeff R n φ = coeff φ n :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat) (a : R), Eq.{succ u1} (PowerSeries.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (coeBase.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Polynomial.coeToPowerSeries.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.monomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) a)) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (PowerSeries.{u1} R)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.monomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) a)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat) (a : R), Eq.{succ u1} (PowerSeries.{u1} R) (Polynomial.ToPowerSeries.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.monomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.monomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) a)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat) (a : R), Eq.{succ u1} (PowerSeries.{u1} R) (Polynomial.ToPowerSeries.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.monomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.monomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) a)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_monomial Polynomial.coe_monomialₓ'. -/
 @[simp, norm_cast]
 theorem coe_monomial (n : ℕ) (a : R) :

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
 
 ! This file was ported from Lean 3 source module ring_theory.power_series.basic
-! leanprover-community/mathlib commit 2d5739b61641ee4e7e53eca5688a08f66f2e6a60
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -20,6 +20,9 @@ import Mathbin.Tactic.Linarith.Default
 /-!
 # Formal power series
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines (multivariate) formal power series
 and develops the basic properties of these objects.
 

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

@@ -75,11 +75,13 @@ noncomputable section
 
 open Classical BigOperators Polynomial
 
+#print MvPowerSeries /-
 /-- Multivariate formal power series, where `σ` is the index set of the variables
 and `R` is the coefficient ring.-/
 def MvPowerSeries (σ : Type _) (R : Type _) :=
   (σ →₀ ℕ) → R
 #align mv_power_series MvPowerSeries
+-/
 
 namespace MvPowerSeries
 
@@ -119,34 +121,62 @@ section Semiring
 
 variable (R) [Semiring R]
 
+#print MvPowerSeries.monomial /-
 /-- The `n`th monomial with coefficient `a` as multivariate formal power series.-/
 def monomial (n : σ →₀ ℕ) : R →ₗ[R] MvPowerSeries σ R :=
   LinearMap.stdBasis R _ n
 #align mv_power_series.monomial MvPowerSeries.monomial
+-/
 
+#print MvPowerSeries.coeff /-
 /-- The `n`th coefficient of a multivariate formal power series.-/
 def coeff (n : σ →₀ ℕ) : MvPowerSeries σ R →ₗ[R] R :=
   LinearMap.proj n
 #align mv_power_series.coeff MvPowerSeries.coeff
+-/
 
 variable {R}
 
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 /-- Two multivariate formal power series are equal if all their coefficients are equal.-/
 @[ext]
 theorem ext {φ ψ} (h : ∀ n : σ →₀ ℕ, coeff R n φ = coeff R n ψ) : φ = ψ :=
   funext h
 #align mv_power_series.ext MvPowerSeries.ext
 
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 /-- Two multivariate formal power series are equal
  if and only if all their coefficients are equal.-/
 theorem ext_iff {φ ψ : MvPowerSeries σ R} : φ = ψ ↔ ∀ n : σ →₀ ℕ, coeff R n φ = coeff R n ψ :=
   Function.funext_iff
 #align mv_power_series.ext_iff MvPowerSeries.ext_iff
 
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 theorem monomial_def [DecidableEq σ] (n : σ →₀ ℕ) : monomial R n = LinearMap.stdBasis R _ n := by
   convert rfl
 #align mv_power_series.monomial_def MvPowerSeries.monomial_def
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_monomial MvPowerSeries.coeff_monomialₓ'. -/
 -- unify the `decidable` arguments
 theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
     coeff R m (monomial R n a) = if m = n then a else 0 := by
@@ -154,25 +184,55 @@ theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
     Pi.zero_apply]
 #align mv_power_series.coeff_monomial MvPowerSeries.coeff_monomial
 
+/- warning: mv_power_series.coeff_monomial_same -> MvPowerSeries.coeff_monomial_same is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_monomial_same MvPowerSeries.coeff_monomial_sameₓ'. -/
 @[simp]
 theorem coeff_monomial_same (n : σ →₀ ℕ) (a : R) : coeff R n (monomial R n a) = a :=
   LinearMap.stdBasis_same R _ n a
 #align mv_power_series.coeff_monomial_same MvPowerSeries.coeff_monomial_same
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_monomial_ne MvPowerSeries.coeff_monomial_neₓ'. -/
 theorem coeff_monomial_ne {m n : σ →₀ ℕ} (h : m ≠ n) (a : R) : coeff R m (monomial R n a) = 0 :=
   LinearMap.stdBasis_ne R _ _ _ h a
 #align mv_power_series.coeff_monomial_ne MvPowerSeries.coeff_monomial_ne
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.eq_of_coeff_monomial_ne_zero MvPowerSeries.eq_of_coeff_monomial_ne_zeroₓ'. -/
 theorem eq_of_coeff_monomial_ne_zero {m n : σ →₀ ℕ} {a : R} (h : coeff R m (monomial R n a) ≠ 0) :
     m = n :=
   by_contra fun h' => h <| coeff_monomial_ne h' a
 #align mv_power_series.eq_of_coeff_monomial_ne_zero MvPowerSeries.eq_of_coeff_monomial_ne_zero
 
+/- warning: mv_power_series.coeff_comp_monomial -> MvPowerSeries.coeff_comp_monomial is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_comp_monomial MvPowerSeries.coeff_comp_monomialₓ'. -/
 @[simp]
 theorem coeff_comp_monomial (n : σ →₀ ℕ) : (coeff R n).comp (monomial R n) = LinearMap.id :=
   LinearMap.ext <| coeff_monomial_same n
 #align mv_power_series.coeff_comp_monomial MvPowerSeries.coeff_comp_monomial
 
+/- warning: mv_power_series.coeff_zero -> MvPowerSeries.coeff_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero MvPowerSeries.coeff_zeroₓ'. -/
 @[simp]
 theorem coeff_zero (n : σ →₀ ℕ) : coeff R n (0 : MvPowerSeries σ R) = 0 :=
   rfl
@@ -183,14 +243,32 @@ variable (m n : σ →₀ ℕ) (φ ψ : MvPowerSeries σ R)
 instance : One (MvPowerSeries σ R) :=
   ⟨monomial R (0 : σ →₀ ℕ) 1⟩
 
+/- warning: mv_power_series.coeff_one -> MvPowerSeries.coeff_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_one MvPowerSeries.coeff_oneₓ'. -/
 theorem coeff_one [DecidableEq σ] : coeff R n (1 : MvPowerSeries σ R) = if n = 0 then 1 else 0 :=
   coeff_monomial _ _ _
 #align mv_power_series.coeff_one MvPowerSeries.coeff_one
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_one MvPowerSeries.coeff_zero_oneₓ'. -/
 theorem coeff_zero_one : coeff R (0 : σ →₀ ℕ) 1 = 1 :=
   coeff_monomial_same 0 1
 #align mv_power_series.coeff_zero_one MvPowerSeries.coeff_zero_one
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.monomial_zero_one MvPowerSeries.monomial_zero_oneₓ'. -/
 theorem monomial_zero_one : monomial R (0 : σ →₀ ℕ) 1 = 1 :=
   rfl
 #align mv_power_series.monomial_zero_one MvPowerSeries.monomial_zero_one
@@ -205,19 +283,43 @@ instance : AddMonoidWithOne (MvPowerSeries σ R) :=
 instance : Mul (MvPowerSeries σ R) :=
   ⟨fun φ ψ n => ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ⟩
 
+/- warning: mv_power_series.coeff_mul -> MvPowerSeries.coeff_mul is a dubious translation:
+lean 3 declaration is
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 theorem coeff_mul :
     coeff R n (φ * ψ) = ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ :=
   rfl
 #align mv_power_series.coeff_mul MvPowerSeries.coeff_mul
 
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 protected theorem zero_mul : (0 : MvPowerSeries σ R) * φ = 0 :=
   ext fun n => by simp [coeff_mul]
 #align mv_power_series.zero_mul MvPowerSeries.zero_mul
 
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 protected theorem mul_zero : φ * 0 = 0 :=
   ext fun n => by simp [coeff_mul]
 #align mv_power_series.mul_zero MvPowerSeries.mul_zero
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_monomial_mul MvPowerSeries.coeff_monomial_mulₓ'. -/
 theorem coeff_monomial_mul (a : R) :
     coeff R m (monomial R n a * φ) = if n ≤ m then a * coeff R (m - n) φ else 0 :=
   by
@@ -229,6 +331,12 @@ theorem coeff_monomial_mul (a : R) :
   simp only [Finset.sum_singleton, coeff_monomial_same, Finset.sum_empty]
 #align mv_power_series.coeff_monomial_mul MvPowerSeries.coeff_monomial_mul
 
+/- warning: mv_power_series.coeff_mul_monomial -> MvPowerSeries.coeff_mul_monomial is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_mul_monomial MvPowerSeries.coeff_mul_monomialₓ'. -/
 theorem coeff_mul_monomial (a : R) :
     coeff R m (φ * monomial R n a) = if n ≤ m then coeff R (m - n) φ * a else 0 :=
   by
@@ -240,18 +348,36 @@ theorem coeff_mul_monomial (a : R) :
   simp only [Finset.sum_singleton, coeff_monomial_same, Finset.sum_empty]
 #align mv_power_series.coeff_mul_monomial MvPowerSeries.coeff_mul_monomial
 
+/- warning: mv_power_series.coeff_add_monomial_mul -> MvPowerSeries.coeff_add_monomial_mul is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_add_monomial_mul MvPowerSeries.coeff_add_monomial_mulₓ'. -/
 theorem coeff_add_monomial_mul (a : R) : coeff R (m + n) (monomial R m a * φ) = a * coeff R n φ :=
   by
   rw [coeff_monomial_mul, if_pos, add_tsub_cancel_left]
   exact le_add_right le_rfl
 #align mv_power_series.coeff_add_monomial_mul MvPowerSeries.coeff_add_monomial_mul
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_add_mul_monomial MvPowerSeries.coeff_add_mul_monomialₓ'. -/
 theorem coeff_add_mul_monomial (a : R) : coeff R (m + n) (φ * monomial R n a) = coeff R m φ * a :=
   by
   rw [coeff_mul_monomial, if_pos, add_tsub_cancel_right]
   exact le_add_left le_rfl
 #align mv_power_series.coeff_add_mul_monomial MvPowerSeries.coeff_add_mul_monomial
 
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 @[simp]
 theorem commute_monomial {a : R} {n} : Commute φ (monomial R n a) ↔ ∀ m, Commute (coeff R m φ) a :=
   by
@@ -262,22 +388,52 @@ theorem commute_monomial {a : R} {n} : Commute φ (monomial R n a) ↔ ∀ m, Co
     split_ifs <;> [apply h, rfl]
 #align mv_power_series.commute_monomial MvPowerSeries.commute_monomial
 
+/- warning: mv_power_series.one_mul -> MvPowerSeries.one_mul is a dubious translation:
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 protected theorem one_mul : (1 : MvPowerSeries σ R) * φ = φ :=
   ext fun n => by simpa using coeff_add_monomial_mul 0 n φ 1
 #align mv_power_series.one_mul MvPowerSeries.one_mul
 
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 protected theorem mul_one : φ * 1 = φ :=
   ext fun n => by simpa using coeff_add_mul_monomial n 0 φ 1
 #align mv_power_series.mul_one MvPowerSeries.mul_one
 
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 protected theorem mul_add (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : φ₁ * (φ₂ + φ₃) = φ₁ * φ₂ + φ₁ * φ₃ :=
   ext fun n => by simp only [coeff_mul, mul_add, Finset.sum_add_distrib, LinearMap.map_add]
 #align mv_power_series.mul_add MvPowerSeries.mul_add
 
+/- warning: mv_power_series.add_mul -> MvPowerSeries.add_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.add_mul MvPowerSeries.add_mulₓ'. -/
 protected theorem add_mul (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : (φ₁ + φ₂) * φ₃ = φ₁ * φ₃ + φ₂ * φ₃ :=
   ext fun n => by simp only [coeff_mul, add_mul, Finset.sum_add_distrib, LinearMap.map_add]
 #align mv_power_series.add_mul MvPowerSeries.add_mul
 
+/- warning: mv_power_series.mul_assoc -> MvPowerSeries.mul_assoc is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.mul_assoc MvPowerSeries.mul_assocₓ'. -/
 protected theorem mul_assoc (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : φ₁ * φ₂ * φ₃ = φ₁ * (φ₂ * φ₃) :=
   by
   ext1 n
@@ -333,6 +489,12 @@ section Semiring
 
 variable [Semiring R]
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.monomial_mul_monomial MvPowerSeries.monomial_mul_monomialₓ'. -/
 theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
     monomial R m a * monomial R n b = monomial R (m + n) (a * b) :=
   by
@@ -350,103 +512,213 @@ theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
 
 variable (σ) (R)
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.C MvPowerSeries.Cₓ'. -/
 /-- The constant multivariate formal power series.-/
-def c : R →+* MvPowerSeries σ R :=
+def C : R →+* MvPowerSeries σ R :=
   { monomial R (0 : σ →₀ ℕ) with
     map_one' := rfl
     map_mul' := fun a b => (monomial_mul_monomial 0 0 a b).symm
     map_zero' := (monomial R (0 : _)).map_zero }
-#align mv_power_series.C MvPowerSeries.c
+#align mv_power_series.C MvPowerSeries.C
 
 variable {σ} {R}
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.monomial_zero_eq_C MvPowerSeries.monomial_zero_eq_Cₓ'. -/
 @[simp]
-theorem monomial_zero_eq_c : ⇑(monomial R (0 : σ →₀ ℕ)) = c σ R :=
+theorem monomial_zero_eq_C : ⇑(monomial R (0 : σ →₀ ℕ)) = C σ R :=
   rfl
-#align mv_power_series.monomial_zero_eq_C MvPowerSeries.monomial_zero_eq_c
-
-theorem monomial_zero_eq_c_apply (a : R) : monomial R (0 : σ →₀ ℕ) a = c σ R a :=
+#align mv_power_series.monomial_zero_eq_C MvPowerSeries.monomial_zero_eq_C
+
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.monomial_zero_eq_C_apply MvPowerSeries.monomial_zero_eq_C_applyₓ'. -/
+theorem monomial_zero_eq_C_apply (a : R) : monomial R (0 : σ →₀ ℕ) a = C σ R a :=
   rfl
-#align mv_power_series.monomial_zero_eq_C_apply MvPowerSeries.monomial_zero_eq_c_apply
-
-theorem coeff_c [DecidableEq σ] (n : σ →₀ ℕ) (a : R) :
-    coeff R n (c σ R a) = if n = 0 then a else 0 :=
+#align mv_power_series.monomial_zero_eq_C_apply MvPowerSeries.monomial_zero_eq_C_apply
+
+/- warning: mv_power_series.coeff_C -> MvPowerSeries.coeff_C is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_C MvPowerSeries.coeff_Cₓ'. -/
+theorem coeff_C [DecidableEq σ] (n : σ →₀ ℕ) (a : R) :
+    coeff R n (C σ R a) = if n = 0 then a else 0 :=
   coeff_monomial _ _ _
-#align mv_power_series.coeff_C MvPowerSeries.coeff_c
-
-theorem coeff_zero_c (a : R) : coeff R (0 : σ →₀ ℕ) (c σ R a) = a :=
+#align mv_power_series.coeff_C MvPowerSeries.coeff_C
+
+/- warning: mv_power_series.coeff_zero_C -> MvPowerSeries.coeff_zero_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_C MvPowerSeries.coeff_zero_Cₓ'. -/
+theorem coeff_zero_C (a : R) : coeff R (0 : σ →₀ ℕ) (C σ R a) = a :=
   coeff_monomial_same 0 a
-#align mv_power_series.coeff_zero_C MvPowerSeries.coeff_zero_c
+#align mv_power_series.coeff_zero_C MvPowerSeries.coeff_zero_C
 
+#print MvPowerSeries.X /-
 /-- The variables of the multivariate formal power series ring.-/
-def x (s : σ) : MvPowerSeries σ R :=
+def X (s : σ) : MvPowerSeries σ R :=
   monomial R (single s 1) 1
-#align mv_power_series.X MvPowerSeries.x
+#align mv_power_series.X MvPowerSeries.X
+-/
 
-theorem coeff_x [DecidableEq σ] (n : σ →₀ ℕ) (s : σ) :
-    coeff R n (x s : MvPowerSeries σ R) = if n = single s 1 then 1 else 0 :=
+/- warning: mv_power_series.coeff_X -> MvPowerSeries.coeff_X is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_X MvPowerSeries.coeff_Xₓ'. -/
+theorem coeff_X [DecidableEq σ] (n : σ →₀ ℕ) (s : σ) :
+    coeff R n (X s : MvPowerSeries σ R) = if n = single s 1 then 1 else 0 :=
   coeff_monomial _ _ _
-#align mv_power_series.coeff_X MvPowerSeries.coeff_x
-
-theorem coeff_index_single_x [DecidableEq σ] (s t : σ) :
-    coeff R (single t 1) (x s : MvPowerSeries σ R) = if t = s then 1 else 0 := by
+#align mv_power_series.coeff_X MvPowerSeries.coeff_X
+
+/- warning: mv_power_series.coeff_index_single_X -> MvPowerSeries.coeff_index_single_X is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_index_single_X MvPowerSeries.coeff_index_single_Xₓ'. -/
+theorem coeff_index_single_X [DecidableEq σ] (s t : σ) :
+    coeff R (single t 1) (X s : MvPowerSeries σ R) = if t = s then 1 else 0 := by
   simp only [coeff_X, single_left_inj one_ne_zero]
-#align mv_power_series.coeff_index_single_X MvPowerSeries.coeff_index_single_x
-
+#align mv_power_series.coeff_index_single_X MvPowerSeries.coeff_index_single_X
+
+/- warning: mv_power_series.coeff_index_single_self_X -> MvPowerSeries.coeff_index_single_self_X is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_index_single_self_X MvPowerSeries.coeff_index_single_self_Xₓ'. -/
 @[simp]
-theorem coeff_index_single_self_x (s : σ) : coeff R (single s 1) (x s : MvPowerSeries σ R) = 1 :=
+theorem coeff_index_single_self_X (s : σ) : coeff R (single s 1) (X s : MvPowerSeries σ R) = 1 :=
   coeff_monomial_same _ _
-#align mv_power_series.coeff_index_single_self_X MvPowerSeries.coeff_index_single_self_x
-
-theorem coeff_zero_x (s : σ) : coeff R (0 : σ →₀ ℕ) (x s : MvPowerSeries σ R) = 0 :=
+#align mv_power_series.coeff_index_single_self_X MvPowerSeries.coeff_index_single_self_X
+
+/- warning: mv_power_series.coeff_zero_X -> MvPowerSeries.coeff_zero_X is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_X MvPowerSeries.coeff_zero_Xₓ'. -/
+theorem coeff_zero_X (s : σ) : coeff R (0 : σ →₀ ℕ) (X s : MvPowerSeries σ R) = 0 :=
   by
   rw [coeff_X, if_neg]
   intro h
   exact one_ne_zero (single_eq_zero.mp h.symm)
-#align mv_power_series.coeff_zero_X MvPowerSeries.coeff_zero_x
-
-theorem commute_x (φ : MvPowerSeries σ R) (s : σ) : Commute φ (x s) :=
+#align mv_power_series.coeff_zero_X MvPowerSeries.coeff_zero_X
+
+/- warning: mv_power_series.commute_X -> MvPowerSeries.commute_X is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (φ : MvPowerSeries.{u1, u2} σ R) (s : σ), Commute.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.hasMul.{u1, u2} σ R _inst_1) φ (MvPowerSeries.X.{u1, u2} σ R _inst_1 s)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.commute_X MvPowerSeries.commute_Xₓ'. -/
+theorem commute_X (φ : MvPowerSeries σ R) (s : σ) : Commute φ (X s) :=
   φ.commute_monomial.mpr fun m => Commute.one_right _
-#align mv_power_series.commute_X MvPowerSeries.commute_x
-
-theorem x_def (s : σ) : x s = monomial R (single s 1) 1 :=
+#align mv_power_series.commute_X MvPowerSeries.commute_X
+
+/- warning: mv_power_series.X_def -> MvPowerSeries.X_def is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.X_def MvPowerSeries.X_defₓ'. -/
+theorem X_def (s : σ) : X s = monomial R (single s 1) 1 :=
   rfl
-#align mv_power_series.X_def MvPowerSeries.x_def
-
-theorem x_pow_eq (s : σ) (n : ℕ) : (x s : MvPowerSeries σ R) ^ n = monomial R (single s n) 1 :=
+#align mv_power_series.X_def MvPowerSeries.X_def
+
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.X_pow_eq MvPowerSeries.X_pow_eqₓ'. -/
+theorem X_pow_eq (s : σ) (n : ℕ) : (X s : MvPowerSeries σ R) ^ n = monomial R (single s n) 1 :=
   by
   induction' n with n ih
   · rw [pow_zero, Finsupp.single_zero, monomial_zero_one]
   · rw [pow_succ', ih, Nat.succ_eq_add_one, Finsupp.single_add, X, monomial_mul_monomial, one_mul]
-#align mv_power_series.X_pow_eq MvPowerSeries.x_pow_eq
-
-theorem coeff_x_pow [DecidableEq σ] (m : σ →₀ ℕ) (s : σ) (n : ℕ) :
-    coeff R m ((x s : MvPowerSeries σ R) ^ n) = if m = single s n then 1 else 0 := by
+#align mv_power_series.X_pow_eq MvPowerSeries.X_pow_eq
+
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_X_pow MvPowerSeries.coeff_X_powₓ'. -/
+theorem coeff_X_pow [DecidableEq σ] (m : σ →₀ ℕ) (s : σ) (n : ℕ) :
+    coeff R m ((X s : MvPowerSeries σ R) ^ n) = if m = single s n then 1 else 0 := by
   rw [X_pow_eq s n, coeff_monomial]
-#align mv_power_series.coeff_X_pow MvPowerSeries.coeff_x_pow
-
+#align mv_power_series.coeff_X_pow MvPowerSeries.coeff_X_pow
+
+/- warning: mv_power_series.coeff_mul_C -> MvPowerSeries.coeff_mul_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_mul_C MvPowerSeries.coeff_mul_Cₓ'. -/
 @[simp]
-theorem coeff_mul_c (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
-    coeff R n (φ * c σ R a) = coeff R n φ * a := by simpa using coeff_add_mul_monomial n 0 φ a
-#align mv_power_series.coeff_mul_C MvPowerSeries.coeff_mul_c
-
+theorem coeff_mul_C (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
+    coeff R n (φ * C σ R a) = coeff R n φ * a := by simpa using coeff_add_mul_monomial n 0 φ a
+#align mv_power_series.coeff_mul_C MvPowerSeries.coeff_mul_C
+
+/- warning: mv_power_series.coeff_C_mul -> MvPowerSeries.coeff_C_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_C_mul MvPowerSeries.coeff_C_mulₓ'. -/
 @[simp]
-theorem coeff_c_mul (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
-    coeff R n (c σ R a * φ) = a * coeff R n φ := by simpa using coeff_add_monomial_mul 0 n φ a
-#align mv_power_series.coeff_C_mul MvPowerSeries.coeff_c_mul
-
-theorem coeff_zero_mul_x (φ : MvPowerSeries σ R) (s : σ) : coeff R (0 : σ →₀ ℕ) (φ * x s) = 0 :=
+theorem coeff_C_mul (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
+    coeff R n (C σ R a * φ) = a * coeff R n φ := by simpa using coeff_add_monomial_mul 0 n φ a
+#align mv_power_series.coeff_C_mul MvPowerSeries.coeff_C_mul
+
+/- warning: mv_power_series.coeff_zero_mul_X -> MvPowerSeries.coeff_zero_mul_X is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_mul_X MvPowerSeries.coeff_zero_mul_Xₓ'. -/
+theorem coeff_zero_mul_X (φ : MvPowerSeries σ R) (s : σ) : coeff R (0 : σ →₀ ℕ) (φ * X s) = 0 :=
   by
   have : ¬single s 1 ≤ 0 := fun h => by simpa using h s
   simp only [X, coeff_mul_monomial, if_neg this]
-#align mv_power_series.coeff_zero_mul_X MvPowerSeries.coeff_zero_mul_x
-
-theorem coeff_zero_x_mul (φ : MvPowerSeries σ R) (s : σ) : coeff R (0 : σ →₀ ℕ) (x s * φ) = 0 := by
+#align mv_power_series.coeff_zero_mul_X MvPowerSeries.coeff_zero_mul_X
+
+/- warning: mv_power_series.coeff_zero_X_mul -> MvPowerSeries.coeff_zero_X_mul is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_X_mul MvPowerSeries.coeff_zero_X_mulₓ'. -/
+theorem coeff_zero_X_mul (φ : MvPowerSeries σ R) (s : σ) : coeff R (0 : σ →₀ ℕ) (X s * φ) = 0 := by
   rw [← (φ.commute_X s).Eq, coeff_zero_mul_X]
-#align mv_power_series.coeff_zero_X_mul MvPowerSeries.coeff_zero_x_mul
+#align mv_power_series.coeff_zero_X_mul MvPowerSeries.coeff_zero_X_mul
 
 variable (σ) (R)
 
+/- warning: mv_power_series.constant_coeff -> MvPowerSeries.constantCoeff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.constant_coeff MvPowerSeries.constantCoeffₓ'. -/
 /-- The constant coefficient of a formal power series.-/
 def constantCoeff : MvPowerSeries σ R →+* R :=
   { coeff R (0 : σ →₀ ℕ) with
@@ -458,41 +730,85 @@ def constantCoeff : MvPowerSeries σ R →+* R :=
 
 variable {σ} {R}
 
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 @[simp]
 theorem coeff_zero_eq_constantCoeff : ⇑(coeff R (0 : σ →₀ ℕ)) = constantCoeff σ R :=
   rfl
 #align mv_power_series.coeff_zero_eq_constant_coeff MvPowerSeries.coeff_zero_eq_constantCoeff
 
+/- warning: mv_power_series.coeff_zero_eq_constant_coeff_apply -> MvPowerSeries.coeff_zero_eq_constantCoeff_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_zero_eq_constant_coeff_apply MvPowerSeries.coeff_zero_eq_constantCoeff_applyₓ'. -/
 theorem coeff_zero_eq_constantCoeff_apply (φ : MvPowerSeries σ R) :
     coeff R (0 : σ →₀ ℕ) φ = constantCoeff σ R φ :=
   rfl
 #align mv_power_series.coeff_zero_eq_constant_coeff_apply MvPowerSeries.coeff_zero_eq_constantCoeff_apply
 
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u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u2} σ R _inst_1)))))) (MvPowerSeries.C.{u1, u2} σ R _inst_1) a)) a
+Case conversion may be inaccurate. Consider using '#align mv_power_series.constant_coeff_C MvPowerSeries.constantCoeff_Cₓ'. -/
 @[simp]
-theorem constantCoeff_c (a : R) : constantCoeff σ R (c σ R a) = a :=
+theorem constantCoeff_C (a : R) : constantCoeff σ R (C σ R a) = a :=
   rfl
-#align mv_power_series.constant_coeff_C MvPowerSeries.constantCoeff_c
+#align mv_power_series.constant_coeff_C MvPowerSeries.constantCoeff_C
 
+#print MvPowerSeries.constantCoeff_comp_C /-
 @[simp]
-theorem constantCoeff_comp_c : (constantCoeff σ R).comp (c σ R) = RingHom.id R :=
+theorem constantCoeff_comp_C : (constantCoeff σ R).comp (C σ R) = RingHom.id R :=
   rfl
-#align mv_power_series.constant_coeff_comp_C MvPowerSeries.constantCoeff_comp_c
+#align mv_power_series.constant_coeff_comp_C MvPowerSeries.constantCoeff_comp_C
+-/
 
+/- warning: mv_power_series.constant_coeff_zero -> MvPowerSeries.constantCoeff_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.constant_coeff_zero MvPowerSeries.constantCoeff_zeroₓ'. -/
 @[simp]
 theorem constantCoeff_zero : constantCoeff σ R 0 = 0 :=
   rfl
 #align mv_power_series.constant_coeff_zero MvPowerSeries.constantCoeff_zero
 
+/- warning: mv_power_series.constant_coeff_one -> MvPowerSeries.constantCoeff_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.constant_coeff_one MvPowerSeries.constantCoeff_oneₓ'. -/
 @[simp]
 theorem constantCoeff_one : constantCoeff σ R 1 = 1 :=
   rfl
 #align mv_power_series.constant_coeff_one MvPowerSeries.constantCoeff_one
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.constant_coeff_X MvPowerSeries.constantCoeff_Xₓ'. -/
 @[simp]
-theorem constantCoeff_x (s : σ) : constantCoeff σ R (x s) = 0 :=
-  coeff_zero_x s
-#align mv_power_series.constant_coeff_X MvPowerSeries.constantCoeff_x
-
+theorem constantCoeff_X (s : σ) : constantCoeff σ R (X s) = 0 :=
+  coeff_zero_X s
+#align mv_power_series.constant_coeff_X MvPowerSeries.constantCoeff_X
+
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.is_unit_constant_coeff MvPowerSeries.isUnit_constantCoeffₓ'. -/
 /-- If a multivariate formal power series is invertible,
  then so is its constant coefficient.-/
 theorem isUnit_constantCoeff (φ : MvPowerSeries σ R) (h : IsUnit φ) :
@@ -500,18 +816,31 @@ theorem isUnit_constantCoeff (φ : MvPowerSeries σ R) (h : IsUnit φ) :
   h.map _
 #align mv_power_series.is_unit_constant_coeff MvPowerSeries.isUnit_constantCoeff
 
+/- warning: mv_power_series.coeff_smul -> MvPowerSeries.coeff_smul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_smul MvPowerSeries.coeff_smulₓ'. -/
 @[simp]
 theorem coeff_smul (f : MvPowerSeries σ R) (n) (a : R) : coeff _ n (a • f) = a * coeff _ n f :=
   rfl
 #align mv_power_series.coeff_smul MvPowerSeries.coeff_smul
 
-theorem smul_eq_c_mul (f : MvPowerSeries σ R) (a : R) : a • f = c σ R a * f :=
+/- warning: mv_power_series.smul_eq_C_mul -> MvPowerSeries.smul_eq_C_mul is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] (f : MvPowerSeries.{u1, u2} σ R) (a : R), Eq.{succ (max u1 u2)} (MvPowerSeries.{u1, u2} σ R) (SMul.smul.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (SMulZeroClass.toHasSmul.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (AddZeroClass.toHasZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (SMulWithZero.toSmulZeroClass.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Module.toMulActionWithZero.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) _inst_1 (MvPowerSeries.addCommMonoid.{u1, u2} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (MvPowerSeries.module.{u1, u2, u2} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))))) a f) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u2} σ R) (instHMul.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.hasMul.{u1, u2} σ R _inst_1)) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) => R -> (MvPowerSeries.{u1, u2} σ R)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) (MvPowerSeries.C.{u1, u2} σ R _inst_1) a) f)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.smul_eq_C_mul MvPowerSeries.smul_eq_C_mulₓ'. -/
+theorem smul_eq_C_mul (f : MvPowerSeries σ R) (a : R) : a • f = C σ R a * f :=
   by
   ext
   simp
-#align mv_power_series.smul_eq_C_mul MvPowerSeries.smul_eq_c_mul
+#align mv_power_series.smul_eq_C_mul MvPowerSeries.smul_eq_C_mul
 
-theorem x_inj [Nontrivial R] {s t : σ} : (x s : MvPowerSeries σ R) = x t ↔ s = t :=
+#print MvPowerSeries.X_inj /-
+theorem X_inj [Nontrivial R] {s t : σ} : (X s : MvPowerSeries σ R) = X t ↔ s = t :=
   ⟨by
     intro h; replace h := congr_arg (coeff R (single s 1)) h; rw [coeff_X, if_pos rfl, coeff_X] at h
     split_ifs  at h with H
@@ -521,8 +850,9 @@ theorem x_inj [Nontrivial R] {s t : σ} : (x s : MvPowerSeries σ R) = x t ↔ s
       · exfalso
         exact one_ne_zero H.1
     · exfalso
-      exact one_ne_zero h, congr_arg x⟩
-#align mv_power_series.X_inj MvPowerSeries.x_inj
+      exact one_ne_zero h, congr_arg X⟩
+#align mv_power_series.X_inj MvPowerSeries.X_inj
+-/
 
 end Semiring
 
@@ -534,6 +864,12 @@ variable (f : R →+* S) (g : S →+* T)
 
 variable (σ)
 
+/- warning: mv_power_series.map -> MvPowerSeries.map is a dubious translation:
+lean 3 declaration is
+  forall (σ : Type.{u1}) {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S], (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S _inst_2)) -> (RingHom.{max u1 u2, max u1 u3} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ S) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPowerSeries.{u1, u3} σ S) (MvPowerSeries.semiring.{u1, u3} σ S _inst_2)))
+but is expected to have type
+  forall (σ : Type.{u1}) {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u3} S], (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S _inst_2)) -> (RingHom.{max u2 u1, max u3 u1} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ S) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u2} σ R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPowerSeries.{u1, u3} σ S) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u3} σ S _inst_2)))
+Case conversion may be inaccurate. Consider using '#align mv_power_series.map MvPowerSeries.mapₓ'. -/
 /-- The map between multivariate formal power series induced by a map on the coefficients.-/
 def map : MvPowerSeries σ R →+* MvPowerSeries σ S
     where
@@ -556,26 +892,56 @@ def map : MvPowerSeries σ R →+* MvPowerSeries σ S
 
 variable {σ}
 
+/- warning: mv_power_series.map_id -> MvPowerSeries.map_id is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R], Eq.{succ (max u1 u2)} (RingHom.{max u1 u2, max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1))) (MvPowerSeries.map.{u1, u2, u2} σ R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (RingHom.id.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R _inst_1)))
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.map_id MvPowerSeries.map_idₓ'. -/
 @[simp]
 theorem map_id : map σ (RingHom.id R) = RingHom.id _ :=
   rfl
 #align mv_power_series.map_id MvPowerSeries.map_id
 
+/- warning: mv_power_series.map_comp -> MvPowerSeries.map_comp is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.map_comp MvPowerSeries.map_compₓ'. -/
 theorem map_comp : map σ (g.comp f) = (map σ g).comp (map σ f) :=
   rfl
 #align mv_power_series.map_comp MvPowerSeries.map_comp
 
+/- warning: mv_power_series.coeff_map -> MvPowerSeries.coeff_map is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_map MvPowerSeries.coeff_mapₓ'. -/
 @[simp]
 theorem coeff_map (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) : coeff S n (map σ f φ) = f (coeff R n φ) :=
   rfl
 #align mv_power_series.coeff_map MvPowerSeries.coeff_map
 
+/- warning: mv_power_series.constant_coeff_map -> MvPowerSeries.constantCoeff_map is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.constant_coeff_map MvPowerSeries.constantCoeff_mapₓ'. -/
 @[simp]
 theorem constantCoeff_map (φ : MvPowerSeries σ R) :
     constantCoeff σ S (map σ f φ) = f (constantCoeff σ R φ) :=
   rfl
 #align mv_power_series.constant_coeff_map MvPowerSeries.constantCoeff_map
 
+/- warning: mv_power_series.map_monomial -> MvPowerSeries.map_monomial is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.map_monomial MvPowerSeries.map_monomialₓ'. -/
 @[simp]
 theorem map_monomial (n : σ →₀ ℕ) (a : R) : map σ f (monomial R n a) = monomial S n (f a) :=
   by
@@ -583,14 +949,26 @@ theorem map_monomial (n : σ →₀ ℕ) (a : R) : map σ f (monomial R n a) = m
   simp [coeff_monomial, apply_ite f]
 #align mv_power_series.map_monomial MvPowerSeries.map_monomial
 
+/- warning: mv_power_series.map_C -> MvPowerSeries.map_C is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.map_C MvPowerSeries.map_Cₓ'. -/
 @[simp]
-theorem map_c (a : R) : map σ f (c σ R a) = c σ S (f a) :=
+theorem map_C (a : R) : map σ f (C σ R a) = C σ S (f a) :=
   map_monomial _ _ _
-#align mv_power_series.map_C MvPowerSeries.map_c
-
+#align mv_power_series.map_C MvPowerSeries.map_C
+
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.map_X MvPowerSeries.map_Xₓ'. -/
 @[simp]
-theorem map_x (s : σ) : map σ f (x s) = x s := by simp [MvPowerSeries.x]
-#align mv_power_series.map_X MvPowerSeries.map_x
+theorem map_X (s : σ) : map σ f (X s) = X s := by simp [MvPowerSeries.X]
+#align mv_power_series.map_X MvPowerSeries.map_X
 
 end Map
 
@@ -607,13 +985,25 @@ instance : Algebra R (MvPowerSeries σ A) :=
     smul_def' := fun a σ => by
       ext n
       simp [(coeff A n).map_smul_of_tower a, Algebra.smul_def]
-    toRingHom := (MvPowerSeries.map σ (algebraMap R A)).comp (c σ R) }
-
-theorem c_eq_algebraMap : c σ R = algebraMap R (MvPowerSeries σ R) :=
+    toRingHom := (MvPowerSeries.map σ (algebraMap R A)).comp (C σ R) }
+
+/- warning: mv_power_series.C_eq_algebra_map -> MvPowerSeries.c_eq_algebraMap is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.C_eq_algebra_map MvPowerSeries.c_eq_algebraMapₓ'. -/
+theorem c_eq_algebraMap : C σ R = algebraMap R (MvPowerSeries σ R) :=
   rfl
 #align mv_power_series.C_eq_algebra_map MvPowerSeries.c_eq_algebraMap
 
-theorem algebraMap_apply {r : R} : algebraMap R (MvPowerSeries σ A) r = c σ A (algebraMap R A r) :=
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(MvPowerSeries.{u3, u2} σ A) (MvPowerSeries.instSemiringMvPowerSeries.{u3, u2} σ A _inst_2)))))) (MvPowerSeries.C.{u3, u2} σ A _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} 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+Case conversion may be inaccurate. Consider using '#align mv_power_series.algebra_map_apply MvPowerSeries.algebraMap_applyₓ'. -/
+theorem algebraMap_apply {r : R} : algebraMap R (MvPowerSeries σ A) r = C σ A (algebraMap R A r) :=
   by
   change (MvPowerSeries.map σ (algebraMap R A)).comp (C σ R) r = _
   simp
@@ -636,11 +1026,19 @@ section Trunc
 
 variable [CommSemiring R] (n : σ →₀ ℕ)
 
+#print MvPowerSeries.truncFun /-
 /-- Auxiliary definition for the truncation function. -/
 def truncFun (φ : MvPowerSeries σ R) : MvPolynomial σ R :=
   ∑ m in Finset.Iio n, MvPolynomial.monomial m (coeff R m φ)
 #align mv_power_series.trunc_fun MvPowerSeries.truncFun
+-/
 
+/- warning: mv_power_series.coeff_trunc_fun -> MvPowerSeries.coeff_truncFun is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_trunc_fun MvPowerSeries.coeff_truncFunₓ'. -/
 theorem coeff_truncFun (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
     (truncFun n φ).coeff m = if m < n then coeff R m φ else 0 := by
   simp [trunc_fun, MvPolynomial.coeff_sum]
@@ -648,6 +1046,7 @@ theorem coeff_truncFun (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
 
 variable (R)
 
+#print MvPowerSeries.trunc /-
 /-- The `n`th truncation of a multivariate formal power series to a multivariate polynomial -/
 def trunc : MvPowerSeries σ R →+ MvPolynomial σ R
     where
@@ -661,13 +1060,26 @@ def trunc : MvPowerSeries σ R →+ MvPolynomial σ R
     simp [coeff_trunc_fun, ite_add]
     split_ifs <;> rfl
 #align mv_power_series.trunc MvPowerSeries.trunc
+-/
 
 variable {R}
 
+/- warning: mv_power_series.coeff_trunc -> MvPowerSeries.coeff_trunc is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_trunc MvPowerSeries.coeff_truncₓ'. -/
 theorem coeff_trunc (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
     (trunc R n φ).coeff m = if m < n then coeff R m φ else 0 := by simp [Trunc, coeff_trunc_fun]
 #align mv_power_series.coeff_trunc MvPowerSeries.coeff_trunc
 
+/- warning: mv_power_series.trunc_one -> MvPowerSeries.trunc_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.trunc_one MvPowerSeries.trunc_oneₓ'. -/
 @[simp]
 theorem trunc_one (hnn : n ≠ 0) : trunc R n 1 = 1 :=
   MvPolynomial.ext _ _ fun m => by
@@ -686,8 +1098,14 @@ theorem trunc_one (hnn : n ≠ 0) : trunc R n 1 = 1 :=
       exact Ne.bot_lt hnn
 #align mv_power_series.trunc_one MvPowerSeries.trunc_one
 
+/- warning: mv_power_series.trunc_C -> MvPowerSeries.trunc_c is a dubious translation:
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+but is expected to have type
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(CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (MvPolynomial.C.{u1, u2} R σ _inst_1) a))
+Case conversion may be inaccurate. Consider using '#align mv_power_series.trunc_C MvPowerSeries.trunc_cₓ'. -/
 @[simp]
-theorem trunc_c (hnn : n ≠ 0) (a : R) : trunc R n (c σ R a) = MvPolynomial.C a :=
+theorem trunc_c (hnn : n ≠ 0) (a : R) : trunc R n (C σ R a) = MvPolynomial.C a :=
   MvPolynomial.ext _ _ fun m =>
     by
     rw [coeff_trunc, coeff_C, MvPolynomial.coeff_C]
@@ -701,8 +1119,14 @@ section Semiring
 
 variable [Semiring R]
 
-theorem x_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
-    (x s : MvPowerSeries σ R) ^ n ∣ φ ↔ ∀ m : σ →₀ ℕ, m s < n → coeff R m φ = 0 :=
+/- warning: mv_power_series.X_pow_dvd_iff -> MvPowerSeries.X_pow_dvd_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.X_pow_dvd_iff MvPowerSeries.X_pow_dvd_iffₓ'. -/
+theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
+    (X s : MvPowerSeries σ R) ^ n ∣ φ ↔ ∀ m : σ →₀ ℕ, m s < n → coeff R m φ = 0 :=
   by
   constructor
   · rintro ⟨φ, rfl⟩ m h
@@ -755,16 +1179,22 @@ theorem x_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
           · subst t
             simpa using tsub_add_cancel_of_le H
           · simp [Finsupp.single_apply, hst]
-#align mv_power_series.X_pow_dvd_iff MvPowerSeries.x_pow_dvd_iff
-
-theorem x_dvd_iff {s : σ} {φ : MvPowerSeries σ R} :
-    (x s : MvPowerSeries σ R) ∣ φ ↔ ∀ m : σ →₀ ℕ, m s = 0 → coeff R m φ = 0 :=
+#align mv_power_series.X_pow_dvd_iff MvPowerSeries.X_pow_dvd_iff
+
+/- warning: mv_power_series.X_dvd_iff -> MvPowerSeries.X_dvd_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {s : σ} {φ : MvPowerSeries.{u2, u1} σ R}, Iff (Dvd.dvd.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (semigroupDvd.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (SemigroupWithZero.toSemigroup.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonUnitalSemiring.toSemigroupWithZero.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonUnitalSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R _inst_1))))) (MvPowerSeries.X.{u2, u1} σ R _inst_1 s) φ) (forall (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), (Eq.{1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) s) (FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (_x : σ) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) _x) (Finsupp.funLike.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) m s) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) s) 0 (instOfNatNat 0))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) R (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1)) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} R R (MvPowerSeries.{u2, u1} σ R) R _inst_1 _inst_1 (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MvPowerSeries.coeff.{u2, u1} σ R _inst_1 m) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ R) => R) φ) _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align mv_power_series.X_dvd_iff MvPowerSeries.X_dvd_iffₓ'. -/
+theorem X_dvd_iff {s : σ} {φ : MvPowerSeries σ R} :
+    (X s : MvPowerSeries σ R) ∣ φ ↔ ∀ m : σ →₀ ℕ, m s = 0 → coeff R m φ = 0 :=
   by
   rw [← pow_one (X s : MvPowerSeries σ R), X_pow_dvd_iff]
   constructor <;> intro h m hm
   · exact h m (hm.symm ▸ zero_lt_one)
   · exact h m (Nat.eq_zero_of_le_zero <| Nat.le_of_succ_le_succ hm)
-#align mv_power_series.X_dvd_iff MvPowerSeries.x_dvd_iff
+#align mv_power_series.X_dvd_iff MvPowerSeries.X_dvd_iff
 
 end Semiring
 
@@ -772,6 +1202,7 @@ section Ring
 
 variable [Ring R]
 
+#print MvPowerSeries.inv.aux /-
 /-
 The inverse of a multivariate formal power series is defined by
 well-founded recursion on the coeffients of the inverse.
@@ -780,32 +1211,51 @@ well-founded recursion on the coeffients of the inverse.
  the totalised inverse formal power series `(_)⁻¹` and
  the inverse formal power series that depends on
  an inverse of the constant coefficient `inv_of_unit`.-/
-protected noncomputable def Inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerSeries σ R
+protected noncomputable def inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerSeries σ R
   | n =>
     if n = 0 then a
     else
       -a *
         ∑ x in n.antidiagonal, if h : x.2 < n then coeff R x.1 φ * inv.aux x.2 else 0termination_by'
   ⟨_, Finsupp.lt_wf σ⟩
-#align mv_power_series.inv.aux MvPowerSeries.Inv.aux
+#align mv_power_series.inv.aux MvPowerSeries.inv.aux
+-/
 
+/- warning: mv_power_series.coeff_inv_aux -> MvPowerSeries.coeff_inv_aux is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_inv_aux MvPowerSeries.coeff_inv_auxₓ'. -/
 theorem coeff_inv_aux [DecidableEq σ] (n : σ →₀ ℕ) (a : R) (φ : MvPowerSeries σ R) :
-    coeff R n (Inv.aux a φ) =
+    coeff R n (inv.aux a φ) =
       if n = 0 then a
       else
         -a *
-          ∑ x in n.antidiagonal, if x.2 < n then coeff R x.1 φ * coeff R x.2 (Inv.aux a φ) else 0 :=
-  show Inv.aux a φ n = _ by
+          ∑ x in n.antidiagonal, if x.2 < n then coeff R x.1 φ * coeff R x.2 (inv.aux a φ) else 0 :=
+  show inv.aux a φ n = _ by
     rw [inv.aux]
     convert rfl
 #align mv_power_series.coeff_inv_aux MvPowerSeries.coeff_inv_aux
 
+/- warning: mv_power_series.inv_of_unit -> MvPowerSeries.invOfUnit is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Ring.{u2} R], (MvPowerSeries.{u1, u2} σ R) -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1)) -> (MvPowerSeries.{u1, u2} σ R)
+but is expected to have type
+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Ring.{u2} R], (MvPowerSeries.{u1, u2} σ R) -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) -> (MvPowerSeries.{u1, u2} σ R)
+Case conversion may be inaccurate. Consider using '#align mv_power_series.inv_of_unit MvPowerSeries.invOfUnitₓ'. -/
 -- unify `decidable` instances
 /-- A multivariate formal power series is invertible if the constant coefficient is invertible.-/
 def invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) : MvPowerSeries σ R :=
-  Inv.aux (↑u⁻¹) φ
+  inv.aux (↑u⁻¹) φ
 #align mv_power_series.inv_of_unit MvPowerSeries.invOfUnit
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_inv_of_unit MvPowerSeries.coeff_invOfUnitₓ'. -/
 theorem coeff_invOfUnit [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (u : Rˣ) :
     coeff R n (invOfUnit φ u) =
       if n = 0 then ↑u⁻¹
@@ -816,12 +1266,24 @@ theorem coeff_invOfUnit [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries
   coeff_inv_aux n (↑u⁻¹) φ
 #align mv_power_series.coeff_inv_of_unit MvPowerSeries.coeff_invOfUnit
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.constant_coeff_inv_of_unit MvPowerSeries.constantCoeff_invOfUnitₓ'. -/
 @[simp]
 theorem constantCoeff_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) :
     constantCoeff σ R (invOfUnit φ u) = ↑u⁻¹ := by
   rw [← coeff_zero_eq_constant_coeff_apply, coeff_inv_of_unit, if_pos rfl]
 #align mv_power_series.constant_coeff_inv_of_unit MvPowerSeries.constantCoeff_invOfUnit
 
+/- warning: mv_power_series.mul_inv_of_unit -> MvPowerSeries.mul_invOfUnit is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : Ring.{u2} R] (φ : MvPowerSeries.{u1, u2} σ R) (u : Units.{u2} R (Ring.toMonoid.{u2} R _inst_1)), (Eq.{succ u2} R (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (RingHom.{max u1 u2, u2} (MvPowerSeries.{u1, u2} σ R) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R (Ring.toSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (fun (_x : RingHom.{max u1 u2, u2} (MvPowerSeries.{u1, u2} σ R) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R (Ring.toSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) => (MvPowerSeries.{u1, u2} σ R) -> R) (RingHom.hasCoeToFun.{max u1 u2, u2} (MvPowerSeries.{u1, u2} σ R) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.semiring.{u1, u2} σ R (Ring.toSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (MvPowerSeries.constantCoeff.{u1, u2} σ R (Ring.toSemiring.{u2} R _inst_1)) φ) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1)) R (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1)) R (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1)) R (coeBase.{succ u2, succ u2} (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1)) R (Units.hasCoe.{u2} R (Ring.toMonoid.{u2} R _inst_1))))) u)) -> (Eq.{succ (max u1 u2)} (MvPowerSeries.{u1, u2} σ R) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u2} σ R) (instHMul.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.hasMul.{u1, u2} σ R (Ring.toSemiring.{u2} R _inst_1))) φ (MvPowerSeries.invOfUnit.{u1, u2} σ R _inst_1 φ u)) (OfNat.ofNat.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) 1 (OfNat.mk.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) 1 (One.one.{max u1 u2} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.hasOne.{u1, u2} σ R (Ring.toSemiring.{u2} R _inst_1))))))
+but is expected to have type
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (φ : MvPowerSeries.{u2, u1} σ R) (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPowerSeries.{u2, u1} σ R) => R) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) (fun (_x : MvPowerSeries.{u2, u1} σ R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPowerSeries.{u2, u1} σ R) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R (Ring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{max u2 u1, u1} (MvPowerSeries.{u2, u1} σ R) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (MvPowerSeries.constantCoeff.{u2, u1} σ R (Ring.toSemiring.{u1} R _inst_1)) φ) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u)) -> (Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.{u2, u1} σ R) (instHMul.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instMulMvPowerSeries.{u2, u1} σ R (Ring.toSemiring.{u1} R _inst_1))) φ (MvPowerSeries.invOfUnit.{u2, u1} σ R _inst_1 φ u)) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) 1 (One.toOfNat1.{max u2 u1} (MvPowerSeries.{u2, u1} σ R) (MvPowerSeries.instOneMvPowerSeries.{u2, u1} σ R (Ring.toSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align mv_power_series.mul_inv_of_unit MvPowerSeries.mul_invOfUnitₓ'. -/
 theorem mul_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) (h : constantCoeff σ R φ = u) :
     φ * invOfUnit φ u = 1 :=
   ext fun n =>
@@ -877,6 +1339,12 @@ section LocalRing
 
 variable {S : Type _} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalRingHom f]
 
+/- warning: mv_power_series.map.is_local_ring_hom -> MvPowerSeries.map.isLocalRingHom is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} S] (f : RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2)))) [_inst_3 : IsLocalRingHom.{u2, u3} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) f], IsLocalRingHom.{max u1 u2, max u1 u3} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ S) (MvPowerSeries.semiring.{u1, u2} σ R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (MvPowerSeries.semiring.{u1, u3} σ S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) (MvPowerSeries.map.{u1, u2, u3} σ R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) f)
+but is expected to have type
+  forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} S] (f : RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) [_inst_3 : IsLocalRingHom.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) f], IsLocalRingHom.{max u1 u2, max u1 u3} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ S) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u2} σ R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u3} σ S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (MvPowerSeries.map.{u1, u2, u3} σ R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) f)
+Case conversion may be inaccurate. Consider using '#align mv_power_series.map.is_local_ring_hom MvPowerSeries.map.isLocalRingHomₓ'. -/
 -- Thanks to the linter for informing us that  this instance does
 -- not actually need R and S to be local rings!
 /-- The map `A[[X]] → B[[X]]` induced by a local ring hom `A → B` is local -/
@@ -897,14 +1365,22 @@ section Field
 
 variable {k : Type _} [Field k]
 
+#print MvPowerSeries.inv /-
 /-- The inverse `1/f` of a multivariable power series `f` over a field -/
 protected def inv (φ : MvPowerSeries σ k) : MvPowerSeries σ k :=
-  Inv.aux (constantCoeff σ k φ)⁻¹ φ
+  inv.aux (constantCoeff σ k φ)⁻¹ φ
 #align mv_power_series.inv MvPowerSeries.inv
+-/
 
 instance : Inv (MvPowerSeries σ k) :=
   ⟨MvPowerSeries.inv⟩
 
+/- warning: mv_power_series.coeff_inv -> MvPowerSeries.coeff_inv is a dubious translation:
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_inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (MvPowerSeries.module.{u1, u2, u2} σ k k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (MvPowerSeries.coeff.{u1, u2} σ k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (Prod.snd.{u1, u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.{u1, 0} σ Nat Nat.hasZero) x)) (Inv.inv.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (MvPowerSeries.hasInv.{u1, u2} σ k _inst_1) φ))) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))))))))))
+but is expected to have type
+  forall {σ : Type.{u2}} {k : Type.{u1}} [_inst_1 : Field.{u1} k] [_inst_2 : DecidableEq.{succ u2} σ] (n : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (φ : MvPowerSeries.{u2, u1} σ k), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) (Inv.inv.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instInvMvPowerSeries.{u2, u1} σ k _inst_1) φ)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (MvPowerSeries.{u2, u1} σ k) k (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (MvPowerSeries.{u2, u1} σ k) (fun (_x : MvPowerSeries.{u2, u1} σ k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPowerSeries.{u2, u1} σ k) => k) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u1} k k (MvPowerSeries.{u2, u1} σ k) k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (MvPowerSeries.instAddCommMonoidMvPowerSeries.{u2, u1} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.instModuleMvPowerSeriesInstAddCommMonoidMvPowerSeries.{u2, u1, u1} σ k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (MvPowerSeries.coeff.{u2, u1} σ k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) n) (Inv.inv.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instInvMvPowerSeries.{u2, u1} σ k _inst_1) φ)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPowerSeries.{u2, u1} σ k) => k) φ) (Eq.{succ u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) n (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (Finsupp.decidableEq.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (fun (a : σ) (b : σ) => _inst_2 a b) (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) n (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPowerSeries.{u2, u1} σ k) => k) φ) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPowerSeries.{u2, u1} σ k) => k) φ) _inst_1) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} 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+Case conversion may be inaccurate. Consider using '#align mv_power_series.coeff_inv MvPowerSeries.coeff_invₓ'. -/
 theorem coeff_inv [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ k) :
     coeff k n φ⁻¹ =
       if n = 0 then (constantCoeff σ k φ)⁻¹
@@ -914,12 +1390,24 @@ theorem coeff_inv [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ k)
   coeff_inv_aux n _ φ
 #align mv_power_series.coeff_inv MvPowerSeries.coeff_inv
 
+/- warning: mv_power_series.constant_coeff_inv -> MvPowerSeries.constantCoeff_inv is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.constant_coeff_inv MvPowerSeries.constantCoeff_invₓ'. -/
 @[simp]
 theorem constantCoeff_inv (φ : MvPowerSeries σ k) :
     constantCoeff σ k φ⁻¹ = (constantCoeff σ k φ)⁻¹ := by
   rw [← coeff_zero_eq_constant_coeff_apply, coeff_inv, if_pos rfl]
 #align mv_power_series.constant_coeff_inv MvPowerSeries.constantCoeff_inv
 
+/- warning: mv_power_series.inv_eq_zero -> MvPowerSeries.inv_eq_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.inv_eq_zero MvPowerSeries.inv_eq_zeroₓ'. -/
 theorem inv_eq_zero {φ : MvPowerSeries σ k} : φ⁻¹ = 0 ↔ constantCoeff σ k φ = 0 :=
   ⟨fun h => by simpa using congr_arg (constant_coeff σ k) h, fun h =>
     ext fun n => by
@@ -928,16 +1416,34 @@ theorem inv_eq_zero {φ : MvPowerSeries σ k} : φ⁻¹ = 0 ↔ constantCoeff σ
         simp only [h, MvPowerSeries.coeff_zero, MulZeroClass.zero_mul, inv_zero, neg_zero]⟩
 #align mv_power_series.inv_eq_zero MvPowerSeries.inv_eq_zero
 
+/- warning: mv_power_series.zero_inv -> MvPowerSeries.zero_inv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.zero_inv MvPowerSeries.zero_invₓ'. -/
 @[simp]
 theorem zero_inv : (0 : MvPowerSeries σ k)⁻¹ = 0 := by rw [inv_eq_zero, constant_coeff_zero]
 #align mv_power_series.zero_inv MvPowerSeries.zero_inv
 
+/- warning: mv_power_series.inv_of_unit_eq -> MvPowerSeries.invOfUnit_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.inv_of_unit_eq MvPowerSeries.invOfUnit_eqₓ'. -/
 @[simp]
 theorem invOfUnit_eq (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
     invOfUnit φ (Units.mk0 _ h) = φ⁻¹ :=
   rfl
 #align mv_power_series.inv_of_unit_eq MvPowerSeries.invOfUnit_eq
 
+/- warning: mv_power_series.inv_of_unit_eq' -> MvPowerSeries.invOfUnit_eq' is a dubious translation:
+lean 3 declaration is
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k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) u)) -> (Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.invOfUnit.{u2, u1} σ k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) φ u) (Inv.inv.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instInvMvPowerSeries.{u2, u1} σ k _inst_1) φ))
+Case conversion may be inaccurate. Consider using '#align mv_power_series.inv_of_unit_eq' MvPowerSeries.invOfUnit_eq'ₓ'. -/
 @[simp]
 theorem invOfUnit_eq' (φ : MvPowerSeries σ k) (u : Units k) (h : constantCoeff σ k φ = u) :
     invOfUnit φ u = φ⁻¹ := by
@@ -945,30 +1451,66 @@ theorem invOfUnit_eq' (φ : MvPowerSeries σ k) (u : Units k) (h : constantCoeff
   congr 1; rw [Units.ext_iff]; exact h.symm
 #align mv_power_series.inv_of_unit_eq' MvPowerSeries.invOfUnit_eq'
 
+/- warning: mv_power_series.mul_inv_cancel -> MvPowerSeries.mul_inv_cancel is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.mul_inv_cancel MvPowerSeries.mul_inv_cancelₓ'. -/
 @[simp]
 protected theorem mul_inv_cancel (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
     φ * φ⁻¹ = 1 := by rw [← inv_of_unit_eq φ h, mul_inv_of_unit φ (Units.mk0 _ h) rfl]
 #align mv_power_series.mul_inv_cancel MvPowerSeries.mul_inv_cancel
 
+/- warning: mv_power_series.inv_mul_cancel -> MvPowerSeries.inv_mul_cancel is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.inv_mul_cancel MvPowerSeries.inv_mul_cancelₓ'. -/
 @[simp]
 protected theorem inv_mul_cancel (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
     φ⁻¹ * φ = 1 := by rw [mul_comm, φ.mul_inv_cancel h]
 #align mv_power_series.inv_mul_cancel MvPowerSeries.inv_mul_cancel
 
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.eq_mul_inv_iff_mul_eq MvPowerSeries.eq_mul_inv_iff_mul_eqₓ'. -/
 protected theorem eq_mul_inv_iff_mul_eq {φ₁ φ₂ φ₃ : MvPowerSeries σ k}
     (h : constantCoeff σ k φ₃ ≠ 0) : φ₁ = φ₂ * φ₃⁻¹ ↔ φ₁ * φ₃ = φ₂ :=
   ⟨fun k => by simp [k, mul_assoc, MvPowerSeries.inv_mul_cancel _ h], fun k => by
     simp [← k, mul_assoc, MvPowerSeries.mul_inv_cancel _ h]⟩
 #align mv_power_series.eq_mul_inv_iff_mul_eq MvPowerSeries.eq_mul_inv_iff_mul_eq
 
+/- warning: mv_power_series.eq_inv_iff_mul_eq_one -> MvPowerSeries.eq_inv_iff_mul_eq_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.eq_inv_iff_mul_eq_one MvPowerSeries.eq_inv_iff_mul_eq_oneₓ'. -/
 protected theorem eq_inv_iff_mul_eq_one {φ ψ : MvPowerSeries σ k} (h : constantCoeff σ k ψ ≠ 0) :
     φ = ψ⁻¹ ↔ φ * ψ = 1 := by rw [← MvPowerSeries.eq_mul_inv_iff_mul_eq h, one_mul]
 #align mv_power_series.eq_inv_iff_mul_eq_one MvPowerSeries.eq_inv_iff_mul_eq_one
 
+/- warning: mv_power_series.inv_eq_iff_mul_eq_one -> MvPowerSeries.inv_eq_iff_mul_eq_one is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.inv_eq_iff_mul_eq_one MvPowerSeries.inv_eq_iff_mul_eq_oneₓ'. -/
 protected theorem inv_eq_iff_mul_eq_one {φ ψ : MvPowerSeries σ k} (h : constantCoeff σ k ψ ≠ 0) :
     ψ⁻¹ = φ ↔ φ * ψ = 1 := by rw [eq_comm, MvPowerSeries.eq_inv_iff_mul_eq_one h]
 #align mv_power_series.inv_eq_iff_mul_eq_one MvPowerSeries.inv_eq_iff_mul_eq_one
 
+/- warning: mv_power_series.mul_inv_rev -> MvPowerSeries.mul_inv_rev is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.mul_inv_rev MvPowerSeries.mul_inv_revₓ'. -/
 @[simp]
 protected theorem mul_inv_rev (φ ψ : MvPowerSeries σ k) : (φ * ψ)⁻¹ = ψ⁻¹ * φ⁻¹ :=
   by
@@ -990,19 +1532,37 @@ instance : InvOneClass (MvPowerSeries σ k) :=
       rw [MvPowerSeries.inv_eq_iff_mul_eq_one, mul_one]
       simp }
 
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(DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) k (MvPowerSeries.{u2, u1} σ k) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} k (MvPowerSeries.{u2, u1} σ k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) k (MvPowerSeries.{u2, u1} σ k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} k (MvPowerSeries.{u2, u1} σ k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))))) (MvPowerSeries.C.{u2, u1} σ k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Inv.inv.{u1} k (Field.toInv.{u1} k _inst_1) r))
+Case conversion may be inaccurate. Consider using '#align mv_power_series.C_inv MvPowerSeries.C_invₓ'. -/
 @[simp]
-theorem c_inv (r : k) : (c σ k r)⁻¹ = c σ k r⁻¹ :=
+theorem C_inv (r : k) : (C σ k r)⁻¹ = C σ k r⁻¹ :=
   by
   rcases eq_or_ne r 0 with (rfl | hr)
   · simp
   rw [MvPowerSeries.inv_eq_iff_mul_eq_one, ← map_mul, inv_mul_cancel hr, map_one]
   simpa using hr
-#align mv_power_series.C_inv MvPowerSeries.c_inv
-
+#align mv_power_series.C_inv MvPowerSeries.C_inv
+
+/- warning: mv_power_series.X_inv -> MvPowerSeries.X_inv is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u2} k] (s : σ), Eq.{succ (max u1 u2)} (MvPowerSeries.{u1, u2} σ k) (Inv.inv.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (MvPowerSeries.hasInv.{u1, u2} σ k _inst_1) (MvPowerSeries.X.{u1, u2} σ k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) s)) (OfNat.ofNat.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) 0 (OfNat.mk.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) 0 (Zero.zero.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (MvPowerSeries.hasZero.{u1, u2} σ k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))))))))
+but is expected to have type
+  forall {σ : Type.{u2}} {k : Type.{u1}} [_inst_1 : Field.{u1} k] (s : σ), Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ k) (Inv.inv.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instInvMvPowerSeries.{u2, u1} σ k _inst_1) (MvPowerSeries.X.{u2, u1} σ k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) s)) (OfNat.ofNat.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) 0 (Zero.toOfNat0.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instZeroMvPowerSeries.{u2, u1} σ k (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align mv_power_series.X_inv MvPowerSeries.X_invₓ'. -/
 @[simp]
-theorem x_inv (s : σ) : (x s : MvPowerSeries σ k)⁻¹ = 0 := by rw [inv_eq_zero, constant_coeff_X]
-#align mv_power_series.X_inv MvPowerSeries.x_inv
-
+theorem X_inv (s : σ) : (X s : MvPowerSeries σ k)⁻¹ = 0 := by rw [inv_eq_zero, constant_coeff_X]
+#align mv_power_series.X_inv MvPowerSeries.X_inv
+
+/- warning: mv_power_series.smul_inv -> MvPowerSeries.smul_inv is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u2} k] (r : k) (φ : MvPowerSeries.{u1, u2} σ k), Eq.{succ (max u1 u2)} (MvPowerSeries.{u1, u2} σ k) (Inv.inv.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (MvPowerSeries.hasInv.{u1, u2} σ k _inst_1) (SMul.smul.{u2, max u1 u2} k (MvPowerSeries.{u1, u2} σ k) (SMulZeroClass.toHasSmul.{u2, max u1 u2} k (MvPowerSeries.{u1, u2} σ k) (AddZeroClass.toHasZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (MvPowerSeries.addCommMonoid.{u1, u2} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))))))) (SMulWithZero.toSmulZeroClass.{u2, max u1 u2} k (MvPowerSeries.{u1, u2} σ k) (MulZeroClass.toHasZero.{u2} k (MulZeroOneClass.toMulZeroClass.{u2} k (MonoidWithZero.toMulZeroOneClass.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))) (AddZeroClass.toHasZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (MvPowerSeries.addCommMonoid.{u1, u2} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))))))) (MulActionWithZero.toSMulWithZero.{u2, max u1 u2} k (MvPowerSeries.{u1, u2} σ k) (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))) (AddZeroClass.toHasZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (AddMonoid.toAddZeroClass.{max u1 u2} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))))) r φ)) (SMul.smul.{u2, max u1 u2} k (MvPowerSeries.{u1, u2} σ k) (SMulZeroClass.toHasSmul.{u2, max u1 u2} k (MvPowerSeries.{u1, u2} σ k) (AddZeroClass.toHasZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (MvPowerSeries.addCommMonoid.{u1, u2} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))))))) (SMulWithZero.toSmulZeroClass.{u2, max u1 u2} k (MvPowerSeries.{u1, u2} σ k) (MulZeroClass.toHasZero.{u2} k (MulZeroOneClass.toMulZeroClass.{u2} k (MonoidWithZero.toMulZeroOneClass.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))) (AddZeroClass.toHasZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (MvPowerSeries.addCommMonoid.{u1, u2} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))))))) (MulActionWithZero.toSMulWithZero.{u2, max u1 u2} k (MvPowerSeries.{u1, u2} σ k) (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))) (AddZeroClass.toHasZero.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (MvPowerSeries.addCommMonoid.{u1, u2} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))))))) (Module.toMulActionWithZero.{u2, max u1 u2} k (MvPowerSeries.{u1, u2} σ k) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (MvPowerSeries.addCommMonoid.{u1, u2} σ k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))) (MvPowerSeries.module.{u1, u2, u2} σ k k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1)))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_1))))))))) (Inv.inv.{u2} k (DivInvMonoid.toHasInv.{u2} k (DivisionRing.toDivInvMonoid.{u2} k (Field.toDivisionRing.{u2} k _inst_1))) r) (Inv.inv.{max u1 u2} (MvPowerSeries.{u1, u2} σ k) (MvPowerSeries.hasInv.{u1, u2} σ k _inst_1) φ))
+but is expected to have type
+  forall {σ : Type.{u2}} {k : Type.{u1}} [_inst_1 : Field.{u1} k] (r : k) (φ : MvPowerSeries.{u2, u1} σ k), Eq.{max (succ u2) (succ u1)} (MvPowerSeries.{u2, u1} σ k) (Inv.inv.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instInvMvPowerSeries.{u2, u1} σ k _inst_1) (HSMul.hSMul.{u1, max u2 u1, max u2 u1} k (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.{u2, u1} σ k) (instHSMul.{u1, max u2 u1} k (MvPowerSeries.{u2, u1} σ k) (Algebra.toSMul.{u1, max u2 u1} k (MvPowerSeries.{u2, u1} σ k) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u2, u1, u1} σ k k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) r φ)) (HSMul.hSMul.{u1, max u2 u1, max u2 u1} k (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.{u2, u1} σ k) (instHSMul.{u1, max u2 u1} k (MvPowerSeries.{u2, u1} σ k) (Algebra.toSMul.{u1, max u2 u1} k (MvPowerSeries.{u2, u1} σ k) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MvPowerSeries.instSemiringMvPowerSeries.{u2, u1} σ k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MvPowerSeries.instAlgebraMvPowerSeriesInstSemiringMvPowerSeries.{u2, u1, u1} σ k k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Inv.inv.{u1} k (Field.toInv.{u1} k _inst_1) r) (Inv.inv.{max u2 u1} (MvPowerSeries.{u2, u1} σ k) (MvPowerSeries.instInvMvPowerSeries.{u2, u1} σ k _inst_1) φ))
+Case conversion may be inaccurate. Consider using '#align mv_power_series.smul_inv MvPowerSeries.smul_invₓ'. -/
 @[simp]
 theorem smul_inv (r : k) (φ : MvPowerSeries σ k) : (r • φ)⁻¹ = r⁻¹ • φ⁻¹ := by
   simp [smul_eq_C_mul, mul_comm]
@@ -1018,20 +1578,40 @@ open Finsupp
 
 variable {σ : Type _} {R : Type _} [CommSemiring R] (φ ψ : MvPolynomial σ R)
 
+#print MvPolynomial.coeToMvPowerSeries /-
 /-- The natural inclusion from multivariate polynomials into multivariate formal power series.-/
 instance coeToMvPowerSeries : Coe (MvPolynomial σ R) (MvPowerSeries σ R) :=
   ⟨fun φ n => coeff n φ⟩
 #align mv_polynomial.coe_to_mv_power_series MvPolynomial.coeToMvPowerSeries
+-/
 
+/- warning: mv_polynomial.coe_def -> MvPolynomial.coe_def is a dubious translation:
+lean 3 declaration is
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 theorem coe_def : (φ : MvPowerSeries σ R) = fun n => coeff n φ :=
   rfl
 #align mv_polynomial.coe_def MvPolynomial.coe_def
 
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 @[simp, norm_cast]
 theorem coeff_coe (n : σ →₀ ℕ) : MvPowerSeries.coeff R n ↑φ = coeff n φ :=
   rfl
 #align mv_polynomial.coeff_coe MvPolynomial.coeff_coe
 
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 @[simp, norm_cast]
 theorem coe_monomial (n : σ →₀ ℕ) (a : R) :
     (monomial n a : MvPowerSeries σ R) = MvPowerSeries.monomial R n a :=
@@ -1041,50 +1621,104 @@ theorem coe_monomial (n : σ →₀ ℕ) (a : R) :
     split_ifs with h₁ h₂ <;> first |rfl|subst m <;> contradiction
 #align mv_polynomial.coe_monomial MvPolynomial.coe_monomial
 
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 @[simp, norm_cast]
 theorem coe_zero : ((0 : MvPolynomial σ R) : MvPowerSeries σ R) = 0 :=
   rfl
 #align mv_polynomial.coe_zero MvPolynomial.coe_zero
 
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 @[simp, norm_cast]
 theorem coe_one : ((1 : MvPolynomial σ R) : MvPowerSeries σ R) = 1 :=
   coe_monomial _ _
 #align mv_polynomial.coe_one MvPolynomial.coe_one
 
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 @[simp, norm_cast]
 theorem coe_add : ((φ + ψ : MvPolynomial σ R) : MvPowerSeries σ R) = φ + ψ :=
   rfl
 #align mv_polynomial.coe_add MvPolynomial.coe_add
 
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 @[simp, norm_cast]
 theorem coe_mul : ((φ * ψ : MvPolynomial σ R) : MvPowerSeries σ R) = φ * ψ :=
   MvPowerSeries.ext fun n => by simp only [coeff_coe, MvPowerSeries.coeff_mul, coeff_mul]
 #align mv_polynomial.coe_mul MvPolynomial.coe_mul
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_C MvPolynomial.coe_Cₓ'. -/
 @[simp, norm_cast]
-theorem coe_c (a : R) : ((C a : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.c σ R a :=
+theorem coe_C (a : R) : ((C a : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.C σ R a :=
   coe_monomial _ _
-#align mv_polynomial.coe_C MvPolynomial.coe_c
-
+#align mv_polynomial.coe_C MvPolynomial.coe_C
+
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 @[simp, norm_cast]
 theorem coe_bit0 :
     ((bit0 φ : MvPolynomial σ R) : MvPowerSeries σ R) = bit0 (φ : MvPowerSeries σ R) :=
   coe_add _ _
 #align mv_polynomial.coe_bit0 MvPolynomial.coe_bit0
 
+/- warning: mv_polynomial.coe_bit1 -> MvPolynomial.coe_bit1 is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_bit1 MvPolynomial.coe_bit1ₓ'. -/
 @[simp, norm_cast]
 theorem coe_bit1 :
     ((bit1 φ : MvPolynomial σ R) : MvPowerSeries σ R) = bit1 (φ : MvPowerSeries σ R) := by
   rw [bit1, bit1, coe_add, coe_one, coe_bit0]
 #align mv_polynomial.coe_bit1 MvPolynomial.coe_bit1
 
+/- warning: mv_polynomial.coe_X -> MvPolynomial.coe_X is a dubious translation:
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 @[simp, norm_cast]
-theorem coe_x (s : σ) : ((X s : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.x s :=
+theorem coe_X (s : σ) : ((X s : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.X s :=
   coe_monomial _ _
-#align mv_polynomial.coe_X MvPolynomial.coe_x
+#align mv_polynomial.coe_X MvPolynomial.coe_X
 
 variable (σ R)
 
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 theorem coe_injective : Function.Injective (coe : MvPolynomial σ R → MvPowerSeries σ R) :=
   fun x y h => by
   ext
@@ -1093,19 +1727,43 @@ theorem coe_injective : Function.Injective (coe : MvPolynomial σ R → MvPowerS
 
 variable {σ R φ ψ}
 
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 @[simp, norm_cast]
 theorem coe_inj : (φ : MvPowerSeries σ R) = ψ ↔ φ = ψ :=
   (coe_injective σ R).eq_iff
 #align mv_polynomial.coe_inj MvPolynomial.coe_inj
 
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 @[simp]
 theorem coe_eq_zero_iff : (φ : MvPowerSeries σ R) = 0 ↔ φ = 0 := by rw [← coe_zero, coe_inj]
 #align mv_polynomial.coe_eq_zero_iff MvPolynomial.coe_eq_zero_iff
 
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 @[simp]
 theorem coe_eq_one_iff : (φ : MvPowerSeries σ R) = 1 ↔ φ = 1 := by rw [← coe_one, coe_inj]
 #align mv_polynomial.coe_eq_one_iff MvPolynomial.coe_eq_one_iff
 
+/- warning: mv_polynomial.coe_to_mv_power_series.ring_hom -> MvPolynomial.coeToMvPowerSeries.ringHom is a dubious translation:
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 /-- The coercion from multivariable polynomials to multivariable power series
 as a ring homomorphism.
 -/
@@ -1118,6 +1776,12 @@ def coeToMvPowerSeries.ringHom : MvPolynomial σ R →+* MvPowerSeries σ R
   map_mul' := coe_mul
 #align mv_polynomial.coe_to_mv_power_series.ring_hom MvPolynomial.coeToMvPowerSeries.ringHom
 
+/- warning: mv_polynomial.coe_pow -> MvPolynomial.coe_pow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_pow MvPolynomial.coe_powₓ'. -/
 @[simp, norm_cast]
 theorem coe_pow (n : ℕ) :
     ((φ ^ n : MvPolynomial σ R) : MvPowerSeries σ R) = (φ : MvPowerSeries σ R) ^ n :=
@@ -1126,6 +1790,12 @@ theorem coe_pow (n : ℕ) :
 
 variable (φ ψ)
 
+/- warning: mv_polynomial.coe_to_mv_power_series.ring_hom_apply -> MvPolynomial.coeToMvPowerSeries.ringHom_apply is a dubious translation:
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(MvPolynomial.coeToMvPowerSeries.ringHom.{u2, u1} σ R _inst_1) φ) (MvPolynomial.toMvPowerSeries.{u2, u1} σ R _inst_1 φ)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_to_mv_power_series.ring_hom_apply MvPolynomial.coeToMvPowerSeries.ringHom_applyₓ'. -/
 @[simp]
 theorem coeToMvPowerSeries.ringHom_apply : coeToMvPowerSeries.ringHom φ = φ :=
   rfl
@@ -1135,6 +1805,12 @@ section Algebra
 
 variable (A : Type _) [CommSemiring A] [Algebra R A]
 
+/- warning: mv_polynomial.coe_to_mv_power_series.alg_hom -> MvPolynomial.coeToMvPowerSeries.algHom is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_to_mv_power_series.alg_hom MvPolynomial.coeToMvPowerSeries.algHomₓ'. -/
 /-- The coercion from multivariable polynomials to multivariable power series
 as an algebra homomorphism.
 -/
@@ -1143,6 +1819,12 @@ def coeToMvPowerSeries.algHom : MvPolynomial σ R →ₐ[R] MvPowerSeries σ A :
     commutes' := fun r => by simp [algebraMap_apply, MvPowerSeries.algebraMap_apply] }
 #align mv_polynomial.coe_to_mv_power_series.alg_hom MvPolynomial.coeToMvPowerSeries.algHom
 
+/- warning: mv_polynomial.coe_to_mv_power_series.alg_hom_apply -> MvPolynomial.coeToMvPowerSeries.algHom_apply is a dubious translation:
+lean 3 declaration is
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_inst_2) (algebraMap.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (MvPolynomial.toMvPowerSeries.{u3, u1} σ R _inst_1 φ))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_to_mv_power_series.alg_hom_apply MvPolynomial.coeToMvPowerSeries.algHom_applyₓ'. -/
 @[simp]
 theorem coeToMvPowerSeries.algHom_apply :
     coeToMvPowerSeries.algHom A φ = MvPowerSeries.map σ (algebraMap R A) ↑φ :=
@@ -1157,21 +1839,45 @@ namespace MvPowerSeries
 
 variable {σ R A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : MvPowerSeries σ R)
 
+/- warning: mv_power_series.algebra_mv_polynomial -> MvPowerSeries.algebraMvPolynomial is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)], Algebra.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u3} σ A) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1) (MvPowerSeries.semiring.{u1, u3} σ A (CommSemiring.toSemiring.{u3} A _inst_2))
+but is expected to have type
+  forall {σ : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)], Algebra.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPowerSeries.{u1, u3} σ A) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u3} σ A (CommSemiring.toSemiring.{u3} A _inst_2))
+Case conversion may be inaccurate. Consider using '#align mv_power_series.algebra_mv_polynomial MvPowerSeries.algebraMvPolynomialₓ'. -/
 instance algebraMvPolynomial : Algebra (MvPolynomial σ R) (MvPowerSeries σ A) :=
   RingHom.toAlgebra (MvPolynomial.coeToMvPowerSeries.algHom A).toRingHom
 #align mv_power_series.algebra_mv_polynomial MvPowerSeries.algebraMvPolynomial
 
+/- warning: mv_power_series.algebra_mv_power_series -> MvPowerSeries.algebraMvPowerSeries is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)], Algebra.{max u1 u2, max u1 u3} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ A) (MvPowerSeries.commSemiring.{u1, u2} σ R _inst_1) (MvPowerSeries.semiring.{u1, u3} σ A (CommSemiring.toSemiring.{u3} A _inst_2))
+but is expected to have type
+  forall {σ : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)], Algebra.{max u2 u1, max u3 u1} (MvPowerSeries.{u1, u2} σ R) (MvPowerSeries.{u1, u3} σ A) (MvPowerSeries.instCommSemiringMvPowerSeries.{u1, u2} σ R _inst_1) (MvPowerSeries.instSemiringMvPowerSeries.{u1, u3} σ A (CommSemiring.toSemiring.{u3} A _inst_2))
+Case conversion may be inaccurate. Consider using '#align mv_power_series.algebra_mv_power_series MvPowerSeries.algebraMvPowerSeriesₓ'. -/
 instance algebraMvPowerSeries : Algebra (MvPowerSeries σ R) (MvPowerSeries σ A) :=
   (map σ (algebraMap R A)).toAlgebra
 #align mv_power_series.algebra_mv_power_series MvPowerSeries.algebraMvPowerSeries
 
 variable (A)
 
+/- warning: mv_power_series.algebra_map_apply' -> MvPowerSeries.algebraMap_apply' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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_inst_2) (algebraMap.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) (MvPolynomial.toMvPowerSeries.{u3, u2} σ R _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align mv_power_series.algebra_map_apply' MvPowerSeries.algebraMap_apply'ₓ'. -/
 theorem algebraMap_apply' (p : MvPolynomial σ R) :
     algebraMap (MvPolynomial σ R) (MvPowerSeries σ A) p = map σ (algebraMap R A) p :=
   rfl
 #align mv_power_series.algebra_map_apply' MvPowerSeries.algebraMap_apply'
 
+/- warning: mv_power_series.algebra_map_apply'' -> MvPowerSeries.algebraMap_apply'' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_power_series.algebra_map_apply'' MvPowerSeries.algebraMap_apply''ₓ'. -/
 theorem algebraMap_apply'' :
     algebraMap (MvPowerSeries σ R) (MvPowerSeries σ A) f = map σ (algebraMap R A) f :=
   rfl
@@ -1179,10 +1885,12 @@ theorem algebraMap_apply'' :
 
 end MvPowerSeries
 
+#print PowerSeries /-
 /-- Formal power series over the coefficient ring `R`.-/
 def PowerSeries (R : Type _) :=
   MvPowerSeries Unit R
 #align power_series PowerSeries
+-/
 
 namespace PowerSeries
 
@@ -1230,22 +1938,34 @@ section Semiring
 
 variable (R) [Semiring R]
 
+#print PowerSeries.coeff /-
 /-- The `n`th coefficient of a formal power series.-/
 def coeff (n : ℕ) : PowerSeries R →ₗ[R] R :=
   MvPowerSeries.coeff R (single () n)
 #align power_series.coeff PowerSeries.coeff
+-/
 
+#print PowerSeries.monomial /-
 /-- The `n`th monomial with coefficient `a` as formal power series.-/
 def monomial (n : ℕ) : R →ₗ[R] PowerSeries R :=
   MvPowerSeries.monomial R (single () n)
 #align power_series.monomial PowerSeries.monomial
+-/
 
 variable {R}
 
+#print PowerSeries.coeff_def /-
 theorem coeff_def {s : Unit →₀ ℕ} {n : ℕ} (h : s () = n) : coeff R n = MvPowerSeries.coeff R s := by
   erw [coeff, ← h, ← Finsupp.unique_single s]
 #align power_series.coeff_def PowerSeries.coeff_def
+-/
 
+/- warning: power_series.ext -> PowerSeries.ext is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.ext PowerSeries.extₓ'. -/
 /-- Two formal power series are equal if all their coefficients are equal.-/
 @[ext]
 theorem ext {φ ψ : PowerSeries R} (h : ∀ n, coeff R n φ = coeff R n ψ) : φ = ψ :=
@@ -1255,20 +1975,40 @@ theorem ext {φ ψ : PowerSeries R} (h : ∀ n, coeff R n φ = coeff R n ψ) : 
     rfl
 #align power_series.ext PowerSeries.ext
 
+/- warning: power_series.ext_iff -> PowerSeries.ext_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.ext_iff PowerSeries.ext_iffₓ'. -/
 /-- Two formal power series are equal if all their coefficients are equal.-/
 theorem ext_iff {φ ψ : PowerSeries R} : φ = ψ ↔ ∀ n, coeff R n φ = coeff R n ψ :=
   ⟨fun h n => congr_arg (coeff R n) h, ext⟩
 #align power_series.ext_iff PowerSeries.ext_iff
 
+#print PowerSeries.mk /-
 /-- Constructor for formal power series.-/
 def mk {R} (f : ℕ → R) : PowerSeries R := fun s => f (s ())
 #align power_series.mk PowerSeries.mk
+-/
 
+/- warning: power_series.coeff_mk -> PowerSeries.coeff_mk is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_mk PowerSeries.coeff_mkₓ'. -/
 @[simp]
 theorem coeff_mk (n : ℕ) (f : ℕ → R) : coeff R n (mk f) = f n :=
   congr_arg f Finsupp.single_eq_same
 #align power_series.coeff_mk PowerSeries.coeff_mk
 
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_monomial PowerSeries.coeff_monomialₓ'. -/
 theorem coeff_monomial (m n : ℕ) (a : R) : coeff R m (monomial R n a) = if m = n then a else 0 :=
   calc
     coeff R m (monomial R n a) = _ := MvPowerSeries.coeff_monomial _ _ _
@@ -1276,43 +2016,83 @@ theorem coeff_monomial (m n : ℕ) (a : R) : coeff R m (monomial R n a) = if m =
     
 #align power_series.coeff_monomial PowerSeries.coeff_monomial
 
+/- warning: power_series.monomial_eq_mk -> PowerSeries.monomial_eq_mk is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.monomial_eq_mk PowerSeries.monomial_eq_mkₓ'. -/
 theorem monomial_eq_mk (n : ℕ) (a : R) : monomial R n a = mk fun m => if m = n then a else 0 :=
   ext fun m => by rw [coeff_monomial, coeff_mk]
 #align power_series.monomial_eq_mk PowerSeries.monomial_eq_mk
 
+/- warning: power_series.coeff_monomial_same -> PowerSeries.coeff_monomial_same is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_monomial_same PowerSeries.coeff_monomial_sameₓ'. -/
 @[simp]
 theorem coeff_monomial_same (n : ℕ) (a : R) : coeff R n (monomial R n a) = a :=
   MvPowerSeries.coeff_monomial_same _ _
 #align power_series.coeff_monomial_same PowerSeries.coeff_monomial_same
 
+#print PowerSeries.coeff_comp_monomial /-
 @[simp]
 theorem coeff_comp_monomial (n : ℕ) : (coeff R n).comp (monomial R n) = LinearMap.id :=
   LinearMap.ext <| coeff_monomial_same n
 #align power_series.coeff_comp_monomial PowerSeries.coeff_comp_monomial
+-/
 
 variable (R)
 
+/- warning: power_series.constant_coeff -> PowerSeries.constantCoeff is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R], RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R], RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)
+Case conversion may be inaccurate. Consider using '#align power_series.constant_coeff PowerSeries.constantCoeffₓ'. -/
 /-- The constant coefficient of a formal power series. -/
 def constantCoeff : PowerSeries R →+* R :=
   MvPowerSeries.constantCoeff Unit R
 #align power_series.constant_coeff PowerSeries.constantCoeff
 
+/- warning: power_series.C -> PowerSeries.C is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R], RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R], RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))
+Case conversion may be inaccurate. Consider using '#align power_series.C PowerSeries.Cₓ'. -/
 /-- The constant formal power series.-/
-def c : R →+* PowerSeries R :=
-  MvPowerSeries.c Unit R
-#align power_series.C PowerSeries.c
+def C : R →+* PowerSeries R :=
+  MvPowerSeries.C Unit R
+#align power_series.C PowerSeries.C
 
 variable {R}
 
+#print PowerSeries.X /-
 /-- The variable of the formal power series ring.-/
-def x : PowerSeries R :=
-  MvPowerSeries.x ()
-#align power_series.X PowerSeries.x
+def X : PowerSeries R :=
+  MvPowerSeries.X ()
+#align power_series.X PowerSeries.X
+-/
 
-theorem commute_x (φ : PowerSeries R) : Commute φ x :=
+/- warning: power_series.commute_X -> PowerSeries.commute_X is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Commute.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) φ (PowerSeries.X.{u1} R _inst_1)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Commute.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) φ (PowerSeries.X.{u1} R _inst_1)
+Case conversion may be inaccurate. Consider using '#align power_series.commute_X PowerSeries.commute_Xₓ'. -/
+theorem commute_X (φ : PowerSeries R) : Commute φ X :=
   φ.commute_X _
-#align power_series.commute_X PowerSeries.commute_x
-
+#align power_series.commute_X PowerSeries.commute_X
+
+/- warning: power_series.coeff_zero_eq_constant_coeff -> PowerSeries.coeff_zero_eq_constantCoeff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((PowerSeries.{u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.constantCoeff.{u1} R _inst_1))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (forall (ᾰ : PowerSeries.{u1} R), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) 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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1))
+Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_eq_constant_coeff PowerSeries.coeff_zero_eq_constantCoeffₓ'. -/
 @[simp]
 theorem coeff_zero_eq_constantCoeff : ⇑(coeff R 0) = constantCoeff R :=
   by
@@ -1320,71 +2100,167 @@ theorem coeff_zero_eq_constantCoeff : ⇑(coeff R 0) = constantCoeff R :=
   rfl
 #align power_series.coeff_zero_eq_constant_coeff PowerSeries.coeff_zero_eq_constantCoeff
 
+/- warning: power_series.coeff_zero_eq_constant_coeff_apply -> PowerSeries.coeff_zero_eq_constantCoeff_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) φ) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) φ) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)
+Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_eq_constant_coeff_apply PowerSeries.coeff_zero_eq_constantCoeff_applyₓ'. -/
 theorem coeff_zero_eq_constantCoeff_apply (φ : PowerSeries R) : coeff R 0 φ = constantCoeff R φ :=
   by rw [coeff_zero_eq_constant_coeff] <;> rfl
 #align power_series.coeff_zero_eq_constant_coeff_apply PowerSeries.coeff_zero_eq_constantCoeff_apply
 
+/- warning: power_series.monomial_zero_eq_C -> PowerSeries.monomial_zero_eq_C is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.monomial_zero_eq_C PowerSeries.monomial_zero_eq_Cₓ'. -/
 @[simp]
-theorem monomial_zero_eq_c : ⇑(monomial R 0) = c R := by
-  rw [monomial, Finsupp.single_zero, MvPowerSeries.monomial_zero_eq_c, C]
-#align power_series.monomial_zero_eq_C PowerSeries.monomial_zero_eq_c
-
-theorem monomial_zero_eq_c_apply (a : R) : monomial R 0 a = c R a := by simp
-#align power_series.monomial_zero_eq_C_apply PowerSeries.monomial_zero_eq_c_apply
-
-theorem coeff_c (n : ℕ) (a : R) : coeff R n (c R a : PowerSeries R) = if n = 0 then a else 0 := by
+theorem monomial_zero_eq_C : ⇑(monomial R 0) = C R := by
+  rw [monomial, Finsupp.single_zero, MvPowerSeries.monomial_zero_eq_C, C]
+#align power_series.monomial_zero_eq_C PowerSeries.monomial_zero_eq_C
+
+/- warning: power_series.monomial_zero_eq_C_apply -> PowerSeries.monomial_zero_eq_C_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.monomial_zero_eq_C_apply PowerSeries.monomial_zero_eq_C_applyₓ'. -/
+theorem monomial_zero_eq_C_apply (a : R) : monomial R 0 a = C R a := by simp
+#align power_series.monomial_zero_eq_C_apply PowerSeries.monomial_zero_eq_C_apply
+
+/- warning: power_series.coeff_C -> PowerSeries.coeff_C is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_C PowerSeries.coeff_Cₓ'. -/
+theorem coeff_C (n : ℕ) (a : R) : coeff R n (C R a : PowerSeries R) = if n = 0 then a else 0 := by
   rw [← monomial_zero_eq_C_apply, coeff_monomial]
-#align power_series.coeff_C PowerSeries.coeff_c
-
+#align power_series.coeff_C PowerSeries.coeff_C
+
+/- warning: power_series.coeff_zero_C -> PowerSeries.coeff_zero_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_C PowerSeries.coeff_zero_Cₓ'. -/
 @[simp]
-theorem coeff_zero_c (a : R) : coeff R 0 (c R a) = a := by
+theorem coeff_zero_C (a : R) : coeff R 0 (C R a) = a := by
   rw [← monomial_zero_eq_C_apply, coeff_monomial_same 0 a]
-#align power_series.coeff_zero_C PowerSeries.coeff_zero_c
-
-theorem x_eq : (x : PowerSeries R) = monomial R 1 1 :=
+#align power_series.coeff_zero_C PowerSeries.coeff_zero_C
+
+/- warning: power_series.X_eq -> PowerSeries.X_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.X_eq PowerSeries.X_eqₓ'. -/
+theorem X_eq : (X : PowerSeries R) = monomial R 1 1 :=
   rfl
-#align power_series.X_eq PowerSeries.x_eq
-
-theorem coeff_x (n : ℕ) : coeff R n (x : PowerSeries R) = if n = 1 then 1 else 0 := by
+#align power_series.X_eq PowerSeries.X_eq
+
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_X PowerSeries.coeff_Xₓ'. -/
+theorem coeff_X (n : ℕ) : coeff R n (X : PowerSeries R) = if n = 1 then 1 else 0 := by
   rw [X_eq, coeff_monomial]
-#align power_series.coeff_X PowerSeries.coeff_x
-
+#align power_series.coeff_X PowerSeries.coeff_X
+
+/- warning: power_series.coeff_zero_X -> PowerSeries.coeff_zero_X is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (PowerSeries.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (PowerSeries.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) _inst_1))))
+Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_X PowerSeries.coeff_zero_Xₓ'. -/
 @[simp]
-theorem coeff_zero_x : coeff R 0 (x : PowerSeries R) = 0 := by
-  rw [coeff, Finsupp.single_zero, X, MvPowerSeries.coeff_zero_x]
-#align power_series.coeff_zero_X PowerSeries.coeff_zero_x
-
+theorem coeff_zero_X : coeff R 0 (X : PowerSeries R) = 0 := by
+  rw [coeff, Finsupp.single_zero, X, MvPowerSeries.coeff_zero_X]
+#align power_series.coeff_zero_X PowerSeries.coeff_zero_X
+
+/- warning: power_series.coeff_one_X -> PowerSeries.coeff_one_X is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (PowerSeries.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (PowerSeries.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (PowerSeries.X.{u1} R _inst_1)) _inst_1)))
+Case conversion may be inaccurate. Consider using '#align power_series.coeff_one_X PowerSeries.coeff_one_Xₓ'. -/
 @[simp]
-theorem coeff_one_x : coeff R 1 (x : PowerSeries R) = 1 := by rw [coeff_X, if_pos rfl]
-#align power_series.coeff_one_X PowerSeries.coeff_one_x
-
+theorem coeff_one_X : coeff R 1 (X : PowerSeries R) = 1 := by rw [coeff_X, if_pos rfl]
+#align power_series.coeff_one_X PowerSeries.coeff_one_X
+
+/- warning: power_series.X_ne_zero -> PowerSeries.X_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Ne.{succ u1} (PowerSeries.{u1} R) (PowerSeries.X.{u1} R _inst_1) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (OfNat.mk.{u1} (PowerSeries.{u1} R) 0 (Zero.zero.{u1} (PowerSeries.{u1} R) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Ne.{succ u1} (PowerSeries.{u1} R) (PowerSeries.X.{u1} R _inst_1) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (Zero.toOfNat0.{u1} (PowerSeries.{u1} R) (PowerSeries.instZeroPowerSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align power_series.X_ne_zero PowerSeries.X_ne_zeroₓ'. -/
 @[simp]
-theorem x_ne_zero [Nontrivial R] : (x : PowerSeries R) ≠ 0 := fun H => by
+theorem X_ne_zero [Nontrivial R] : (X : PowerSeries R) ≠ 0 := fun H => by
   simpa only [coeff_one_X, one_ne_zero, map_zero] using congr_arg (coeff R 1) H
-#align power_series.X_ne_zero PowerSeries.x_ne_zero
-
-theorem x_pow_eq (n : ℕ) : (x : PowerSeries R) ^ n = monomial R n 1 :=
-  MvPowerSeries.x_pow_eq _ n
-#align power_series.X_pow_eq PowerSeries.x_pow_eq
-
-theorem coeff_x_pow (m n : ℕ) : coeff R m ((x : PowerSeries R) ^ n) = if m = n then 1 else 0 := by
+#align power_series.X_ne_zero PowerSeries.X_ne_zero
+
+/- warning: power_series.X_pow_eq -> PowerSeries.X_pow_eq is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.X_pow_eq PowerSeries.X_pow_eqₓ'. -/
+theorem X_pow_eq (n : ℕ) : (X : PowerSeries R) ^ n = monomial R n 1 :=
+  MvPowerSeries.X_pow_eq _ n
+#align power_series.X_pow_eq PowerSeries.X_pow_eq
+
+/- warning: power_series.coeff_X_pow -> PowerSeries.coeff_X_pow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow PowerSeries.coeff_X_powₓ'. -/
+theorem coeff_X_pow (m n : ℕ) : coeff R m ((X : PowerSeries R) ^ n) = if m = n then 1 else 0 := by
   rw [X_pow_eq, coeff_monomial]
-#align power_series.coeff_X_pow PowerSeries.coeff_x_pow
-
+#align power_series.coeff_X_pow PowerSeries.coeff_X_pow
+
+/- warning: power_series.coeff_X_pow_self -> PowerSeries.coeff_X_pow_self is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow_self PowerSeries.coeff_X_pow_selfₓ'. -/
 @[simp]
-theorem coeff_x_pow_self (n : ℕ) : coeff R n ((x : PowerSeries R) ^ n) = 1 := by
+theorem coeff_X_pow_self (n : ℕ) : coeff R n ((X : PowerSeries R) ^ n) = 1 := by
   rw [coeff_X_pow, if_pos rfl]
-#align power_series.coeff_X_pow_self PowerSeries.coeff_x_pow_self
-
+#align power_series.coeff_X_pow_self PowerSeries.coeff_X_pow_self
+
+/- warning: power_series.coeff_one -> PowerSeries.coeff_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_one PowerSeries.coeff_oneₓ'. -/
 @[simp]
 theorem coeff_one (n : ℕ) : coeff R n (1 : PowerSeries R) = if n = 0 then 1 else 0 :=
-  coeff_c n 1
+  coeff_C n 1
 #align power_series.coeff_one PowerSeries.coeff_one
 
+/- warning: power_series.coeff_zero_one -> PowerSeries.coeff_zero_one is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_one PowerSeries.coeff_zero_oneₓ'. -/
 theorem coeff_zero_one : coeff R 0 (1 : PowerSeries R) = 1 :=
-  coeff_zero_c 1
+  coeff_zero_C 1
 #align power_series.coeff_zero_one PowerSeries.coeff_zero_one
 
+/- warning: power_series.coeff_mul -> PowerSeries.coeff_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul PowerSeries.coeff_mulₓ'. -/
 theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
     coeff R n (φ * ψ) = ∑ p in Finset.Nat.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ :=
   by
@@ -1406,86 +2282,172 @@ theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
       exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
 #align power_series.coeff_mul PowerSeries.coeff_mul
 
+/- warning: power_series.coeff_mul_C -> PowerSeries.coeff_mul_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_C PowerSeries.coeff_mul_Cₓ'. -/
 @[simp]
-theorem coeff_mul_c (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (φ * c R a) = coeff R n φ * a :=
-  MvPowerSeries.coeff_mul_c _ φ a
-#align power_series.coeff_mul_C PowerSeries.coeff_mul_c
-
+theorem coeff_mul_C (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (φ * C R a) = coeff R n φ * a :=
+  MvPowerSeries.coeff_mul_C _ φ a
+#align power_series.coeff_mul_C PowerSeries.coeff_mul_C
+
+/- warning: power_series.coeff_C_mul -> PowerSeries.coeff_C_mul is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_C_mul PowerSeries.coeff_C_mulₓ'. -/
 @[simp]
-theorem coeff_c_mul (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (c R a * φ) = a * coeff R n φ :=
-  MvPowerSeries.coeff_c_mul _ φ a
-#align power_series.coeff_C_mul PowerSeries.coeff_c_mul
-
+theorem coeff_C_mul (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (C R a * φ) = a * coeff R n φ :=
+  MvPowerSeries.coeff_C_mul _ φ a
+#align power_series.coeff_C_mul PowerSeries.coeff_C_mul
+
+/- warning: power_series.coeff_smul -> PowerSeries.coeff_smul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_smul PowerSeries.coeff_smulₓ'. -/
 @[simp]
 theorem coeff_smul {S : Type _} [Semiring S] [Module R S] (n : ℕ) (φ : PowerSeries S) (a : R) :
     coeff S n (a • φ) = a • coeff S n φ :=
   rfl
 #align power_series.coeff_smul PowerSeries.coeff_smul
 
-theorem smul_eq_c_mul (f : PowerSeries R) (a : R) : a • f = c R a * f :=
+/- warning: power_series.smul_eq_C_mul -> PowerSeries.smul_eq_C_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.smul_eq_C_mul PowerSeries.smul_eq_C_mulₓ'. -/
+theorem smul_eq_C_mul (f : PowerSeries R) (a : R) : a • f = C R a * f :=
   by
   ext
   simp
-#align power_series.smul_eq_C_mul PowerSeries.smul_eq_c_mul
-
+#align power_series.smul_eq_C_mul PowerSeries.smul_eq_C_mul
+
+/- warning: power_series.coeff_succ_mul_X -> PowerSeries.coeff_succ_mul_X is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_succ_mul_X PowerSeries.coeff_succ_mul_Xₓ'. -/
 @[simp]
-theorem coeff_succ_mul_x (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (φ * x) = coeff R n φ :=
+theorem coeff_succ_mul_X (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (φ * X) = coeff R n φ :=
   by
   simp only [coeff, Finsupp.single_add]
   convert φ.coeff_add_mul_monomial (single () n) (single () 1) _
   rw [mul_one]
-#align power_series.coeff_succ_mul_X PowerSeries.coeff_succ_mul_x
-
+#align power_series.coeff_succ_mul_X PowerSeries.coeff_succ_mul_X
+
+/- warning: power_series.coeff_succ_X_mul -> PowerSeries.coeff_succ_X_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] (n : Nat) (φ : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ)) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ)
+Case conversion may be inaccurate. Consider using '#align power_series.coeff_succ_X_mul PowerSeries.coeff_succ_X_mulₓ'. -/
 @[simp]
-theorem coeff_succ_x_mul (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (x * φ) = coeff R n φ :=
+theorem coeff_succ_X_mul (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (X * φ) = coeff R n φ :=
   by
   simp only [coeff, Finsupp.single_add, add_comm n 1]
   convert φ.coeff_add_monomial_mul (single () 1) (single () n) _
   rw [one_mul]
-#align power_series.coeff_succ_X_mul PowerSeries.coeff_succ_x_mul
-
+#align power_series.coeff_succ_X_mul PowerSeries.coeff_succ_X_mul
+
+/- warning: power_series.constant_coeff_C -> PowerSeries.constantCoeff_C is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.constant_coeff_C PowerSeries.constantCoeff_Cₓ'. -/
 @[simp]
-theorem constantCoeff_c (a : R) : constantCoeff R (c R a) = a :=
+theorem constantCoeff_C (a : R) : constantCoeff R (C R a) = a :=
   rfl
-#align power_series.constant_coeff_C PowerSeries.constantCoeff_c
+#align power_series.constant_coeff_C PowerSeries.constantCoeff_C
 
+#print PowerSeries.constantCoeff_comp_C /-
 @[simp]
-theorem constantCoeff_comp_c : (constantCoeff R).comp (c R) = RingHom.id R :=
+theorem constantCoeff_comp_C : (constantCoeff R).comp (C R) = RingHom.id R :=
   rfl
-#align power_series.constant_coeff_comp_C PowerSeries.constantCoeff_comp_c
+#align power_series.constant_coeff_comp_C PowerSeries.constantCoeff_comp_C
+-/
 
+/- warning: power_series.constant_coeff_zero -> PowerSeries.constantCoeff_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.constant_coeff_zero PowerSeries.constantCoeff_zeroₓ'. -/
 @[simp]
 theorem constantCoeff_zero : constantCoeff R 0 = 0 :=
   rfl
 #align power_series.constant_coeff_zero PowerSeries.constantCoeff_zero
 
+/- warning: power_series.constant_coeff_one -> PowerSeries.constantCoeff_one is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.constant_coeff_one PowerSeries.constantCoeff_oneₓ'. -/
 @[simp]
 theorem constantCoeff_one : constantCoeff R 1 = 1 :=
   rfl
 #align power_series.constant_coeff_one PowerSeries.constantCoeff_one
 
+/- warning: power_series.constant_coeff_X -> PowerSeries.constantCoeff_X is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.constant_coeff_X PowerSeries.constantCoeff_Xₓ'. -/
 @[simp]
-theorem constantCoeff_x : constantCoeff R x = 0 :=
-  MvPowerSeries.coeff_zero_x _
-#align power_series.constant_coeff_X PowerSeries.constantCoeff_x
-
-theorem coeff_zero_mul_x (φ : PowerSeries R) : coeff R 0 (φ * x) = 0 := by simp
-#align power_series.coeff_zero_mul_X PowerSeries.coeff_zero_mul_x
-
-theorem coeff_zero_x_mul (φ : PowerSeries R) : coeff R 0 (x * φ) = 0 := by simp
-#align power_series.coeff_zero_X_mul PowerSeries.coeff_zero_x_mul
+theorem constantCoeff_X : constantCoeff R X = 0 :=
+  MvPowerSeries.coeff_zero_X _
+#align power_series.constant_coeff_X PowerSeries.constantCoeff_X
+
+/- warning: power_series.coeff_zero_mul_X -> PowerSeries.coeff_zero_mul_X is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_mul_X PowerSeries.coeff_zero_mul_Xₓ'. -/
+theorem coeff_zero_mul_X (φ : PowerSeries R) : coeff R 0 (φ * X) = 0 := by simp
+#align power_series.coeff_zero_mul_X PowerSeries.coeff_zero_mul_X
+
+/- warning: power_series.coeff_zero_X_mul -> PowerSeries.coeff_zero_X_mul is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_zero_X_mul PowerSeries.coeff_zero_X_mulₓ'. -/
+theorem coeff_zero_X_mul (φ : PowerSeries R) : coeff R 0 (X * φ) = 0 := by simp
+#align power_series.coeff_zero_X_mul PowerSeries.coeff_zero_X_mul
 
 -- The following section duplicates the api of `data.polynomial.coeff` and should attempt to keep
 -- up to date with that
 section
 
-theorem coeff_c_mul_x_pow (x : R) (k n : ℕ) :
-    coeff R n (c R x * x ^ k : PowerSeries R) = if n = k then x else 0 := by
+/- warning: power_series.coeff_C_mul_X_pow -> PowerSeries.coeff_C_mul_X_pow is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_C_mul_X_pow PowerSeries.coeff_C_mul_X_powₓ'. -/
+theorem coeff_C_mul_X_pow (x : R) (k n : ℕ) :
+    coeff R n (C R x * X ^ k : PowerSeries R) = if n = k then x else 0 := by
   simp [X_pow_eq, coeff_monomial]
-#align power_series.coeff_C_mul_X_pow PowerSeries.coeff_c_mul_x_pow
-
+#align power_series.coeff_C_mul_X_pow PowerSeries.coeff_C_mul_X_pow
+
+/- warning: power_series.coeff_mul_X_pow -> PowerSeries.coeff_mul_X_pow is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_X_powₓ'. -/
 @[simp]
-theorem coeff_mul_x_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * x ^ n) = coeff R d p :=
+theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * X ^ n) = coeff R d p :=
   by
   rw [coeff_mul, Finset.sum_eq_single (d, n), coeff_X_pow, if_pos rfl, mul_one]
   · rintro ⟨i, j⟩ h1 h2
@@ -1495,10 +2457,16 @@ theorem coeff_mul_x_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * x
     rw [Finset.Nat.mem_antidiagonal, add_right_cancel_iff] at h1
     subst h1
   · exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
-#align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_x_pow
-
+#align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_X_pow
+
+/- warning: power_series.coeff_X_pow_mul -> PowerSeries.coeff_X_pow_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow_mul PowerSeries.coeff_X_pow_mulₓ'. -/
 @[simp]
-theorem coeff_x_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (x ^ n * p) = coeff R d p :=
+theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (X ^ n * p) = coeff R d p :=
   by
   rw [coeff_mul, Finset.sum_eq_single (n, d), coeff_X_pow, if_pos rfl, one_mul]
   · rintro ⟨i, j⟩ h1 h2
@@ -1509,20 +2477,32 @@ theorem coeff_x_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (x ^ n
     subst h1
   · rw [add_comm]
     exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
-#align power_series.coeff_X_pow_mul PowerSeries.coeff_x_pow_mul
-
-theorem coeff_mul_x_pow' (p : PowerSeries R) (n d : ℕ) :
-    coeff R d (p * x ^ n) = ite (n ≤ d) (coeff R (d - n) p) 0 :=
+#align power_series.coeff_X_pow_mul PowerSeries.coeff_X_pow_mul
+
+/- warning: power_series.coeff_mul_X_pow' -> PowerSeries.coeff_mul_X_pow' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_X_pow' PowerSeries.coeff_mul_X_pow'ₓ'. -/
+theorem coeff_mul_X_pow' (p : PowerSeries R) (n d : ℕ) :
+    coeff R d (p * X ^ n) = ite (n ≤ d) (coeff R (d - n) p) 0 :=
   by
   split_ifs
   · rw [← tsub_add_cancel_of_le h, coeff_mul_X_pow, add_tsub_cancel_right]
   · refine' (coeff_mul _ _ _).trans (Finset.sum_eq_zero fun x hx => _)
     rw [coeff_X_pow, if_neg, MulZeroClass.mul_zero]
     exact ((le_of_add_le_right (finset.nat.mem_antidiagonal.mp hx).le).trans_lt <| not_le.mp h).Ne
-#align power_series.coeff_mul_X_pow' PowerSeries.coeff_mul_x_pow'
-
-theorem coeff_x_pow_mul' (p : PowerSeries R) (n d : ℕ) :
-    coeff R d (x ^ n * p) = ite (n ≤ d) (coeff R (d - n) p) 0 :=
+#align power_series.coeff_mul_X_pow' PowerSeries.coeff_mul_X_pow'
+
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_X_pow_mul' PowerSeries.coeff_X_pow_mul'ₓ'. -/
+theorem coeff_X_pow_mul' (p : PowerSeries R) (n d : ℕ) :
+    coeff R d (X ^ n * p) = ite (n ≤ d) (coeff R (d - n) p) 0 :=
   by
   split_ifs
   · rw [← tsub_add_cancel_of_le h, coeff_X_pow_mul]
@@ -1532,18 +2512,30 @@ theorem coeff_x_pow_mul' (p : PowerSeries R) (n d : ℕ) :
     have := finset.nat.mem_antidiagonal.mp hx
     rw [add_comm] at this
     exact ((le_of_add_le_right this.le).trans_lt <| not_le.mp h).Ne
-#align power_series.coeff_X_pow_mul' PowerSeries.coeff_x_pow_mul'
+#align power_series.coeff_X_pow_mul' PowerSeries.coeff_X_pow_mul'
 
 end
 
+/- warning: power_series.is_unit_constant_coeff -> PowerSeries.isUnit_constantCoeff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.is_unit_constant_coeff PowerSeries.isUnit_constantCoeffₓ'. -/
 /-- If a formal power series is invertible, then so is its constant coefficient.-/
 theorem isUnit_constantCoeff (φ : PowerSeries R) (h : IsUnit φ) : IsUnit (constantCoeff R φ) :=
   MvPowerSeries.isUnit_constantCoeff φ h
 #align power_series.is_unit_constant_coeff PowerSeries.isUnit_constantCoeff
 
+/- warning: power_series.eq_shift_mul_X_add_const -> PowerSeries.eq_shift_mul_X_add_const is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.eq_shift_mul_X_add_const PowerSeries.eq_shift_mul_X_add_constₓ'. -/
 /-- Split off the constant coefficient. -/
-theorem eq_shift_mul_x_add_const (φ : PowerSeries R) :
-    φ = (mk fun p => coeff R (p + 1) φ) * x + c R (constantCoeff R φ) :=
+theorem eq_shift_mul_X_add_const (φ : PowerSeries R) :
+    φ = (mk fun p => coeff R (p + 1) φ) * X + C R (constantCoeff R φ) :=
   by
   ext (_ | n)
   ·
@@ -1552,11 +2544,17 @@ theorem eq_shift_mul_x_add_const (φ : PowerSeries R) :
   ·
     simp only [coeff_succ_mul_X, coeff_mk, LinearMap.map_add, coeff_C, n.succ_ne_zero, sub_zero,
       if_false, add_zero]
-#align power_series.eq_shift_mul_X_add_const PowerSeries.eq_shift_mul_x_add_const
-
+#align power_series.eq_shift_mul_X_add_const PowerSeries.eq_shift_mul_X_add_const
+
+/- warning: power_series.eq_X_mul_shift_add_const -> PowerSeries.eq_X_mul_shift_add_const is a dubious translation:
+lean 3 declaration is
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(RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1) φ)))
+Case conversion may be inaccurate. Consider using '#align power_series.eq_X_mul_shift_add_const PowerSeries.eq_X_mul_shift_add_constₓ'. -/
 /-- Split off the constant coefficient. -/
-theorem eq_x_mul_shift_add_const (φ : PowerSeries R) :
-    φ = (x * mk fun p => coeff R (p + 1) φ) + c R (constantCoeff R φ) :=
+theorem eq_X_mul_shift_add_const (φ : PowerSeries R) :
+    φ = (X * mk fun p => coeff R (p + 1) φ) + C R (constantCoeff R φ) :=
   by
   ext (_ | n)
   ·
@@ -1565,7 +2563,7 @@ theorem eq_x_mul_shift_add_const (φ : PowerSeries R) :
   ·
     simp only [coeff_succ_X_mul, coeff_mk, LinearMap.map_add, coeff_C, n.succ_ne_zero, sub_zero,
       if_false, add_zero]
-#align power_series.eq_X_mul_shift_add_const PowerSeries.eq_x_mul_shift_add_const
+#align power_series.eq_X_mul_shift_add_const PowerSeries.eq_X_mul_shift_add_const
 
 section Map
 
@@ -1573,60 +2571,108 @@ variable {S : Type _} {T : Type _} [Semiring S] [Semiring T]
 
 variable (f : R →+* S) (g : S →+* T)
 
+/- warning: power_series.map -> PowerSeries.map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S], (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) -> (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.semiring.{u2} S _inst_2)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S], (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) -> (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2)))
+Case conversion may be inaccurate. Consider using '#align power_series.map PowerSeries.mapₓ'. -/
 /-- The map between formal power series induced by a map on the coefficients.-/
 def map : PowerSeries R →+* PowerSeries S :=
   MvPowerSeries.map _ f
 #align power_series.map PowerSeries.map
 
+/- warning: power_series.map_id -> PowerSeries.map_id is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.map_id PowerSeries.map_idₓ'. -/
 @[simp]
 theorem map_id : (map (RingHom.id R) : PowerSeries R → PowerSeries R) = id :=
   rfl
 #align power_series.map_id PowerSeries.map_id
 
+/- warning: power_series.map_comp -> PowerSeries.map_comp is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.map_comp PowerSeries.map_compₓ'. -/
 theorem map_comp : map (g.comp f) = (map g).comp (map f) :=
   rfl
 #align power_series.map_comp PowerSeries.map_comp
 
+/- warning: power_series.coeff_map -> PowerSeries.coeff_map is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_map PowerSeries.coeff_mapₓ'. -/
 @[simp]
 theorem coeff_map (n : ℕ) (φ : PowerSeries R) : coeff S n (map f φ) = f (coeff R n φ) :=
   rfl
 #align power_series.coeff_map PowerSeries.coeff_map
 
+/- warning: power_series.map_C -> PowerSeries.map_C is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.map_C PowerSeries.map_Cₓ'. -/
 @[simp]
-theorem map_c (r : R) : map f (c _ r) = c _ (f r) :=
+theorem map_C (r : R) : map f (C _ r) = C _ (f r) :=
   by
   ext
   simp [coeff_C, apply_ite f]
-#align power_series.map_C PowerSeries.map_c
-
+#align power_series.map_C PowerSeries.map_C
+
+/- warning: power_series.map_X -> PowerSeries.map_X is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} (PowerSeries.{u2} S) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.semiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.semiring.{u2} S _inst_2))) => (PowerSeries.{u1} R) -> (PowerSeries.{u2} S)) (RingHom.hasCoeToFun.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.semiring.{u2} S _inst_2))) (PowerSeries.map.{u1, u2} R _inst_1 S _inst_2 f) (PowerSeries.X.{u1} R _inst_1)) (PowerSeries.X.{u2} S _inst_2)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u2} S) (PowerSeries.X.{u1} R _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u2} S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2))) (PowerSeries.{u1} R) (PowerSeries.{u2} S) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} (PowerSeries.{u2} S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2))) (PowerSeries.{u1} R) (PowerSeries.{u2} S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2))) (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u2} S _inst_2)))))) (PowerSeries.map.{u1, u2} R _inst_1 S _inst_2 f) (PowerSeries.X.{u1} R _inst_1)) (PowerSeries.X.{u2} S _inst_2)
+Case conversion may be inaccurate. Consider using '#align power_series.map_X PowerSeries.map_Xₓ'. -/
 @[simp]
-theorem map_x : map f x = x := by
+theorem map_X : map f X = X := by
   ext
   simp [coeff_X, apply_ite f]
-#align power_series.map_X PowerSeries.map_x
+#align power_series.map_X PowerSeries.map_X
 
 end Map
 
-theorem x_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
-    (x : PowerSeries R) ^ n ∣ φ ↔ ∀ m, m < n → coeff R m φ = 0 :=
+/- warning: power_series.X_pow_dvd_iff -> PowerSeries.X_pow_dvd_iff 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] {n : Nat} {φ : PowerSeries.{u1} R}, Iff (Dvd.dvd.{u1} (PowerSeries.{u1} R) (semigroupDvd.{u1} (PowerSeries.{u1} R) (SemigroupWithZero.toSemigroup.{u1} (PowerSeries.{u1} R) (NonUnitalSemiring.toSemigroupWithZero.{u1} (PowerSeries.{u1} R) (Semiring.toNonUnitalSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n) φ) (forall (m : Nat), (LT.lt.{0} Nat instLTNat m n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 m) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align power_series.X_pow_dvd_iff PowerSeries.X_pow_dvd_iffₓ'. -/
+theorem X_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
+    (X : PowerSeries R) ^ n ∣ φ ↔ ∀ m, m < n → coeff R m φ = 0 :=
   by
-  convert@MvPowerSeries.x_pow_dvd_iff Unit R _ () n φ; apply propext
+  convert@MvPowerSeries.X_pow_dvd_iff Unit R _ () n φ; apply propext
   classical
     constructor <;> intro h m hm
     · rw [Finsupp.unique_single m]
       convert h _ hm
     · apply h
       simpa only [Finsupp.single_eq_same] using hm
-#align power_series.X_pow_dvd_iff PowerSeries.x_pow_dvd_iff
-
-theorem x_dvd_iff {φ : PowerSeries R} : (x : PowerSeries R) ∣ φ ↔ constantCoeff R φ = 0 :=
+#align power_series.X_pow_dvd_iff PowerSeries.X_pow_dvd_iff
+
+/- warning: power_series.X_dvd_iff -> PowerSeries.X_dvd_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R}, Iff (Dvd.Dvd.{u1} (PowerSeries.{u1} R) (semigroupDvd.{u1} (PowerSeries.{u1} R) (SemigroupWithZero.toSemigroup.{u1} (PowerSeries.{u1} R) (NonUnitalSemiring.toSemigroupWithZero.{u1} (PowerSeries.{u1} R) (Semiring.toNonUnitalSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ) (Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.constantCoeff.{u1} R _inst_1) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R}, Iff (Dvd.dvd.{u1} (PowerSeries.{u1} R) (semigroupDvd.{u1} (PowerSeries.{u1} R) (SemigroupWithZero.toSemigroup.{u1} (PowerSeries.{u1} R) (NonUnitalSemiring.toSemigroupWithZero.{u1} (PowerSeries.{u1} R) (Semiring.toNonUnitalSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) φ) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) φ) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (PowerSeries.constantCoeff.{u1} R _inst_1) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) φ) _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align power_series.X_dvd_iff PowerSeries.X_dvd_iffₓ'. -/
+theorem X_dvd_iff {φ : PowerSeries R} : (X : PowerSeries R) ∣ φ ↔ constantCoeff R φ = 0 :=
   by
   rw [← pow_one (X : PowerSeries R), X_pow_dvd_iff, ← coeff_zero_eq_constant_coeff_apply]
   constructor <;> intro h
   · exact h 0 zero_lt_one
   · intro m hm
     rwa [Nat.eq_zero_of_le_zero (Nat.le_of_succ_le_succ hm)]
-#align power_series.X_dvd_iff PowerSeries.x_dvd_iff
+#align power_series.X_dvd_iff PowerSeries.X_dvd_iff
 
 end Semiring
 
@@ -1636,6 +2682,12 @@ variable [CommSemiring R]
 
 open Finset Nat
 
+/- warning: power_series.rescale -> PowerSeries.rescale is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R], R -> (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R], R -> (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align power_series.rescale PowerSeries.rescaleₓ'. -/
 /-- The ring homomorphism taking a power series `f(X)` to `f(aX)`. -/
 noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R
     where
@@ -1662,14 +2714,26 @@ noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R
     rw [← H, pow_add, mul_mul_mul_comm]
 #align power_series.rescale PowerSeries.rescale
 
+/- warning: power_series.coeff_rescale -> PowerSeries.coeff_rescale is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : PowerSeries.{u1} R) (a : R) (n : Nat), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.module.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_rescale PowerSeries.coeff_rescaleₓ'. -/
 @[simp]
 theorem coeff_rescale (f : PowerSeries R) (a : R) (n : ℕ) :
     coeff R n (rescale a f) = a ^ n * coeff R n f :=
   coeff_mk n _
 #align power_series.coeff_rescale PowerSeries.coeff_rescale
 
+/- warning: power_series.rescale_zero -> PowerSeries.rescale_zero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.rescale_zero PowerSeries.rescale_zeroₓ'. -/
 @[simp]
-theorem rescale_zero : rescale 0 = (c R).comp (constantCoeff R) :=
+theorem rescale_zero : rescale 0 = (C R).comp (constantCoeff R) :=
   by
   ext
   simp only [Function.comp_apply, RingHom.coe_comp, rescale, RingHom.coe_mk,
@@ -1679,9 +2743,21 @@ theorem rescale_zero : rescale 0 = (c R).comp (constantCoeff R) :=
   · rw [zero_pow' n h, MulZeroClass.zero_mul]
 #align power_series.rescale_zero PowerSeries.rescale_zero
 
-theorem rescale_zero_apply : rescale 0 x = c R (constantCoeff R x) := by simp
+/- warning: power_series.rescale_zero_apply -> PowerSeries.rescale_zero_apply is a dubious translation:
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(Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (PowerSeries.constantCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align power_series.rescale_zero_apply PowerSeries.rescale_zero_applyₓ'. -/
+theorem rescale_zero_apply : rescale 0 X = C R (constantCoeff R X) := by simp
 #align power_series.rescale_zero_apply PowerSeries.rescale_zero_apply
 
+/- warning: power_series.rescale_one -> PowerSeries.rescale_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R], Eq.{succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.rescale.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) (RingHom.id.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R], Eq.{succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.rescale.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (RingHom.id.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align power_series.rescale_one PowerSeries.rescale_oneₓ'. -/
 @[simp]
 theorem rescale_one : rescale 1 = RingHom.id (PowerSeries R) :=
   by
@@ -1689,12 +2765,24 @@ theorem rescale_one : rescale 1 = RingHom.id (PowerSeries R) :=
   simp only [RingHom.id_apply, rescale, one_pow, coeff_mk, one_mul, RingHom.coe_mk]
 #align power_series.rescale_one PowerSeries.rescale_one
 
+/- warning: power_series.rescale_mk -> PowerSeries.rescale_mk is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Nat -> R) (a : R), Eq.{succ u1} (PowerSeries.{u1} R) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (PowerSeries.{u1} R) -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.rescale.{u1} R _inst_1 a) (PowerSeries.mk.{u1} R f)) (PowerSeries.mk.{u1} R (fun (n : Nat) => 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 (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) a n) (f n)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Nat -> R) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u1} R) (PowerSeries.mk.{u1} R f)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (PowerSeries.rescale.{u1} R _inst_1 a) (PowerSeries.mk.{u1} R f)) (PowerSeries.mk.{u1} R (fun (n : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) a n) (f n)))
+Case conversion may be inaccurate. Consider using '#align power_series.rescale_mk PowerSeries.rescale_mkₓ'. -/
 theorem rescale_mk (f : ℕ → R) (a : R) : rescale a (mk f) = mk fun n : ℕ => a ^ n * f n :=
   by
   ext
   rw [coeff_rescale, coeff_mk, coeff_mk]
 #align power_series.rescale_mk PowerSeries.rescale_mk
 
+/- warning: power_series.rescale_rescale -> PowerSeries.rescale_rescale is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : PowerSeries.{u1} R) (a : R) (b : R), Eq.{succ u1} (PowerSeries.{u1} R) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (PowerSeries.{u1} R) -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.rescale.{u1} R _inst_1 b) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (PowerSeries.{u1} R) -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.rescale.{u1} R _inst_1 a) f)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (PowerSeries.{u1} R) -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.rescale.{u1} R _inst_1 (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 (CommSemiring.toSemiring.{u1} R _inst_1)))))) a b)) f)
+but is expected to have type
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(Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} 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(CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) 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+Case conversion may be inaccurate. Consider using '#align power_series.rescale_rescale PowerSeries.rescale_rescaleₓ'. -/
 theorem rescale_rescale (f : PowerSeries R) (a b : R) :
     rescale b (rescale a f) = rescale (a * b) f :=
   by
@@ -1703,6 +2791,12 @@ theorem rescale_rescale (f : PowerSeries R) (a b : R) :
   rw [mul_pow, mul_comm _ (b ^ n), mul_assoc]
 #align power_series.rescale_rescale PowerSeries.rescale_rescale
 
+/- warning: power_series.rescale_mul -> PowerSeries.rescale_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.rescale_mul PowerSeries.rescale_mulₓ'. -/
 theorem rescale_mul (a b : R) : rescale (a * b) = (rescale b).comp (rescale a) :=
   by
   ext
@@ -1711,16 +2805,30 @@ theorem rescale_mul (a b : R) : rescale (a * b) = (rescale b).comp (rescale a) :
 
 section Trunc
 
+#print PowerSeries.trunc /-
 /-- The `n`th truncation of a formal power series to a polynomial -/
 def trunc (n : ℕ) (φ : PowerSeries R) : R[X] :=
   ∑ m in Ico 0 n, Polynomial.monomial m (coeff R m φ)
 #align power_series.trunc PowerSeries.trunc
+-/
 
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_trunc PowerSeries.coeff_truncₓ'. -/
 theorem coeff_trunc (m) (n) (φ : PowerSeries R) :
     (trunc n φ).coeff m = if m < n then coeff R m φ else 0 := by
   simp [Trunc, Polynomial.coeff_sum, Polynomial.coeff_monomial, Nat.lt_succ_iff]
 #align power_series.coeff_trunc PowerSeries.coeff_trunc
 
+/- warning: power_series.trunc_zero -> PowerSeries.trunc_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.trunc_zero PowerSeries.trunc_zeroₓ'. -/
 @[simp]
 theorem trunc_zero (n) : trunc n (0 : PowerSeries R) = 0 :=
   Polynomial.ext fun m =>
@@ -1729,6 +2837,12 @@ theorem trunc_zero (n) : trunc n (0 : PowerSeries R) = 0 :=
     split_ifs <;> rfl
 #align power_series.trunc_zero PowerSeries.trunc_zero
 
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+Case conversion may be inaccurate. Consider using '#align power_series.trunc_one PowerSeries.trunc_oneₓ'. -/
 @[simp]
 theorem trunc_one (n) : trunc (n + 1) (1 : PowerSeries R) = 1 :=
   Polynomial.ext fun m => by
@@ -1745,13 +2859,25 @@ theorem trunc_one (n) : trunc (n + 1) (1 : PowerSeries R) = 1 :=
       exact Nat.zero_lt_succ _
 #align power_series.trunc_one PowerSeries.trunc_one
 
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+Case conversion may be inaccurate. Consider using '#align power_series.trunc_C PowerSeries.trunc_Cₓ'. -/
 @[simp]
-theorem trunc_c (n) (a : R) : trunc (n + 1) (c R a) = Polynomial.C a :=
+theorem trunc_C (n) (a : R) : trunc (n + 1) (C R a) = Polynomial.C a :=
   Polynomial.ext fun m => by
     rw [coeff_trunc, coeff_C, Polynomial.coeff_C]
     split_ifs with H <;> first |rfl|try simp_all
-#align power_series.trunc_C PowerSeries.trunc_c
-
+#align power_series.trunc_C PowerSeries.trunc_C
+
+/- warning: power_series.trunc_add -> PowerSeries.trunc_add is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat) (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.trunc.{u1} R _inst_1 n (HAdd.hAdd.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHAdd.{u1} (PowerSeries.{u1} R) (Distrib.toHasAdd.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) φ ψ)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.trunc.{u1} R _inst_1 n φ) (PowerSeries.trunc.{u1} R _inst_1 n ψ))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.trunc_add PowerSeries.trunc_addₓ'. -/
 @[simp]
 theorem trunc_add (n) (φ ψ : PowerSeries R) : trunc n (φ + ψ) = trunc n φ + trunc n ψ :=
   Polynomial.ext fun m =>
@@ -1768,18 +2894,26 @@ section Ring
 
 variable [Ring R]
 
+#print PowerSeries.inv.aux /-
 /-- Auxiliary function used for computing inverse of a power series -/
-protected def Inv.aux : R → PowerSeries R → PowerSeries R :=
-  MvPowerSeries.Inv.aux
-#align power_series.inv.aux PowerSeries.Inv.aux
+protected def inv.aux : R → PowerSeries R → PowerSeries R :=
+  MvPowerSeries.inv.aux
+#align power_series.inv.aux PowerSeries.inv.aux
+-/
 
+/- warning: power_series.coeff_inv_aux -> PowerSeries.coeff_inv_aux is a dubious translation:
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+but is expected to have type
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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align power_series.coeff_inv_aux PowerSeries.coeff_inv_auxₓ'. -/
 theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
-    coeff R n (Inv.aux a φ) =
+    coeff R n (inv.aux a φ) =
       if n = 0 then a
       else
         -a *
           ∑ x in Finset.Nat.antidiagonal n,
-            if x.2 < n then coeff R x.1 φ * coeff R x.2 (Inv.aux a φ) else 0 :=
+            if x.2 < n then coeff R x.1 φ * coeff R x.2 (inv.aux a φ) else 0 :=
   by
   rw [coeff, inv.aux, MvPowerSeries.coeff_inv_aux]
   simp only [Finsupp.single_eq_zero]
@@ -1817,11 +2951,23 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
       exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
 #align power_series.coeff_inv_aux PowerSeries.coeff_inv_aux
 
+/- warning: power_series.inv_of_unit -> PowerSeries.invOfUnit is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], (PowerSeries.{u1} R) -> (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) -> (PowerSeries.{u1} R)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], (PowerSeries.{u1} R) -> (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (PowerSeries.{u1} R)
+Case conversion may be inaccurate. Consider using '#align power_series.inv_of_unit PowerSeries.invOfUnitₓ'. -/
 /-- A formal power series is invertible if the constant coefficient is invertible.-/
 def invOfUnit (φ : PowerSeries R) (u : Rˣ) : PowerSeries R :=
   MvPowerSeries.invOfUnit φ u
 #align power_series.inv_of_unit PowerSeries.invOfUnit
 
+/- warning: power_series.coeff_inv_of_unit -> PowerSeries.coeff_invOfUnit is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_inv_of_unit PowerSeries.coeff_invOfUnitₓ'. -/
 theorem coeff_invOfUnit (n : ℕ) (φ : PowerSeries R) (u : Rˣ) :
     coeff R n (invOfUnit φ u) =
       if n = 0 then ↑u⁻¹
@@ -1832,27 +2978,51 @@ theorem coeff_invOfUnit (n : ℕ) (φ : PowerSeries R) (u : Rˣ) :
   coeff_inv_aux n (↑u⁻¹) φ
 #align power_series.coeff_inv_of_unit PowerSeries.coeff_invOfUnit
 
+/- warning: power_series.constant_coeff_inv_of_unit -> PowerSeries.constantCoeff_invOfUnit is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.constant_coeff_inv_of_unit PowerSeries.constantCoeff_invOfUnitₓ'. -/
 @[simp]
 theorem constantCoeff_invOfUnit (φ : PowerSeries R) (u : Rˣ) :
     constantCoeff R (invOfUnit φ u) = ↑u⁻¹ := by
   rw [← coeff_zero_eq_constant_coeff_apply, coeff_inv_of_unit, if_pos rfl]
 #align power_series.constant_coeff_inv_of_unit PowerSeries.constantCoeff_invOfUnit
 
+/- warning: power_series.mul_inv_of_unit -> PowerSeries.mul_invOfUnit is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.mul_inv_of_unit PowerSeries.mul_invOfUnitₓ'. -/
 theorem mul_invOfUnit (φ : PowerSeries R) (u : Rˣ) (h : constantCoeff R φ = u) :
     φ * invOfUnit φ u = 1 :=
   MvPowerSeries.mul_invOfUnit φ u <| h
 #align power_series.mul_inv_of_unit PowerSeries.mul_invOfUnit
 
+/- warning: power_series.sub_const_eq_shift_mul_X -> PowerSeries.sub_const_eq_shift_mul_X is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.sub_const_eq_shift_mul_X PowerSeries.sub_const_eq_shift_mul_Xₓ'. -/
 /-- Two ways of removing the constant coefficient of a power series are the same. -/
-theorem sub_const_eq_shift_mul_x (φ : PowerSeries R) :
-    φ - c R (constantCoeff R φ) = (PowerSeries.mk fun p => coeff R (p + 1) φ) * x :=
-  sub_eq_iff_eq_add.mpr (eq_shift_mul_x_add_const φ)
-#align power_series.sub_const_eq_shift_mul_X PowerSeries.sub_const_eq_shift_mul_x
-
-theorem sub_const_eq_x_mul_shift (φ : PowerSeries R) :
-    φ - c R (constantCoeff R φ) = x * PowerSeries.mk fun p => coeff R (p + 1) φ :=
-  sub_eq_iff_eq_add.mpr (eq_x_mul_shift_add_const φ)
-#align power_series.sub_const_eq_X_mul_shift PowerSeries.sub_const_eq_x_mul_shift
+theorem sub_const_eq_shift_mul_X (φ : PowerSeries R) :
+    φ - C R (constantCoeff R φ) = (PowerSeries.mk fun p => coeff R (p + 1) φ) * X :=
+  sub_eq_iff_eq_add.mpr (eq_shift_mul_X_add_const φ)
+#align power_series.sub_const_eq_shift_mul_X PowerSeries.sub_const_eq_shift_mul_X
+
+/- warning: power_series.sub_const_eq_X_mul_shift -> PowerSeries.sub_const_eq_X_mul_shift is a dubious translation:
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(Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (PowerSeries.constantCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1)) φ)) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (Ring.toSub.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R _inst_1))) φ (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} 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(PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (PowerSeries.constantCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1)) φ))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ)) (PowerSeries.instRingPowerSeries.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1))))) (PowerSeries.X.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)) (PowerSeries.mk.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (fun (p : Nat) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) 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R (Ring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) φ)))
+Case conversion may be inaccurate. Consider using '#align power_series.sub_const_eq_X_mul_shift PowerSeries.sub_const_eq_X_mul_shiftₓ'. -/
+theorem sub_const_eq_X_mul_shift (φ : PowerSeries R) :
+    φ - C R (constantCoeff R φ) = X * PowerSeries.mk fun p => coeff R (p + 1) φ :=
+  sub_eq_iff_eq_add.mpr (eq_X_mul_shift_add_const φ)
+#align power_series.sub_const_eq_X_mul_shift PowerSeries.sub_const_eq_X_mul_shift
 
 end Ring
 
@@ -1860,27 +3030,51 @@ section CommRing
 
 variable {A : Type _} [CommRing A]
 
+/- warning: power_series.rescale_X -> PowerSeries.rescale_X is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : CommRing.{u1} A] (a : A), Eq.{succ u1} (PowerSeries.{u1} A) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) => (PowerSeries.{u1} A) -> (PowerSeries.{u1} A)) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (PowerSeries.rescale.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1) a) (PowerSeries.X.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)))) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (PowerSeries.{u1} A) (instHMul.{u1} (PowerSeries.{u1} A) (Distrib.toHasMul.{u1} (PowerSeries.{u1} A) (Ring.toDistrib.{u1} (PowerSeries.{u1} A) (PowerSeries.ring.{u1} A (CommRing.toRing.{u1} A _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} A (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))))) (fun (_x : RingHom.{u1, u1} A (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))))) => A -> (PowerSeries.{u1} A)) (RingHom.hasCoeToFun.{u1, u1} A (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))))) (PowerSeries.C.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))) a) (PowerSeries.X.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))))
+but is expected to have type
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(NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (PowerSeries.{u1} A) (PowerSeries.{u1} A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) 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(PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))))))) (PowerSeries.rescale.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1) a) (PowerSeries.X.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => PowerSeries.{u1} A) a) (PowerSeries.{u1} A) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} A) => PowerSeries.{u1} A) (PowerSeries.X.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => PowerSeries.{u1} A) a) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => PowerSeries.{u1} A) a) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => PowerSeries.{u1} A) a) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => PowerSeries.{u1} A) a) (PowerSeries.instRingPowerSeries.{u1} A (CommRing.toRing.{u1} A _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} A (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => PowerSeries.{u1} A) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} A (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) A (PowerSeries.{u1} A) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} A (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) A (PowerSeries.{u1} A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} A (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) A (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} A (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))))))) (PowerSeries.C.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) a) (PowerSeries.X.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))
+Case conversion may be inaccurate. Consider using '#align power_series.rescale_X PowerSeries.rescale_Xₓ'. -/
 @[simp]
-theorem rescale_x (a : A) : rescale a x = c A a * x :=
+theorem rescale_X (a : A) : rescale a X = C A a * X :=
   by
   ext
   simp only [coeff_rescale, coeff_C_mul, coeff_X]
   split_ifs with h <;> simp [h]
-#align power_series.rescale_X PowerSeries.rescale_x
-
-theorem rescale_neg_one_x : rescale (-1 : A) x = -x := by
+#align power_series.rescale_X PowerSeries.rescale_X
+
+/- warning: power_series.rescale_neg_one_X -> PowerSeries.rescale_neg_one_X is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : CommRing.{u1} A], Eq.{succ u1} (PowerSeries.{u1} A) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) => (PowerSeries.{u1} A) -> (PowerSeries.{u1} A)) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (PowerSeries.rescale.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1) (Neg.neg.{u1} A (SubNegMonoid.toHasNeg.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddGroupWithOne.toAddGroup.{u1} A (AddCommGroupWithOne.toAddGroupWithOne.{u1} A (Ring.toAddCommGroupWithOne.{u1} A (CommRing.toRing.{u1} A _inst_1)))))) (OfNat.ofNat.{u1} A 1 (OfNat.mk.{u1} A 1 (One.one.{u1} A (AddMonoidWithOne.toOne.{u1} A (AddGroupWithOne.toAddMonoidWithOne.{u1} A (AddCommGroupWithOne.toAddGroupWithOne.{u1} A (Ring.toAddCommGroupWithOne.{u1} A (CommRing.toRing.{u1} A _inst_1)))))))))) (PowerSeries.X.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)))) (Neg.neg.{u1} (PowerSeries.{u1} A) (SubNegMonoid.toHasNeg.{u1} (PowerSeries.{u1} A) (AddGroup.toSubNegMonoid.{u1} (PowerSeries.{u1} A) (PowerSeries.addGroup.{u1} A (AddGroupWithOne.toAddGroup.{u1} A (AddCommGroupWithOne.toAddGroupWithOne.{u1} A (Ring.toAddCommGroupWithOne.{u1} A (CommRing.toRing.{u1} A _inst_1))))))) (PowerSeries.X.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))))
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : CommRing.{u1} A], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} A) => PowerSeries.{u1} A) (PowerSeries.X.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (PowerSeries.{u1} A) (fun (_x : PowerSeries.{u1} A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} A) => PowerSeries.{u1} A) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (PowerSeries.{u1} A) (PowerSeries.{u1} A) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (PowerSeries.{u1} A) (PowerSeries.{u1} A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))))))) (PowerSeries.rescale.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1) (Neg.neg.{u1} A (Ring.toNeg.{u1} A (CommRing.toRing.{u1} A _inst_1)) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))))) (PowerSeries.X.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Neg.neg.{u1} (PowerSeries.{u1} A) (Ring.toNeg.{u1} (PowerSeries.{u1} A) (PowerSeries.instRingPowerSeries.{u1} A (CommRing.toRing.{u1} A _inst_1))) (PowerSeries.X.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))
+Case conversion may be inaccurate. Consider using '#align power_series.rescale_neg_one_X PowerSeries.rescale_neg_one_Xₓ'. -/
+theorem rescale_neg_one_X : rescale (-1 : A) X = -X := by
   rw [rescale_X, map_neg, map_one, neg_one_mul]
-#align power_series.rescale_neg_one_X PowerSeries.rescale_neg_one_x
-
+#align power_series.rescale_neg_one_X PowerSeries.rescale_neg_one_X
+
+/- warning: power_series.eval_neg_hom -> PowerSeries.evalNegHom is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : CommRing.{u1} A], RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (NonAssocRing.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} A) (PowerSeries.ring.{u1} A (CommRing.toRing.{u1} A _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} A) (PowerSeries.ring.{u1} A (CommRing.toRing.{u1} A _inst_1))))
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : CommRing.{u1} A], RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))
+Case conversion may be inaccurate. Consider using '#align power_series.eval_neg_hom PowerSeries.evalNegHomₓ'. -/
 /-- The ring homomorphism taking a power series `f(X)` to `f(-X)`. -/
 noncomputable def evalNegHom : PowerSeries A →+* PowerSeries A :=
   rescale (-1 : A)
 #align power_series.eval_neg_hom PowerSeries.evalNegHom
 
+/- warning: power_series.eval_neg_hom_X -> PowerSeries.evalNegHom_X is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : CommRing.{u1} A], Eq.{succ u1} (PowerSeries.{u1} A) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (NonAssocRing.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} A) (PowerSeries.ring.{u1} A (CommRing.toRing.{u1} A _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} A) (PowerSeries.ring.{u1} A (CommRing.toRing.{u1} A _inst_1))))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (NonAssocRing.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} A) (PowerSeries.ring.{u1} A (CommRing.toRing.{u1} A _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} A) (PowerSeries.ring.{u1} A (CommRing.toRing.{u1} A _inst_1))))) => (PowerSeries.{u1} A) -> (PowerSeries.{u1} A)) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (NonAssocRing.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} A) (PowerSeries.ring.{u1} A (CommRing.toRing.{u1} A _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} A) (PowerSeries.ring.{u1} A (CommRing.toRing.{u1} A _inst_1))))) (PowerSeries.evalNegHom.{u1} A _inst_1) (PowerSeries.X.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)))) (Neg.neg.{u1} (PowerSeries.{u1} A) (SubNegMonoid.toHasNeg.{u1} (PowerSeries.{u1} A) (AddGroup.toSubNegMonoid.{u1} (PowerSeries.{u1} A) (PowerSeries.addGroup.{u1} A (AddGroupWithOne.toAddGroup.{u1} A (AddCommGroupWithOne.toAddGroupWithOne.{u1} A (Ring.toAddCommGroupWithOne.{u1} A (CommRing.toRing.{u1} A _inst_1))))))) (PowerSeries.X.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))))
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : CommRing.{u1} A], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} A) => PowerSeries.{u1} A) (PowerSeries.X.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (PowerSeries.{u1} A) (fun (_x : PowerSeries.{u1} A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} A) => PowerSeries.{u1} A) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (PowerSeries.{u1} A) (PowerSeries.{u1} A) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (PowerSeries.{u1} A) (PowerSeries.{u1} A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))) (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} A) (PowerSeries.{u1} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} A) (PowerSeries.instSemiringPowerSeries.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))))))) (PowerSeries.evalNegHom.{u1} A _inst_1) (PowerSeries.X.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)))) (Neg.neg.{u1} (PowerSeries.{u1} A) (Ring.toNeg.{u1} (PowerSeries.{u1} A) (PowerSeries.instRingPowerSeries.{u1} A (CommRing.toRing.{u1} A _inst_1))) (PowerSeries.X.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))))
+Case conversion may be inaccurate. Consider using '#align power_series.eval_neg_hom_X PowerSeries.evalNegHom_Xₓ'. -/
 @[simp]
-theorem evalNegHom_x : evalNegHom (x : PowerSeries A) = -x :=
-  rescale_neg_one_x
-#align power_series.eval_neg_hom_X PowerSeries.evalNegHom_x
+theorem evalNegHom_X : evalNegHom (X : PowerSeries A) = -X :=
+  rescale_neg_one_X
+#align power_series.eval_neg_hom_X PowerSeries.evalNegHom_X
 
 end CommRing
 
@@ -1888,6 +3082,12 @@ section Domain
 
 variable [Ring R]
 
+/- warning: power_series.eq_zero_or_eq_zero_of_mul_eq_zero -> PowerSeries.eq_zero_or_eq_zero_of_mul_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))] (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), (Eq.{succ u1} (PowerSeries.{u1} R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (Ring.toDistrib.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R _inst_1)))) φ ψ) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (OfNat.mk.{u1} (PowerSeries.{u1} R) 0 (Zero.zero.{u1} (PowerSeries.{u1} R) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} R) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R _inst_1)))))))))) -> (Or (Eq.{succ u1} (PowerSeries.{u1} R) φ (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (OfNat.mk.{u1} (PowerSeries.{u1} R) 0 (Zero.zero.{u1} (PowerSeries.{u1} R) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} R) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R _inst_1)))))))))) (Eq.{succ u1} (PowerSeries.{u1} R) ψ (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (OfNat.mk.{u1} (PowerSeries.{u1} R) 0 (Zero.zero.{u1} (PowerSeries.{u1} R) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} R) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R _inst_1)))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))] (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), (Eq.{succ u1} (PowerSeries.{u1} R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} R) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} R) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R _inst_1))))) φ ψ) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (Zero.toOfNat0.{u1} (PowerSeries.{u1} R) (PowerSeries.instZeroPowerSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) -> (Or (Eq.{succ u1} (PowerSeries.{u1} R) φ (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (Zero.toOfNat0.{u1} (PowerSeries.{u1} R) (PowerSeries.instZeroPowerSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Eq.{succ u1} (PowerSeries.{u1} R) ψ (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (Zero.toOfNat0.{u1} (PowerSeries.{u1} R) (PowerSeries.instZeroPowerSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))
+Case conversion may be inaccurate. Consider using '#align power_series.eq_zero_or_eq_zero_of_mul_eq_zero PowerSeries.eq_zero_or_eq_zero_of_mul_eq_zeroₓ'. -/
 theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSeries R) (h : φ * ψ = 0) :
     φ = 0 ∨ ψ = 0 := by
   rw [or_iff_not_imp_left]
@@ -1941,9 +3141,15 @@ section IsDomain
 
 variable [CommRing R] [IsDomain R]
 
+/- warning: power_series.span_X_is_prime -> PowerSeries.span_X_isPrime is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], Ideal.IsPrime.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.span.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} (PowerSeries.{u1} R) (Set.{u1} (PowerSeries.{u1} R)) (Set.hasSingleton.{u1} (PowerSeries.{u1} R)) (PowerSeries.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], Ideal.IsPrime.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.span.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} (PowerSeries.{u1} R) (Set.{u1} (PowerSeries.{u1} R)) (Set.instSingletonSet.{u1} (PowerSeries.{u1} R)) (PowerSeries.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align power_series.span_X_is_prime PowerSeries.span_X_isPrimeₓ'. -/
 /-- The ideal spanned by the variable in the power series ring
  over an integral domain is a prime ideal.-/
-theorem span_x_isPrime : (Ideal.span ({x} : Set (PowerSeries R))).IsPrime :=
+theorem span_X_isPrime : (Ideal.span ({X} : Set (PowerSeries R))).IsPrime :=
   by
   suffices Ideal.span ({X} : Set (PowerSeries R)) = (constant_coeff R).ker
     by
@@ -1952,17 +3158,29 @@ theorem span_x_isPrime : (Ideal.span ({x} : Set (PowerSeries R))).IsPrime :=
   apply Ideal.ext
   intro φ
   rw [RingHom.mem_ker, Ideal.mem_span_singleton, X_dvd_iff]
-#align power_series.span_X_is_prime PowerSeries.span_x_isPrime
-
+#align power_series.span_X_is_prime PowerSeries.span_X_isPrime
+
+/- warning: power_series.X_prime -> PowerSeries.X_prime is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], Prime.{u1} (PowerSeries.{u1} R) (CommSemiring.toCommMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PowerSeries.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], Prime.{u1} (PowerSeries.{u1} R) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (PowerSeries.{u1} R) (IsDomain.toCancelCommMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (PowerSeries.instIsDomainPowerSeriesInstSemiringPowerSeriesToSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))) (PowerSeries.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))
+Case conversion may be inaccurate. Consider using '#align power_series.X_prime PowerSeries.X_primeₓ'. -/
 /-- The variable of the power series ring over an integral domain is prime.-/
-theorem x_prime : Prime (x : PowerSeries R) :=
+theorem X_prime : Prime (X : PowerSeries R) :=
   by
   rw [← Ideal.span_singleton_prime]
   · exact span_X_is_prime
   · intro h
     simpa using congr_arg (coeff R 1) h
-#align power_series.X_prime PowerSeries.x_prime
-
+#align power_series.X_prime PowerSeries.X_prime
+
+/- warning: power_series.rescale_injective -> PowerSeries.rescale_injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) -> (Function.Injective.{succ u1, succ u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (PowerSeries.{u1} R) -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (PowerSeries.rescale.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) a)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (Function.Injective.{succ u1, succ u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (PowerSeries.rescale.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) a)))
+Case conversion may be inaccurate. Consider using '#align power_series.rescale_injective PowerSeries.rescale_injectiveₓ'. -/
 theorem rescale_injective {a : R} (ha : a ≠ 0) : Function.Injective (rescale a) :=
   by
   intro p q h
@@ -1981,6 +3199,12 @@ section LocalRing
 
 variable {S : Type _} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalRingHom f]
 
+/- warning: power_series.map.is_local_ring_hom -> PowerSeries.map.isLocalRingHom is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) [_inst_3 : IsLocalRingHom.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f], IsLocalRingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (PowerSeries.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PowerSeries.semiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (PowerSeries.map.{u1, u2} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f)
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) [_inst_3 : IsLocalRingHom.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f], IsLocalRingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} S) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PowerSeries.instSemiringPowerSeries.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (PowerSeries.map.{u1, u2} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f)
+Case conversion may be inaccurate. Consider using '#align power_series.map.is_local_ring_hom PowerSeries.map.isLocalRingHomₓ'. -/
 instance map.isLocalRingHom : IsLocalRingHom (map f) :=
   MvPowerSeries.map.isLocalRingHom f
 #align power_series.map.is_local_ring_hom PowerSeries.map.isLocalRingHom
@@ -1996,11 +3220,23 @@ section Algebra
 
 variable {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
-theorem c_eq_algebraMap {r : R} : c R r = (algebraMap R (PowerSeries R)) r :=
+/- warning: power_series.C_eq_algebra_map -> PowerSeries.C_eq_algebraMap is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.C_eq_algebra_map PowerSeries.C_eq_algebraMapₓ'. -/
+theorem C_eq_algebraMap {r : R} : C R r = (algebraMap R (PowerSeries R)) r :=
   rfl
-#align power_series.C_eq_algebra_map PowerSeries.c_eq_algebraMap
-
-theorem algebraMap_apply {r : R} : algebraMap R (PowerSeries A) r = c A (algebraMap R A r) :=
+#align power_series.C_eq_algebra_map PowerSeries.C_eq_algebraMap
+
+/- warning: power_series.algebra_map_apply -> PowerSeries.algebraMap_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.algebra_map_apply PowerSeries.algebraMap_applyₓ'. -/
+theorem algebraMap_apply {r : R} : algebraMap R (PowerSeries A) r = C A (algebraMap R A r) :=
   MvPowerSeries.algebraMap_apply
 #align power_series.algebra_map_apply PowerSeries.algebraMap_apply
 
@@ -2013,18 +3249,32 @@ section Field
 
 variable {k : Type _} [Field k]
 
+#print PowerSeries.inv /-
 /-- The inverse 1/f of a power series f defined over a field -/
 protected def inv : PowerSeries k → PowerSeries k :=
   MvPowerSeries.inv
 #align power_series.inv PowerSeries.inv
+-/
 
 instance : Inv (PowerSeries k) :=
   ⟨PowerSeries.inv⟩
 
-theorem inv_eq_inv_aux (φ : PowerSeries k) : φ⁻¹ = Inv.aux (constantCoeff k φ)⁻¹ φ :=
+/- warning: power_series.inv_eq_inv_aux -> PowerSeries.inv_eq_inv_aux is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.inv_eq_inv_aux PowerSeries.inv_eq_inv_auxₓ'. -/
+theorem inv_eq_inv_aux (φ : PowerSeries k) : φ⁻¹ = inv.aux (constantCoeff k φ)⁻¹ φ :=
   rfl
 #align power_series.inv_eq_inv_aux PowerSeries.inv_eq_inv_aux
 
+/- warning: power_series.coeff_inv -> PowerSeries.coeff_inv is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] (n : Nat) (φ : PowerSeries.{u1} k), Eq.{succ u1} k (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) => (PowerSeries.{u1} k) -> k) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} k k (PowerSeries.{u1} k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.coeff.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) n) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) φ)) (ite.{succ u1} k (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Nat.decidableEq n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) => (PowerSeries.{u1} k) -> k) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (PowerSeries.constantCoeff.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) φ)) (HMul.hMul.{u1, u1, u1} k k k (instHMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Neg.neg.{u1} k (SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) => (PowerSeries.{u1} k) -> k) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (PowerSeries.constantCoeff.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) φ))) (Finset.sum.{u1, 0} k (Prod.{0, 0} Nat Nat) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Finset.Nat.antidiagonal n) (fun (x : Prod.{0, 0} Nat Nat) => ite.{succ u1} k (LT.lt.{0} Nat Nat.hasLt (Prod.snd.{0, 0} Nat Nat x) n) (Nat.decidableLt (Prod.snd.{0, 0} Nat Nat x) n) (HMul.hMul.{u1, u1, u1} k k k (instHMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) => (PowerSeries.{u1} k) -> k) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} k k (PowerSeries.{u1} k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k 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_inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) => (PowerSeries.{u1} k) -> k) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} k k (PowerSeries.{u1} k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.coeff.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (Prod.snd.{0, 0} Nat Nat x)) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) φ))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))))))))
+but is expected to have type
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] (n : Nat) (φ : PowerSeries.{u1} k), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} k) => k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} k) => k) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} k k (PowerSeries.{u1} k) k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.coeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) n) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ)) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (instDecidableEqNat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} k) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toMul.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) φ)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} k) => k) φ) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) _inst_1)))))) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) _inst_1))) (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} k) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toMul.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k 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(Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (PowerSeries.coeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Prod.fst.{0, 0} Nat Nat x)) φ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (PowerSeries.instAddCommMonoidPowerSeries.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k 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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_inv PowerSeries.coeff_invₓ'. -/
 theorem coeff_inv (n) (φ : PowerSeries k) :
     coeff k n φ⁻¹ =
       if n = 0 then (constantCoeff k φ)⁻¹
@@ -2035,57 +3285,123 @@ theorem coeff_inv (n) (φ : PowerSeries k) :
   by rw [inv_eq_inv_aux, coeff_inv_aux n (constant_coeff k φ)⁻¹ φ]
 #align power_series.coeff_inv PowerSeries.coeff_inv
 
+/- warning: power_series.constant_coeff_inv -> PowerSeries.constantCoeff_inv is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ)) (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} k) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toMul.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) φ))
+Case conversion may be inaccurate. Consider using '#align power_series.constant_coeff_inv PowerSeries.constantCoeff_invₓ'. -/
 @[simp]
 theorem constantCoeff_inv (φ : PowerSeries k) : constantCoeff k φ⁻¹ = (constantCoeff k φ)⁻¹ :=
   MvPowerSeries.constantCoeff_inv φ
 #align power_series.constant_coeff_inv PowerSeries.constantCoeff_inv
 
+/- warning: power_series.inv_eq_zero -> PowerSeries.inv_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {φ : PowerSeries.{u1} k}, Iff (Eq.{succ u1} (PowerSeries.{u1} k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) φ) (OfNat.ofNat.{u1} (PowerSeries.{u1} k) 0 (OfNat.mk.{u1} (PowerSeries.{u1} k) 0 (Zero.zero.{u1} (PowerSeries.{u1} k) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} k) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} k) (PowerSeries.ring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))) (Eq.{succ u1} k (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) => (PowerSeries.{u1} k) -> k) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (PowerSeries.constantCoeff.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) φ) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))
+but is expected to have type
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(Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} k) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalNonAssocSemiring.toMul.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align power_series.inv_eq_zero PowerSeries.inv_eq_zeroₓ'. -/
 theorem inv_eq_zero {φ : PowerSeries k} : φ⁻¹ = 0 ↔ constantCoeff k φ = 0 :=
   MvPowerSeries.inv_eq_zero
 #align power_series.inv_eq_zero PowerSeries.inv_eq_zero
 
+/- warning: power_series.zero_inv -> PowerSeries.zero_inv is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k], Eq.{succ u1} (PowerSeries.{u1} k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) (OfNat.ofNat.{u1} (PowerSeries.{u1} k) 0 (OfNat.mk.{u1} (PowerSeries.{u1} k) 0 (Zero.zero.{u1} (PowerSeries.{u1} k) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} k) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} k) (PowerSeries.ring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))) (OfNat.ofNat.{u1} (PowerSeries.{u1} k) 0 (OfNat.mk.{u1} (PowerSeries.{u1} k) 0 (Zero.zero.{u1} (PowerSeries.{u1} k) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} k) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} k) (PowerSeries.ring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))
+but is expected to have type
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k], Eq.{succ u1} (PowerSeries.{u1} k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) (OfNat.ofNat.{u1} (PowerSeries.{u1} k) 0 (Zero.toOfNat0.{u1} (PowerSeries.{u1} k) (PowerSeries.instZeroPowerSeries.{u1} k (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (OfNat.ofNat.{u1} (PowerSeries.{u1} k) 0 (Zero.toOfNat0.{u1} (PowerSeries.{u1} k) (PowerSeries.instZeroPowerSeries.{u1} k (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align power_series.zero_inv PowerSeries.zero_invₓ'. -/
 @[simp]
 theorem zero_inv : (0 : PowerSeries k)⁻¹ = 0 :=
   MvPowerSeries.zero_inv
 #align power_series.zero_inv PowerSeries.zero_inv
 
+/- warning: power_series.inv_of_unit_eq -> PowerSeries.invOfUnit_eq is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(Units.mk0.{u1} k (DivisionSemiring.toGroupWithZero.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) (fun (_x : PowerSeries.{u1} k) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) 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(Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) φ) h)) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ)
+Case conversion may be inaccurate. Consider using '#align power_series.inv_of_unit_eq PowerSeries.invOfUnit_eqₓ'. -/
 @[simp]
 theorem invOfUnit_eq (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) :
     invOfUnit φ (Units.mk0 _ h) = φ⁻¹ :=
   MvPowerSeries.invOfUnit_eq _ _
 #align power_series.inv_of_unit_eq PowerSeries.invOfUnit_eq
 
+/- warning: power_series.inv_of_unit_eq' -> PowerSeries.invOfUnit_eq' is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] (φ : PowerSeries.{u1} k) (u : Units.{u1} k (Ring.toMonoid.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))), (Eq.{succ u1} k (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) => (PowerSeries.{u1} k) -> k) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (PowerSeries.constantCoeff.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) φ) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} k (Ring.toMonoid.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) k (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) k (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) k (coeBase.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) k (Units.hasCoe.{u1} k (Ring.toMonoid.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) u)) -> (Eq.{succ u1} (PowerSeries.{u1} k) (PowerSeries.invOfUnit.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) φ u) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) φ))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.inv_of_unit_eq' PowerSeries.invOfUnit_eq'ₓ'. -/
 @[simp]
 theorem invOfUnit_eq' (φ : PowerSeries k) (u : Units k) (h : constantCoeff k φ = u) :
     invOfUnit φ u = φ⁻¹ :=
   MvPowerSeries.invOfUnit_eq' φ _ h
 #align power_series.inv_of_unit_eq' PowerSeries.invOfUnit_eq'
 
+/- warning: power_series.mul_inv_cancel -> PowerSeries.mul_inv_cancel is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ) _inst_1))))))) -> (Eq.{succ u1} (PowerSeries.{u1} k) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} k) (PowerSeries.{u1} k) (PowerSeries.{u1} k) (instHMul.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} k) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} k) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} k) (PowerSeries.instRingPowerSeries.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) φ (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ)) (OfNat.ofNat.{u1} (PowerSeries.{u1} k) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} k) (Semiring.toOne.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))))
+Case conversion may be inaccurate. Consider using '#align power_series.mul_inv_cancel PowerSeries.mul_inv_cancelₓ'. -/
 @[simp]
 protected theorem mul_inv_cancel (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) : φ * φ⁻¹ = 1 :=
   MvPowerSeries.mul_inv_cancel φ h
 #align power_series.mul_inv_cancel PowerSeries.mul_inv_cancel
 
+/- warning: power_series.inv_mul_cancel -> PowerSeries.inv_mul_cancel is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] (φ : PowerSeries.{u1} k), (Ne.{succ u1} k (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) => (PowerSeries.{u1} k) -> k) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} k) k (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (PowerSeries.constantCoeff.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) φ) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))))) -> (Eq.{succ u1} (PowerSeries.{u1} k) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} k) (PowerSeries.{u1} k) (PowerSeries.{u1} k) (instHMul.{u1} (PowerSeries.{u1} k) (Distrib.toHasMul.{u1} (PowerSeries.{u1} k) (Ring.toDistrib.{u1} (PowerSeries.{u1} k) (PowerSeries.ring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) φ) φ) (OfNat.ofNat.{u1} (PowerSeries.{u1} k) 1 (OfNat.mk.{u1} (PowerSeries.{u1} k) 1 (One.one.{u1} (PowerSeries.{u1} k) (AddMonoidWithOne.toOne.{u1} (PowerSeries.{u1} k) (AddGroupWithOne.toAddMonoidWithOne.{u1} (PowerSeries.{u1} k) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (PowerSeries.{u1} k) (Ring.toAddCommGroupWithOne.{u1} (PowerSeries.{u1} k) (PowerSeries.ring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.inv_mul_cancel PowerSeries.inv_mul_cancelₓ'. -/
 @[simp]
 protected theorem inv_mul_cancel (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) : φ⁻¹ * φ = 1 :=
   MvPowerSeries.inv_mul_cancel φ h
 #align power_series.inv_mul_cancel PowerSeries.inv_mul_cancel
 
+/- warning: power_series.eq_mul_inv_iff_mul_eq -> PowerSeries.eq_mul_inv_iff_mul_eq is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) φ₃) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ₃) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ₃) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ₃) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ₃) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ₃) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) φ₃) _inst_1))))))) -> (Iff (Eq.{succ u1} (PowerSeries.{u1} k) φ₁ (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} k) (PowerSeries.{u1} k) (PowerSeries.{u1} k) (instHMul.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} k) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} k) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} k) (PowerSeries.instRingPowerSeries.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) φ₂ (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ₃))) (Eq.{succ u1} (PowerSeries.{u1} k) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} k) (PowerSeries.{u1} k) (PowerSeries.{u1} k) (instHMul.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} k) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} k) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} k) (PowerSeries.instRingPowerSeries.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) φ₁ φ₃) φ₂))
+Case conversion may be inaccurate. Consider using '#align power_series.eq_mul_inv_iff_mul_eq PowerSeries.eq_mul_inv_iff_mul_eqₓ'. -/
 theorem eq_mul_inv_iff_mul_eq {φ₁ φ₂ φ₃ : PowerSeries k} (h : constantCoeff k φ₃ ≠ 0) :
     φ₁ = φ₂ * φ₃⁻¹ ↔ φ₁ * φ₃ = φ₂ :=
   MvPowerSeries.eq_mul_inv_iff_mul_eq h
 #align power_series.eq_mul_inv_iff_mul_eq PowerSeries.eq_mul_inv_iff_mul_eq
 
+/- warning: power_series.eq_inv_iff_mul_eq_one -> PowerSeries.eq_inv_iff_mul_eq_one is a dubious translation:
+lean 3 declaration is
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(Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) ψ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) ψ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) ψ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) ψ) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) ψ) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) ψ) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) ψ) _inst_1))))))) -> (Iff (Eq.{succ u1} (PowerSeries.{u1} k) φ (Inv.inv.{u1} (PowerSeries.{u1} k) 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+Case conversion may be inaccurate. Consider using '#align power_series.eq_inv_iff_mul_eq_one PowerSeries.eq_inv_iff_mul_eq_oneₓ'. -/
 theorem eq_inv_iff_mul_eq_one {φ ψ : PowerSeries k} (h : constantCoeff k ψ ≠ 0) :
     φ = ψ⁻¹ ↔ φ * ψ = 1 :=
   MvPowerSeries.eq_inv_iff_mul_eq_one h
 #align power_series.eq_inv_iff_mul_eq_one PowerSeries.eq_inv_iff_mul_eq_one
 
+/- warning: power_series.inv_eq_iff_mul_eq_one -> PowerSeries.inv_eq_iff_mul_eq_one is a dubious translation:
+lean 3 declaration is
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(Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))) (PowerSeries.constantCoeff.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) ψ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) ψ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) ψ) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) ψ) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) ψ) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) ψ) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} k) => k) ψ) _inst_1))))))) -> (Iff (Eq.{succ u1} (PowerSeries.{u1} k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) ψ) φ) (Eq.{succ u1} (PowerSeries.{u1} k) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} k) (PowerSeries.{u1} k) (PowerSeries.{u1} k) (instHMul.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} k) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} k) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} k) (PowerSeries.instRingPowerSeries.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) φ ψ) (OfNat.ofNat.{u1} (PowerSeries.{u1} k) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} k) (Semiring.toOne.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align power_series.inv_eq_iff_mul_eq_one PowerSeries.inv_eq_iff_mul_eq_oneₓ'. -/
 theorem inv_eq_iff_mul_eq_one {φ ψ : PowerSeries k} (h : constantCoeff k ψ ≠ 0) :
     ψ⁻¹ = φ ↔ φ * ψ = 1 :=
   MvPowerSeries.inv_eq_iff_mul_eq_one h
 #align power_series.inv_eq_iff_mul_eq_one PowerSeries.inv_eq_iff_mul_eq_one
 
+/- warning: power_series.mul_inv_rev -> PowerSeries.mul_inv_rev is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] (φ : PowerSeries.{u1} k) (ψ : PowerSeries.{u1} k), Eq.{succ u1} (PowerSeries.{u1} k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} k) (PowerSeries.{u1} k) (PowerSeries.{u1} k) (instHMul.{u1} (PowerSeries.{u1} k) (Distrib.toHasMul.{u1} (PowerSeries.{u1} k) (Ring.toDistrib.{u1} (PowerSeries.{u1} k) (PowerSeries.ring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) φ ψ)) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} k) (PowerSeries.{u1} k) (PowerSeries.{u1} k) (instHMul.{u1} (PowerSeries.{u1} k) (Distrib.toHasMul.{u1} (PowerSeries.{u1} k) (Ring.toDistrib.{u1} (PowerSeries.{u1} k) (PowerSeries.ring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) ψ) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) φ))
+but is expected to have type
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] (φ : PowerSeries.{u1} k) (ψ : PowerSeries.{u1} k), Eq.{succ u1} (PowerSeries.{u1} k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} k) (PowerSeries.{u1} k) (PowerSeries.{u1} k) (instHMul.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} k) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} k) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} k) (PowerSeries.instRingPowerSeries.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) φ ψ)) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} k) (PowerSeries.{u1} k) (PowerSeries.{u1} k) (instHMul.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} k) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} k) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} k) (PowerSeries.instRingPowerSeries.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) ψ) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ))
+Case conversion may be inaccurate. Consider using '#align power_series.mul_inv_rev PowerSeries.mul_inv_revₓ'. -/
 @[simp]
 protected theorem mul_inv_rev (φ ψ : PowerSeries k) : (φ * ψ)⁻¹ = ψ⁻¹ * φ⁻¹ :=
   MvPowerSeries.mul_inv_rev _ _
@@ -2094,16 +3410,34 @@ protected theorem mul_inv_rev (φ ψ : PowerSeries k) : (φ * ψ)⁻¹ = ψ⁻¹
 instance : InvOneClass (PowerSeries k) :=
   MvPowerSeries.invOneClass
 
+/- warning: power_series.C_inv -> PowerSeries.C_inv is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] (r : k), Eq.{succ u1} (PowerSeries.{u1} k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (fun (_x : RingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) => k -> (PowerSeries.{u1} k)) (RingHom.hasCoeToFun.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.C.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) r)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (fun (_x : RingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) => k -> (PowerSeries.{u1} k)) (RingHom.hasCoeToFun.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.semiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (PowerSeries.C.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) r))
+but is expected to have type
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] (r : k), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : k) => PowerSeries.{u1} k) r) (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : k) => PowerSeries.{u1} k) r) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) k (fun (_x : k) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : k) => PowerSeries.{u1} k) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) k (PowerSeries.{u1} k) (NonUnitalNonAssocSemiring.toMul.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} k) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) k (PowerSeries.{u1} k) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))))) (PowerSeries.C.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) k (fun (_x : k) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : k) => PowerSeries.{u1} k) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) k (PowerSeries.{u1} k) (NonUnitalNonAssocSemiring.toMul.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} k) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) k (PowerSeries.{u1} k) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toNonAssocSemiring.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} k) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))))))) (PowerSeries.C.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Inv.inv.{u1} k (Field.toInv.{u1} k _inst_1) r))
+Case conversion may be inaccurate. Consider using '#align power_series.C_inv PowerSeries.C_invₓ'. -/
 @[simp]
-theorem c_inv (r : k) : (c k r)⁻¹ = c k r⁻¹ :=
-  MvPowerSeries.c_inv _
-#align power_series.C_inv PowerSeries.c_inv
-
+theorem C_inv (r : k) : (C k r)⁻¹ = C k r⁻¹ :=
+  MvPowerSeries.C_inv _
+#align power_series.C_inv PowerSeries.C_inv
+
+/- warning: power_series.X_inv -> PowerSeries.X_inv is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k], Eq.{succ u1} (PowerSeries.{u1} k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) (PowerSeries.X.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (OfNat.ofNat.{u1} (PowerSeries.{u1} k) 0 (OfNat.mk.{u1} (PowerSeries.{u1} k) 0 (Zero.zero.{u1} (PowerSeries.{u1} k) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} k) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} k) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} k) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} k) (PowerSeries.ring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))
+but is expected to have type
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k], Eq.{succ u1} (PowerSeries.{u1} k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) (PowerSeries.X.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))))) (OfNat.ofNat.{u1} (PowerSeries.{u1} k) 0 (Zero.toOfNat0.{u1} (PowerSeries.{u1} k) (PowerSeries.instZeroPowerSeries.{u1} k (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align power_series.X_inv PowerSeries.X_invₓ'. -/
 @[simp]
-theorem x_inv : (x : PowerSeries k)⁻¹ = 0 :=
-  MvPowerSeries.x_inv _
-#align power_series.X_inv PowerSeries.x_inv
-
+theorem X_inv : (X : PowerSeries k)⁻¹ = 0 :=
+  MvPowerSeries.X_inv _
+#align power_series.X_inv PowerSeries.X_inv
+
+/- warning: power_series.smul_inv -> PowerSeries.smul_inv is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] (r : k) (φ : PowerSeries.{u1} k), Eq.{succ u1} (PowerSeries.{u1} k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) (SMul.smul.{u1, u1} k (PowerSeries.{u1} k) (SMulZeroClass.toHasSmul.{u1, u1} k (PowerSeries.{u1} k) (AddZeroClass.toHasZero.{u1} (PowerSeries.{u1} k) (AddMonoid.toAddZeroClass.{u1} (PowerSeries.{u1} k) (AddCommMonoid.toAddMonoid.{u1} (PowerSeries.{u1} k) (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} k (PowerSeries.{u1} k) (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} (PowerSeries.{u1} k) (AddMonoid.toAddZeroClass.{u1} (PowerSeries.{u1} k) (AddCommMonoid.toAddMonoid.{u1} (PowerSeries.{u1} k) (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (PowerSeries.{u1} k) (AddMonoid.toAddZeroClass.{u1} (PowerSeries.{u1} k) (AddCommMonoid.toAddMonoid.{u1} (PowerSeries.{u1} k) (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (Module.toMulActionWithZero.{u1, u1} k (PowerSeries.{u1} k) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) r φ)) (SMul.smul.{u1, u1} k (PowerSeries.{u1} k) (SMulZeroClass.toHasSmul.{u1, u1} k (PowerSeries.{u1} k) (AddZeroClass.toHasZero.{u1} (PowerSeries.{u1} k) (AddMonoid.toAddZeroClass.{u1} (PowerSeries.{u1} k) (AddCommMonoid.toAddMonoid.{u1} (PowerSeries.{u1} k) (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} k (PowerSeries.{u1} k) (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} (PowerSeries.{u1} k) (AddMonoid.toAddZeroClass.{u1} (PowerSeries.{u1} k) (AddCommMonoid.toAddMonoid.{u1} (PowerSeries.{u1} k) (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k (PowerSeries.{u1} k) (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (PowerSeries.{u1} k) (AddMonoid.toAddZeroClass.{u1} (PowerSeries.{u1} k) (AddCommMonoid.toAddMonoid.{u1} (PowerSeries.{u1} k) (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (Module.toMulActionWithZero.{u1, u1} k (PowerSeries.{u1} k) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (PowerSeries.addCommMonoid.{u1} k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (PowerSeries.module.{u1, u1} k k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) r) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.hasInv.{u1} k _inst_1) φ))
+but is expected to have type
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] (r : k) (φ : PowerSeries.{u1} k), Eq.{succ u1} (PowerSeries.{u1} k) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) (HSMul.hSMul.{u1, u1, u1} k (PowerSeries.{u1} k) (PowerSeries.{u1} k) (instHSMul.{u1, u1} k (PowerSeries.{u1} k) (Algebra.toSMul.{u1, u1} k (PowerSeries.{u1} k) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (PowerSeries.instAlgebraPowerSeriesInstSemiringPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) r φ)) (HSMul.hSMul.{u1, u1, u1} k (PowerSeries.{u1} k) (PowerSeries.{u1} k) (instHSMul.{u1, u1} k (PowerSeries.{u1} k) (Algebra.toSMul.{u1, u1} k (PowerSeries.{u1} k) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (PowerSeries.instSemiringPowerSeries.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (PowerSeries.instAlgebraPowerSeriesInstSemiringPowerSeries.{u1, u1} k k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))))) (Inv.inv.{u1} k (Field.toInv.{u1} k _inst_1) r) (Inv.inv.{u1} (PowerSeries.{u1} k) (PowerSeries.instInvPowerSeries.{u1} k _inst_1) φ))
+Case conversion may be inaccurate. Consider using '#align power_series.smul_inv PowerSeries.smul_invₓ'. -/
 @[simp]
 theorem smul_inv (r : k) (φ : PowerSeries k) : (r • φ)⁻¹ = r⁻¹ • φ⁻¹ :=
   MvPowerSeries.smul_inv _ _
@@ -2127,6 +3461,12 @@ open multiplicity
 
 variable [Semiring R] {φ : PowerSeries R}
 
+/- warning: power_series.exists_coeff_ne_zero_iff_ne_zero -> PowerSeries.exists_coeff_ne_zero_iff_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R}, Iff (Exists.{1} Nat (fun (n : Nat) => Ne.{succ u1} 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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (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)) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1)) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.module.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) (Ne.{succ u1} (PowerSeries.{u1} R) φ (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (OfNat.mk.{u1} (PowerSeries.{u1} R) 0 (Zero.zero.{u1} (PowerSeries.{u1} R) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R}, Iff (Exists.{1} Nat (fun (n : Nat) => Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 n) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) (Ne.{succ u1} (PowerSeries.{u1} R) φ (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (Zero.toOfNat0.{u1} (PowerSeries.{u1} R) (PowerSeries.instZeroPowerSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align power_series.exists_coeff_ne_zero_iff_ne_zero PowerSeries.exists_coeff_ne_zero_iff_ne_zeroₓ'. -/
 theorem exists_coeff_ne_zero_iff_ne_zero : (∃ n : ℕ, coeff R n φ ≠ 0) ↔ φ ≠ 0 :=
   by
   refine' not_iff_not.mp _
@@ -2134,18 +3474,32 @@ theorem exists_coeff_ne_zero_iff_ne_zero : (∃ n : ℕ, coeff R n φ ≠ 0) ↔
   simp [PowerSeries.ext_iff]
 #align power_series.exists_coeff_ne_zero_iff_ne_zero PowerSeries.exists_coeff_ne_zero_iff_ne_zero
 
+#print PowerSeries.order /-
 /-- The order of a formal power series `φ` is the greatest `n : part_enat`
 such that `X^n` divides `φ`. The order is `⊤` if and only if `φ = 0`. -/
 def order (φ : PowerSeries R) : PartENat :=
   if h : φ = 0 then ⊤ else Nat.find (exists_coeff_ne_zero_iff_ne_zero.mpr h)
 #align power_series.order PowerSeries.order
+-/
 
+/- warning: power_series.order_zero -> PowerSeries.order_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (OfNat.mk.{u1} (PowerSeries.{u1} R) 0 (Zero.zero.{u1} (PowerSeries.{u1} R) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))))))) (Top.top.{0} PartENat PartENat.hasTop)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (Zero.toOfNat0.{u1} (PowerSeries.{u1} R) (PowerSeries.instZeroPowerSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (Top.top.{0} PartENat PartENat.instTopPartENat)
+Case conversion may be inaccurate. Consider using '#align power_series.order_zero PowerSeries.order_zeroₓ'. -/
 /-- The order of the `0` power series is infinite.-/
 @[simp]
 theorem order_zero : order (0 : PowerSeries R) = ⊤ :=
   dif_pos rfl
 #align power_series.order_zero PowerSeries.order_zero
 
+/- warning: power_series.order_finite_iff_ne_zero -> PowerSeries.order_finite_iff_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R}, Iff (Part.Dom.{0} Nat (PowerSeries.order.{u1} R _inst_1 φ)) (Ne.{succ u1} (PowerSeries.{u1} R) φ (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (OfNat.mk.{u1} (PowerSeries.{u1} R) 0 (Zero.zero.{u1} (PowerSeries.{u1} R) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R}, Iff (Part.Dom.{0} Nat (PowerSeries.order.{u1} R _inst_1 φ)) (Ne.{succ u1} (PowerSeries.{u1} R) φ (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (Zero.toOfNat0.{u1} (PowerSeries.{u1} R) (PowerSeries.instZeroPowerSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align power_series.order_finite_iff_ne_zero PowerSeries.order_finite_iff_ne_zeroₓ'. -/
 theorem order_finite_iff_ne_zero : (order φ).Dom ↔ φ ≠ 0 :=
   by
   simp only [order]
@@ -2158,6 +3512,12 @@ theorem order_finite_iff_ne_zero : (order φ).Dom ↔ φ ≠ 0 :=
     simp [h]
 #align power_series.order_finite_iff_ne_zero PowerSeries.order_finite_iff_ne_zero
 
+/- warning: power_series.coeff_order -> PowerSeries.coeff_order is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_order PowerSeries.coeff_orderₓ'. -/
 /-- If the order of a formal power series is finite,
 then the coefficient indexed by the order is nonzero.-/
 theorem coeff_order (h : (order φ).Dom) : coeff R (φ.order.get h) φ ≠ 0 :=
@@ -2167,6 +3527,12 @@ theorem coeff_order (h : (order φ).Dom) : coeff R (φ.order.get h) φ ≠ 0 :=
   exact Nat.find_spec h
 #align power_series.coeff_order PowerSeries.coeff_order
 
+/- warning: power_series.order_le -> PowerSeries.order_le is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.order_le PowerSeries.order_leₓ'. -/
 /-- If the `n`th coefficient of a formal power series is nonzero,
 then the order of the power series is less than or equal to `n`.-/
 theorem order_le (n : ℕ) (h : coeff R n φ ≠ 0) : order φ ≤ n :=
@@ -2178,6 +3544,12 @@ theorem order_le (n : ℕ) (h : coeff R n φ ≠ 0) : order φ ≤ n :=
   · exact exists_coeff_ne_zero_iff_ne_zero.mp ⟨n, h⟩
 #align power_series.order_le PowerSeries.order_le
 
+/- warning: power_series.coeff_of_lt_order -> PowerSeries.coeff_of_lt_order is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_of_lt_order PowerSeries.coeff_of_lt_orderₓ'. -/
 /-- The `n`th coefficient of a formal power series is `0` if `n` is strictly
 smaller than the order of the power series.-/
 theorem coeff_of_lt_order (n : ℕ) (h : ↑n < order φ) : coeff R n φ = 0 :=
@@ -2186,6 +3558,12 @@ theorem coeff_of_lt_order (n : ℕ) (h : ↑n < order φ) : coeff R n φ = 0 :=
   exact order_le _ h
 #align power_series.coeff_of_lt_order PowerSeries.coeff_of_lt_order
 
+/- warning: power_series.order_eq_top -> PowerSeries.order_eq_top is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R}, Iff (Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 φ) (Top.top.{0} PartENat PartENat.hasTop)) (Eq.{succ u1} (PowerSeries.{u1} R) φ (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (OfNat.mk.{u1} (PowerSeries.{u1} R) 0 (Zero.zero.{u1} (PowerSeries.{u1} R) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align power_series.order_eq_top PowerSeries.order_eq_topₓ'. -/
 /-- The `0` power series is the unique power series with infinite order.-/
 @[simp]
 theorem order_eq_top {φ : PowerSeries R} : φ.order = ⊤ ↔ φ = 0 :=
@@ -2199,6 +3577,12 @@ theorem order_eq_top {φ : PowerSeries R} : φ.order = ⊤ ↔ φ = 0 :=
     exact order_zero
 #align power_series.order_eq_top PowerSeries.order_eq_top
 
+/- warning: power_series.nat_le_order -> PowerSeries.nat_le_order is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.nat_le_order PowerSeries.nat_le_orderₓ'. -/
 /-- The order of a formal power series is at least `n` if
 the `i`th coefficient is `0` for all `i < n`.-/
 theorem nat_le_order (φ : PowerSeries R) (n : ℕ) (h : ∀ i < n, coeff R i φ = 0) : ↑n ≤ order φ :=
@@ -2209,6 +3593,12 @@ theorem nat_le_order (φ : PowerSeries R) (n : ℕ) (h : ∀ i < n, coeff R i φ
   exact coeff_order this (h _ H)
 #align power_series.nat_le_order PowerSeries.nat_le_order
 
+/- warning: power_series.le_order -> PowerSeries.le_order is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.le_order PowerSeries.le_orderₓ'. -/
 /-- The order of a formal power series is at least `n` if
 the `i`th coefficient is `0` for all `i < n`.-/
 theorem le_order (φ : PowerSeries R) (n : PartENat) (h : ∀ i : ℕ, ↑i < n → coeff R i φ = 0) :
@@ -2222,6 +3612,12 @@ theorem le_order (φ : PowerSeries R) (n : PartENat) (h : ∀ i : ℕ, ↑i < n
     simpa only [PartENat.coe_lt_coe] using h
 #align power_series.le_order PowerSeries.le_order
 
+/- warning: power_series.order_eq_nat -> PowerSeries.order_eq_nat is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align power_series.order_eq_nat PowerSeries.order_eq_natₓ'. -/
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
 and the `i`th coefficient is `0` for all `i < n`.-/
 theorem order_eq_nat {φ : PowerSeries R} {n : ℕ} :
@@ -2232,6 +3628,12 @@ theorem order_eq_nat {φ : PowerSeries R} {n : ℕ} :
   simp [order, dif_neg hφ, Nat.find_eq_iff]
 #align power_series.order_eq_nat PowerSeries.order_eq_nat
 
+/- warning: power_series.order_eq -> PowerSeries.order_eq is a dubious translation:
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+but is expected to have type
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(PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))) (forall (i : Nat), (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) i) n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (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)) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1)) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R _inst_1 _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (Semiring.toModule.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.coeff.{u1} R _inst_1 i) φ) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) φ) _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align power_series.order_eq PowerSeries.order_eqₓ'. -/
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
 and the `i`th coefficient is `0` for all `i < n`.-/
 theorem order_eq {φ : PowerSeries R} {n : PartENat} :
@@ -2251,6 +3653,12 @@ theorem order_eq {φ : PowerSeries R} {n : PartENat} :
   · simpa [PartENat.natCast_inj] using order_eq_nat
 #align power_series.order_eq PowerSeries.order_eq
 
+/- warning: power_series.le_order_add -> PowerSeries.le_order_add is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), LE.le.{0} PartENat PartENat.hasLe (LinearOrder.min.{0} PartENat PartENat.linearOrder (PowerSeries.order.{u1} R _inst_1 φ) (PowerSeries.order.{u1} R _inst_1 ψ)) (PowerSeries.order.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHAdd.{u1} (PowerSeries.{u1} R) (Distrib.toHasAdd.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) φ ψ))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), LE.le.{0} PartENat PartENat.instLEPartENat (Min.min.{0} PartENat (LinearOrder.toMin.{0} PartENat PartENat.linearOrder) (PowerSeries.order.{u1} R _inst_1 φ) (PowerSeries.order.{u1} R _inst_1 ψ)) (PowerSeries.order.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHAdd.{u1} (PowerSeries.{u1} R) (Distrib.toAdd.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) φ ψ))
+Case conversion may be inaccurate. Consider using '#align power_series.le_order_add PowerSeries.le_order_addₓ'. -/
 /-- The order of the sum of two formal power series
  is at least the minimum of their orders.-/
 theorem le_order_add (φ ψ : PowerSeries R) : min (order φ) (order ψ) ≤ order (φ + ψ) :=
@@ -2276,6 +3684,12 @@ private theorem order_add_of_order_eq.aux (φ ψ : PowerSeries R) (h : order φ
         zero_add]
 #align power_series.order_add_of_order_eq.aux power_series.order_add_of_order_eq.aux
 
+/- warning: power_series.order_add_of_order_eq -> PowerSeries.order_add_of_order_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), (Ne.{1} PartENat (PowerSeries.order.{u1} R _inst_1 φ) (PowerSeries.order.{u1} R _inst_1 ψ)) -> (Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHAdd.{u1} (PowerSeries.{u1} R) (Distrib.toHasAdd.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) φ ψ)) (Inf.inf.{0} PartENat (SemilatticeInf.toHasInf.{0} PartENat (Lattice.toSemilatticeInf.{0} PartENat PartENat.lattice)) (PowerSeries.order.{u1} R _inst_1 φ) (PowerSeries.order.{u1} R _inst_1 ψ)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), (Ne.{1} PartENat (PowerSeries.order.{u1} R _inst_1 φ) (PowerSeries.order.{u1} R _inst_1 ψ)) -> (Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHAdd.{u1} (PowerSeries.{u1} R) (Distrib.toAdd.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)))))) φ ψ)) (Inf.inf.{0} PartENat (Lattice.toInf.{0} PartENat PartENat.lattice) (PowerSeries.order.{u1} R _inst_1 φ) (PowerSeries.order.{u1} R _inst_1 ψ)))
+Case conversion may be inaccurate. Consider using '#align power_series.order_add_of_order_eq PowerSeries.order_add_of_order_eqₓ'. -/
 /-- The order of the sum of two formal power series
  is the minimum of their orders if their orders differ.-/
 theorem order_add_of_order_eq (φ ψ : PowerSeries R) (h : order φ ≠ order ψ) :
@@ -2289,6 +3703,12 @@ theorem order_add_of_order_eq (φ ψ : PowerSeries R) (h : order φ ≠ order ψ
   exfalso; exact h (le_antisymm (not_lt.1 H₂) (not_lt.1 H₁))
 #align power_series.order_add_of_order_eq PowerSeries.order_add_of_order_eq
 
+/- warning: power_series.order_mul_ge -> PowerSeries.order_mul_ge is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), LE.le.{0} PartENat PartENat.hasLe (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (PowerSeries.order.{u1} R _inst_1 φ) (PowerSeries.order.{u1} R _inst_1 ψ)) (PowerSeries.order.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)))))) φ ψ))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), LE.le.{0} PartENat PartENat.instLEPartENat (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (PowerSeries.order.{u1} R _inst_1 φ) (PowerSeries.order.{u1} R _inst_1 ψ)) (PowerSeries.order.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) φ ψ))
+Case conversion may be inaccurate. Consider using '#align power_series.order_mul_ge PowerSeries.order_mul_geₓ'. -/
 /-- The order of the product of two formal power series
  is at least the sum of their orders.-/
 theorem order_mul_ge (φ ψ : PowerSeries R) : order φ + order ψ ≤ order (φ * ψ) :=
@@ -2306,6 +3726,12 @@ theorem order_mul_ge (φ ψ : PowerSeries R) : order φ + order ψ ≤ order (φ
   rw [← Nat.cast_add, hij]
 #align power_series.order_mul_ge PowerSeries.order_mul_ge
 
+/- warning: power_series.order_monomial -> PowerSeries.order_monomial is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R) [_inst_2 : Decidable (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))], Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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))) => R -> (PowerSeries.{u1} R)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.module.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) (ite.{1} PartENat (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) _inst_2 (Top.top.{0} PartENat PartENat.hasTop) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) n))
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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (a : R) [_inst_2 : Decidable (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))], Eq.{1} PartENat (PowerSeries.order.{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 (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => PowerSeries.{u1} R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (PowerSeries.{u1} R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{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)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.monomial.{u1} R _inst_1 n) a)) (ite.{1} PartENat (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) _inst_2 (Top.top.{0} PartENat PartENat.instTopPartENat) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n))
+Case conversion may be inaccurate. Consider using '#align power_series.order_monomial PowerSeries.order_monomialₓ'. -/
 /-- The order of the monomial `a*X^n` is infinite if `a = 0` and `n` otherwise.-/
 theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
     order (monomial R n a) = if a = 0 then ⊤ else n :=
@@ -2321,11 +3747,23 @@ theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
       exact ne_of_lt hi
 #align power_series.order_monomial PowerSeries.order_monomial
 
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+Case conversion may be inaccurate. Consider using '#align power_series.order_monomial_of_ne_zero PowerSeries.order_monomial_of_ne_zeroₓ'. -/
 /-- The order of the monomial `a*X^n` is `n` if `a ≠ 0`.-/
 theorem order_monomial_of_ne_zero (n : ℕ) (a : R) (h : a ≠ 0) : order (monomial R n a) = n := by
   rw [order_monomial, if_neg h]
 #align power_series.order_monomial_of_ne_zero PowerSeries.order_monomial_of_ne_zero
 
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+Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_orderₓ'. -/
 /-- If `n` is strictly smaller than the order of `ψ`, then the `n`th coefficient of its product
 with any other power series is `0`. -/
 theorem coeff_mul_of_lt_order {φ ψ : PowerSeries R} {n : ℕ} (h : ↑n < ψ.order) :
@@ -2341,11 +3779,23 @@ theorem coeff_mul_of_lt_order {φ ψ : PowerSeries R} {n : ℕ} (h : ↑n < ψ.o
   linarith
 #align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_order
 
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(CommRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (Ring.toDistrib.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) φ (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (SubNegMonoid.toHasSub.{u1} (PowerSeries.{u1} R) (AddGroup.toSubNegMonoid.{u1} (PowerSeries.{u1} R) (PowerSeries.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_2)))))))) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (OfNat.mk.{u1} (PowerSeries.{u1} R) 1 (One.one.{u1} (PowerSeries.{u1} R) (AddMonoidWithOne.toOne.{u1} (PowerSeries.{u1} R) (AddGroupWithOne.toAddMonoidWithOne.{u1} (PowerSeries.{u1} R) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (PowerSeries.{u1} R) (Ring.toAddCommGroupWithOne.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R (CommRing.toRing.{u1} R _inst_2))))))))) ψ))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) => (PowerSeries.{u1} R) -> R) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (PowerSeries.addCommMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.module.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (PowerSeries.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) n) φ))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_2 : CommRing.{u1} R] {φ : PowerSeries.{u1} R} {ψ : PowerSeries.{u1} R} (n : Nat), (LT.lt.{0} PartENat (Preorder.toLT.{0} PartENat (PartialOrder.toPreorder.{0} PartENat PartENat.partialOrder)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n) (PowerSeries.order.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) ψ)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} R) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} R) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) φ (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (Ring.toSub.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) ψ))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) n) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} R) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} R) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) φ (HSub.hSub.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHSub.{u1} (PowerSeries.{u1} R) (Ring.toSub.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) ψ))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) n) φ))
+Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_one_sub_of_lt_order PowerSeries.coeff_mul_one_sub_of_lt_orderₓ'. -/
 theorem coeff_mul_one_sub_of_lt_order {R : Type _} [CommRing R] {φ ψ : PowerSeries R} (n : ℕ)
     (h : ↑n < ψ.order) : coeff R n (φ * (1 - ψ)) = coeff R n φ := by
   simp [coeff_mul_of_lt_order h, mul_sub]
 #align power_series.coeff_mul_one_sub_of_lt_order PowerSeries.coeff_mul_one_sub_of_lt_order
 
+/- warning: power_series.coeff_mul_prod_one_sub_of_lt_order -> PowerSeries.coeff_mul_prod_one_sub_of_lt_order is a dubious translation:
+lean 3 declaration is
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R) (NonUnitalNonAssocRing.toMul.{u2} (PowerSeries.{u2} R) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (PowerSeries.{u2} R) (Ring.toNonAssocRing.{u2} (PowerSeries.{u2} R) (PowerSeries.instRingPowerSeries.{u2} R (CommRing.toRing.{u2} R _inst_2)))))) φ (Finset.prod.{u2, u1} (PowerSeries.{u2} R) ι (CommRing.toCommMonoid.{u2} (PowerSeries.{u2} R) (PowerSeries.instCommRingPowerSeries.{u2} R _inst_2)) s (fun (i : ι) => HSub.hSub.{u2, u2, u2} (PowerSeries.{u2} R) (PowerSeries.{u2} R) (PowerSeries.{u2} R) (instHSub.{u2} (PowerSeries.{u2} R) (Ring.toSub.{u2} (PowerSeries.{u2} R) (PowerSeries.instRingPowerSeries.{u2} R (CommRing.toRing.{u2} R _inst_2)))) (OfNat.ofNat.{u2} (PowerSeries.{u2} R) 1 (One.toOfNat1.{u2} (PowerSeries.{u2} R) (Semiring.toOne.{u2} (PowerSeries.{u2} R) (PowerSeries.instSemiringPowerSeries.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (f i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (PowerSeries.{u2} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (PowerSeries.{u2} R) (fun (_x : PowerSeries.{u2} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u2} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} R R (PowerSeries.{u2} R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (PowerSeries.instAddCommMonoidPowerSeries.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (PowerSeries.coeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) k) φ))
+Case conversion may be inaccurate. Consider using '#align power_series.coeff_mul_prod_one_sub_of_lt_order PowerSeries.coeff_mul_prod_one_sub_of_lt_orderₓ'. -/
 theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type _} [CommRing R] (k : ℕ) (s : Finset ι)
     (φ : PowerSeries R) (f : ι → PowerSeries R) :
     (∀ i ∈ s, ↑k < (f i).order) → coeff R k (φ * ∏ i in s, 1 - f i) = coeff R k φ :=
@@ -2358,8 +3808,14 @@ theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type _} [CommRing R] (k : ℕ
     exact ih t.2
 #align power_series.coeff_mul_prod_one_sub_of_lt_order PowerSeries.coeff_mul_prod_one_sub_of_lt_order
 
+/- warning: power_series.X_pow_order_dvd -> PowerSeries.X_pow_order_dvd is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} (h : Part.Dom.{0} Nat (PowerSeries.order.{u1} R _inst_1 φ)), Dvd.Dvd.{u1} (PowerSeries.{u1} R) (semigroupDvd.{u1} (PowerSeries.{u1} R) (SemigroupWithZero.toSemigroup.{u1} (PowerSeries.{u1} R) (NonUnitalSemiring.toSemigroupWithZero.{u1} (PowerSeries.{u1} R) (Semiring.toNonUnitalSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) (Part.get.{0} Nat (PowerSeries.order.{u1} R _inst_1 φ) h)) φ
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {φ : PowerSeries.{u1} R} (h : Part.Dom.{0} Nat (PowerSeries.order.{u1} R _inst_1 φ)), Dvd.dvd.{u1} (PowerSeries.{u1} R) (semigroupDvd.{u1} (PowerSeries.{u1} R) (SemigroupWithZero.toSemigroup.{u1} (PowerSeries.{u1} R) (NonUnitalSemiring.toSemigroupWithZero.{u1} (PowerSeries.{u1} R) (Semiring.toNonUnitalSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) (Part.get.{0} Nat (PowerSeries.order.{u1} R _inst_1 φ) h)) φ
+Case conversion may be inaccurate. Consider using '#align power_series.X_pow_order_dvd PowerSeries.X_pow_order_dvdₓ'. -/
 -- TODO: link with `X_pow_dvd_iff`
-theorem x_pow_order_dvd (h : (order φ).Dom) : x ^ (order φ).get h ∣ φ :=
+theorem X_pow_order_dvd (h : (order φ).Dom) : X ^ (order φ).get h ∣ φ :=
   by
   refine' ⟨PowerSeries.mk fun n => coeff R (n + (order φ).get h) φ, _⟩
   ext n
@@ -2370,10 +3826,16 @@ theorem x_pow_order_dvd (h : (order φ).Dom) : x ^ (order φ).get h ∣ φ :=
   · simp only [Finset.sum_empty]
     refine' coeff_of_lt_order _ _
     simpa [PartENat.coe_lt_iff] using fun _ => hn
-#align power_series.X_pow_order_dvd PowerSeries.x_pow_order_dvd
-
-theorem order_eq_multiplicity_x {R : Type _} [Semiring R] (φ : PowerSeries R) :
-    order φ = multiplicity x φ :=
+#align power_series.X_pow_order_dvd PowerSeries.X_pow_order_dvd
+
+/- warning: power_series.order_eq_multiplicity_X -> PowerSeries.order_eq_multiplicity_X is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_2 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_2 φ) (multiplicity.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_2))) (fun (a : PowerSeries.{u1} R) (b : PowerSeries.{u1} R) => Classical.propDecidable (Dvd.Dvd.{u1} (PowerSeries.{u1} R) (semigroupDvd.{u1} (PowerSeries.{u1} R) (Monoid.toSemigroup.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_2))))) a b)) (PowerSeries.X.{u1} R _inst_2) φ)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_2 : Semiring.{u1} R] (φ : PowerSeries.{u1} R), Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_2 φ) (multiplicity.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_2))) (fun (a : PowerSeries.{u1} R) (b : PowerSeries.{u1} R) => Classical.propDecidable ((fun (x._@.Mathlib.RingTheory.Multiplicity._hyg.25 : PowerSeries.{u1} R) (x._@.Mathlib.RingTheory.Multiplicity._hyg.27 : PowerSeries.{u1} R) => Dvd.dvd.{u1} (PowerSeries.{u1} R) (semigroupDvd.{u1} (PowerSeries.{u1} R) (Monoid.toSemigroup.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_2))))) x._@.Mathlib.RingTheory.Multiplicity._hyg.25 x._@.Mathlib.RingTheory.Multiplicity._hyg.27) a b)) (PowerSeries.X.{u1} R _inst_2) φ)
+Case conversion may be inaccurate. Consider using '#align power_series.order_eq_multiplicity_X PowerSeries.order_eq_multiplicity_Xₓ'. -/
+theorem order_eq_multiplicity_X {R : Type _} [Semiring R] (φ : PowerSeries R) :
+    order φ = multiplicity X φ :=
   by
   rcases eq_or_ne φ 0 with (rfl | hφ)
   · simp
@@ -2393,7 +3855,7 @@ theorem order_eq_multiplicity_x {R : Type _} [Semiring R] (φ : PowerSeries R) :
     · exact PartENat.natCast_lt_top _
     · rw [← hn, PartENat.coe_lt_coe]
       exact Nat.lt_succ_self _
-#align power_series.order_eq_multiplicity_X PowerSeries.order_eq_multiplicity_x
+#align power_series.order_eq_multiplicity_X PowerSeries.order_eq_multiplicity_X
 
 end OrderBasic
 
@@ -2401,25 +3863,39 @@ section OrderZeroNeOne
 
 variable [Semiring R] [Nontrivial R]
 
+/- warning: power_series.order_one -> PowerSeries.order_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (OfNat.mk.{u1} (PowerSeries.{u1} R) 1 (One.one.{u1} (PowerSeries.{u1} R) (AddMonoidWithOne.toOne.{u1} (PowerSeries.{u1} R) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))))))) (OfNat.ofNat.{0} PartENat 0 (OfNat.mk.{0} PartENat 0 (Zero.zero.{0} PartENat PartENat.hasZero)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (OfNat.ofNat.{0} PartENat 0 (Zero.toOfNat0.{0} PartENat PartENat.instZeroPartENat))
+Case conversion may be inaccurate. Consider using '#align power_series.order_one PowerSeries.order_oneₓ'. -/
 /-- The order of the formal power series `1` is `0`.-/
 @[simp]
 theorem order_one : order (1 : PowerSeries R) = 0 := by
   simpa using order_monomial_of_ne_zero 0 (1 : R) one_ne_zero
 #align power_series.order_one PowerSeries.order_one
 
+#print PowerSeries.order_X /-
 /-- The order of the formal power series `X` is `1`.-/
 @[simp]
-theorem order_x : order (x : PowerSeries R) = 1 := by
+theorem order_X : order (X : PowerSeries R) = 1 := by
   simpa only [Nat.cast_one] using order_monomial_of_ne_zero 1 (1 : R) one_ne_zero
-#align power_series.order_X PowerSeries.order_x
+#align power_series.order_X PowerSeries.order_X
+-/
 
+/- warning: power_series.order_X_pow -> PowerSeries.order_X_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R] (n : Nat), Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) n)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R] (n : Nat), Eq.{1} PartENat (PowerSeries.order.{u1} R _inst_1 (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))))) (PowerSeries.X.{u1} R _inst_1) n)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n)
+Case conversion may be inaccurate. Consider using '#align power_series.order_X_pow PowerSeries.order_X_powₓ'. -/
 /-- The order of the formal power series `X^n` is `n`.-/
 @[simp]
-theorem order_x_pow (n : ℕ) : order ((x : PowerSeries R) ^ n) = n :=
+theorem order_X_pow (n : ℕ) : order ((X : PowerSeries R) ^ n) = n :=
   by
   rw [X_pow_eq, order_monomial_of_ne_zero]
   exact one_ne_zero
-#align power_series.order_X_pow PowerSeries.order_x_pow
+#align power_series.order_X_pow PowerSeries.order_X_pow
 
 end OrderZeroNeOne
 
@@ -2428,6 +3904,12 @@ section OrderIsDomain
 -- TODO: generalize to `[semiring R] [no_zero_divisors R]`
 variable [CommRing R] [IsDomain R]
 
+/- warning: power_series.order_mul -> PowerSeries.order_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), Eq.{1} PartENat (PowerSeries.order.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (Distrib.toHasMul.{u1} (PowerSeries.{u1} R) (Ring.toDistrib.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) φ ψ)) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (PowerSeries.order.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) φ) (PowerSeries.order.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) ψ))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (φ : PowerSeries.{u1} R) (ψ : PowerSeries.{u1} R), Eq.{1} PartENat (PowerSeries.order.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (PowerSeries.{u1} R) (PowerSeries.{u1} R) (PowerSeries.{u1} R) (instHMul.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocRing.toMul.{u1} (PowerSeries.{u1} R) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (PowerSeries.{u1} R) (Ring.toNonAssocRing.{u1} (PowerSeries.{u1} R) (PowerSeries.instRingPowerSeries.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) φ ψ)) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (PowerSeries.order.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) φ) (PowerSeries.order.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) ψ))
+Case conversion may be inaccurate. Consider using '#align power_series.order_mul PowerSeries.order_mulₓ'. -/
 /-- The order of the product of two formal power series over an integral domain
  is the sum of their orders.-/
 theorem order_mul (φ ψ : PowerSeries R) : order (φ * ψ) = order φ + order ψ :=
@@ -2446,20 +3928,36 @@ open Finsupp
 
 variable {σ : Type _} {R : Type _} [CommSemiring R] (φ ψ : R[X])
 
+#print Polynomial.coeToPowerSeries /-
 /-- The natural inclusion from polynomials into formal power series.-/
 instance coeToPowerSeries : Coe R[X] (PowerSeries R) :=
   ⟨fun φ => PowerSeries.mk fun n => coeff φ n⟩
 #align polynomial.coe_to_power_series Polynomial.coeToPowerSeries
+-/
 
+#print Polynomial.coe_def /-
 theorem coe_def : (φ : PowerSeries R) = PowerSeries.mk (coeff φ) :=
   rfl
 #align polynomial.coe_def Polynomial.coe_def
+-/
 
+/- warning: polynomial.coeff_coe -> Polynomial.coeff_coe is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : PowerSeries.{u1} R) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (PowerSeries.{u1} R) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (PowerSeries.instAddCommMonoidPowerSeries.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) n) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ)) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) φ n)
+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_coe Polynomial.coeff_coeₓ'. -/
 @[simp, norm_cast]
 theorem coeff_coe (n) : PowerSeries.coeff R n φ = coeff φ n :=
   congr_arg (coeff φ) Finsupp.single_eq_same
 #align polynomial.coeff_coe Polynomial.coeff_coe
 
+/- warning: polynomial.coe_monomial -> Polynomial.coe_monomial is a dubious translation:
+lean 3 declaration is
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 @[simp, norm_cast]
 theorem coe_monomial (n : ℕ) (a : R) :
     (monomial n a : PowerSeries R) = PowerSeries.monomial R n a :=
@@ -2468,18 +3966,36 @@ theorem coe_monomial (n : ℕ) (a : R) :
   simp [coeff_coe, PowerSeries.coeff_monomial, Polynomial.coeff_monomial, eq_comm]
 #align polynomial.coe_monomial Polynomial.coe_monomial
 
+/- warning: polynomial.coe_zero -> Polynomial.coe_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.coe_zero Polynomial.coe_zeroₓ'. -/
 @[simp, norm_cast]
 theorem coe_zero : ((0 : R[X]) : PowerSeries R) = 0 :=
   rfl
 #align polynomial.coe_zero Polynomial.coe_zero
 
+/- warning: polynomial.coe_one -> Polynomial.coe_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.coe_one Polynomial.coe_oneₓ'. -/
 @[simp, norm_cast]
 theorem coe_one : ((1 : R[X]) : PowerSeries R) = 1 :=
   by
   have := coe_monomial 0 (1 : R)
-  rwa [PowerSeries.monomial_zero_eq_c_apply] at this
+  rwa [PowerSeries.monomial_zero_eq_C_apply] at this
 #align polynomial.coe_one Polynomial.coe_one
 
+/- warning: polynomial.coe_add -> Polynomial.coe_add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.coe_add Polynomial.coe_addₓ'. -/
 @[simp, norm_cast]
 theorem coe_add : ((φ + ψ : R[X]) : PowerSeries R) = φ + ψ :=
   by
@@ -2487,33 +4003,65 @@ theorem coe_add : ((φ + ψ : R[X]) : PowerSeries R) = φ + ψ :=
   simp
 #align polynomial.coe_add Polynomial.coe_add
 
+/- warning: polynomial.coe_mul -> Polynomial.coe_mul is a dubious translation:
+lean 3 declaration is
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 @[simp, norm_cast]
 theorem coe_mul : ((φ * ψ : R[X]) : PowerSeries R) = φ * ψ :=
   PowerSeries.ext fun n => by simp only [coeff_coe, PowerSeries.coeff_mul, coeff_mul]
 #align polynomial.coe_mul Polynomial.coe_mul
 
+/- warning: polynomial.coe_C -> Polynomial.coe_C is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (a : R), Eq.{succ u1} (PowerSeries.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (coeBase.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Polynomial.coeToPowerSeries.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a)
+but is expected to have type
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R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (PowerSeries.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a)
+Case conversion may be inaccurate. Consider using '#align polynomial.coe_C Polynomial.coe_Cₓ'. -/
 @[simp, norm_cast]
-theorem coe_c (a : R) : ((C a : R[X]) : PowerSeries R) = PowerSeries.c R a :=
+theorem coe_C (a : R) : ((C a : R[X]) : PowerSeries R) = PowerSeries.C R a :=
   by
   have := coe_monomial 0 a
-  rwa [PowerSeries.monomial_zero_eq_c_apply] at this
-#align polynomial.coe_C Polynomial.coe_c
-
+  rwa [PowerSeries.monomial_zero_eq_C_apply] at this
+#align polynomial.coe_C Polynomial.coe_C
+
+/- warning: polynomial.coe_bit0 -> Polynomial.coe_bit0 is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (PowerSeries.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (coeBase.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Polynomial.coeToPowerSeries.{u1} R _inst_1)))) (bit0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ)) (bit0.{u1} (PowerSeries.{u1} R) (Distrib.toHasAdd.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (coeBase.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Polynomial.coeToPowerSeries.{u1} R _inst_1)))) φ))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (PowerSeries.{u1} R) (Polynomial.ToPowerSeries.{u1} R _inst_1 (bit0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ)) (bit0.{u1} (PowerSeries.{u1} R) (Distrib.toAdd.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ))
+Case conversion may be inaccurate. Consider using '#align polynomial.coe_bit0 Polynomial.coe_bit0ₓ'. -/
 @[simp, norm_cast]
 theorem coe_bit0 : ((bit0 φ : R[X]) : PowerSeries R) = bit0 (φ : PowerSeries R) :=
   coe_add φ φ
 #align polynomial.coe_bit0 Polynomial.coe_bit0
 
+/- warning: polynomial.coe_bit1 -> Polynomial.coe_bit1 is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (PowerSeries.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (coeBase.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Polynomial.coeToPowerSeries.{u1} R _inst_1)))) (bit1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ)) (bit1.{u1} (PowerSeries.{u1} R) (AddMonoidWithOne.toOne.{u1} (PowerSeries.{u1} R) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Distrib.toHasAdd.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (coeBase.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Polynomial.coeToPowerSeries.{u1} R _inst_1)))) φ))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (PowerSeries.{u1} R) (Polynomial.ToPowerSeries.{u1} R _inst_1 (bit1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ)) (bit1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Distrib.toAdd.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toDistrib.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ))
+Case conversion may be inaccurate. Consider using '#align polynomial.coe_bit1 Polynomial.coe_bit1ₓ'. -/
 @[simp, norm_cast]
 theorem coe_bit1 : ((bit1 φ : R[X]) : PowerSeries R) = bit1 (φ : PowerSeries R) := by
   rw [bit1, bit1, coe_add, coe_one, coe_bit0]
 #align polynomial.coe_bit1 Polynomial.coe_bit1
 
+#print Polynomial.coe_X /-
 @[simp, norm_cast]
-theorem coe_x : ((X : R[X]) : PowerSeries R) = PowerSeries.x :=
+theorem coe_X : ((X : R[X]) : PowerSeries R) = PowerSeries.X :=
   coe_monomial _ _
-#align polynomial.coe_X Polynomial.coe_x
+#align polynomial.coe_X Polynomial.coe_X
+-/
 
+/- warning: polynomial.constant_coeff_coe -> Polynomial.constantCoeff_coe is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> R) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.constantCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (coeBase.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Polynomial.coeToPowerSeries.{u1} R _inst_1)))) φ)) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) φ (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) R (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (PowerSeries.constantCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ)) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) φ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+Case conversion may be inaccurate. Consider using '#align polynomial.constant_coeff_coe Polynomial.constantCoeff_coeₓ'. -/
 @[simp]
 theorem constantCoeff_coe : PowerSeries.constantCoeff R φ = φ.coeff 0 :=
   rfl
@@ -2521,29 +4069,51 @@ theorem constantCoeff_coe : PowerSeries.constantCoeff R φ = φ.coeff 0 :=
 
 variable (R)
 
+#print Polynomial.coe_injective /-
 theorem coe_injective : Function.Injective (coe : R[X] → PowerSeries R) := fun x y h =>
   by
   ext
   simp_rw [← coeff_coe, h]
 #align polynomial.coe_injective Polynomial.coe_injective
+-/
 
 variable {R φ ψ}
 
+#print Polynomial.coe_inj /-
 @[simp, norm_cast]
 theorem coe_inj : (φ : PowerSeries R) = ψ ↔ φ = ψ :=
   (coe_injective R).eq_iff
 #align polynomial.coe_inj Polynomial.coe_inj
+-/
 
+/- warning: polynomial.coe_eq_zero_iff -> Polynomial.coe_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (PowerSeries.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (coeBase.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Polynomial.coeToPowerSeries.{u1} R _inst_1)))) φ) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (OfNat.mk.{u1} (PowerSeries.{u1} R) 0 (Zero.zero.{u1} (PowerSeries.{u1} R) (MulZeroClass.toHasZero.{u1} (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 0 (Zero.zero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (PowerSeries.{u1} R) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 0 (Zero.toOfNat0.{u1} (PowerSeries.{u1} R) (PowerSeries.instZeroPowerSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)))))) (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.coe_eq_zero_iff Polynomial.coe_eq_zero_iffₓ'. -/
 @[simp]
 theorem coe_eq_zero_iff : (φ : PowerSeries R) = 0 ↔ φ = 0 := by rw [← coe_zero, coe_inj]
 #align polynomial.coe_eq_zero_iff Polynomial.coe_eq_zero_iff
 
+/- warning: polynomial.coe_eq_one_iff -> Polynomial.coe_eq_one_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (PowerSeries.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (coeBase.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Polynomial.coeToPowerSeries.{u1} R _inst_1)))) φ) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (OfNat.mk.{u1} (PowerSeries.{u1} R) 1 (One.one.{u1} (PowerSeries.{u1} R) (AddMonoidWithOne.toOne.{u1} (PowerSeries.{u1} R) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (PowerSeries.{u1} R) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ) (OfNat.ofNat.{u1} (PowerSeries.{u1} R) 1 (One.toOfNat1.{u1} (PowerSeries.{u1} R) (Semiring.toOne.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.coe_eq_one_iff Polynomial.coe_eq_one_iffₓ'. -/
 @[simp]
 theorem coe_eq_one_iff : (φ : PowerSeries R) = 1 ↔ φ = 1 := by rw [← coe_one, coe_inj]
 #align polynomial.coe_eq_one_iff Polynomial.coe_eq_one_iff
 
 variable (φ ψ)
 
+/- warning: polynomial.coe_to_power_series.ring_hom -> Polynomial.coeToPowerSeries.ringHom is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R], RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R], RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))
+Case conversion may be inaccurate. Consider using '#align polynomial.coe_to_power_series.ring_hom Polynomial.coeToPowerSeries.ringHomₓ'. -/
 /-- The coercion from polynomials to power series
 as a ring homomorphism.
 -/
@@ -2556,11 +4126,23 @@ def coeToPowerSeries.ringHom : R[X] →+* PowerSeries R
   map_mul' := coe_mul
 #align polynomial.coe_to_power_series.ring_hom Polynomial.coeToPowerSeries.ringHom
 
+/- warning: polynomial.coe_to_power_series.ring_hom_apply -> Polynomial.coeToPowerSeries.ringHom_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (PowerSeries.{u1} R) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (PowerSeries.{u1} R)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.coeToPowerSeries.ringHom.{u1} R _inst_1) φ) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (coeBase.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Polynomial.coeToPowerSeries.{u1} R _inst_1)))) φ)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => PowerSeries.{u1} R) φ) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => PowerSeries.{u1} R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.coeToPowerSeries.ringHom.{u1} R _inst_1) φ) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ)
+Case conversion may be inaccurate. Consider using '#align polynomial.coe_to_power_series.ring_hom_apply Polynomial.coeToPowerSeries.ringHom_applyₓ'. -/
 @[simp]
 theorem coeToPowerSeries.ringHom_apply : coeToPowerSeries.ringHom φ = φ :=
   rfl
 #align polynomial.coe_to_power_series.ring_hom_apply Polynomial.coeToPowerSeries.ringHom_apply
 
+/- warning: polynomial.coe_pow -> Polynomial.coe_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (n : Nat), Eq.{succ u1} (PowerSeries.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (coeBase.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Polynomial.coeToPowerSeries.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) φ n)) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (coeBase.{succ u1, succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u1} R) (Polynomial.coeToPowerSeries.{u1} R _inst_1)))) φ) n)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (n : Nat), Eq.{succ u1} (PowerSeries.{u1} R) (Polynomial.ToPowerSeries.{u1} R _inst_1 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) φ n)) (HPow.hPow.{u1, 0, u1} (PowerSeries.{u1} R) Nat (PowerSeries.{u1} R) (instHPow.{u1, 0} (PowerSeries.{u1} R) Nat (Monoid.Pow.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.ToPowerSeries.{u1} R _inst_1 φ) n)
+Case conversion may be inaccurate. Consider using '#align polynomial.coe_pow Polynomial.coe_powₓ'. -/
 @[simp, norm_cast]
 theorem coe_pow (n : ℕ) : ((φ ^ n : R[X]) : PowerSeries R) = (φ : PowerSeries R) ^ n :=
   coeToPowerSeries.ringHom.map_pow _ _
@@ -2568,6 +4150,12 @@ theorem coe_pow (n : ℕ) : ((φ ^ n : R[X]) : PowerSeries R) = (φ : PowerSerie
 
 variable (A : Type _) [Semiring A] [Algebra R A]
 
+/- warning: polynomial.coe_to_power_series.alg_hom -> Polynomial.coeToPowerSeries.algHom is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u2} A) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.semiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (PowerSeries.algebra.{u1, u2} R A _inst_2 _inst_1 _inst_3)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u2} A) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.instSemiringPowerSeries.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (PowerSeries.instAlgebraPowerSeriesInstSemiringPowerSeries.{u1, u2} R A _inst_2 _inst_1 _inst_3)
+Case conversion may be inaccurate. Consider using '#align polynomial.coe_to_power_series.alg_hom Polynomial.coeToPowerSeries.algHomₓ'. -/
 /-- The coercion from polynomials to power series
 as an algebra homomorphism.
 -/
@@ -2576,11 +4164,13 @@ def coeToPowerSeries.algHom : R[X] →ₐ[R] PowerSeries A :=
     commutes' := fun r => by simp [algebraMap_apply, PowerSeries.algebraMap_apply] }
 #align polynomial.coe_to_power_series.alg_hom Polynomial.coeToPowerSeries.algHom
 
+#print Polynomial.coeToPowerSeries.algHom_apply /-
 @[simp]
 theorem coeToPowerSeries.algHom_apply :
     coeToPowerSeries.algHom A φ = PowerSeries.map (algebraMap R A) ↑φ :=
   rfl
 #align polynomial.coe_to_power_series.alg_hom_apply Polynomial.coeToPowerSeries.algHom_apply
+-/
 
 end Polynomial
 
@@ -2588,14 +4178,32 @@ namespace PowerSeries
 
 variable {R A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : PowerSeries R)
 
+/- warning: power_series.algebra_polynomial -> PowerSeries.algebraPolynomial is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)], Algebra.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u2} A) (Polynomial.commSemiring.{u1} R _inst_1) (PowerSeries.semiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)], Algebra.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PowerSeries.{u2} A) (Polynomial.commSemiring.{u1} R _inst_1) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))
+Case conversion may be inaccurate. Consider using '#align power_series.algebra_polynomial PowerSeries.algebraPolynomialₓ'. -/
 instance algebraPolynomial : Algebra R[X] (PowerSeries A) :=
   RingHom.toAlgebra (Polynomial.coeToPowerSeries.algHom A).toRingHom
 #align power_series.algebra_polynomial PowerSeries.algebraPolynomial
 
+/- warning: power_series.algebra_power_series -> PowerSeries.algebraPowerSeries is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)], Algebra.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} A) (PowerSeries.commSemiring.{u1} R _inst_1) (PowerSeries.semiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)], Algebra.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} A) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))
+Case conversion may be inaccurate. Consider using '#align power_series.algebra_power_series PowerSeries.algebraPowerSeriesₓ'. -/
 instance algebraPowerSeries : Algebra (PowerSeries R) (PowerSeries A) :=
   (map (algebraMap R A)).toAlgebra
 #align power_series.algebra_power_series PowerSeries.algebraPowerSeries
 
+/- warning: power_series.algebra_polynomial' -> PowerSeries.algebraPolynomial' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_4 : CommSemiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A _inst_4)) _inst_1 (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_4))], Algebra.{u1, u2} R (PowerSeries.{u2} A) _inst_1 (PowerSeries.semiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_4))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_4 : CommSemiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A _inst_4)) _inst_1 (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_4))], Algebra.{u1, u2} R (PowerSeries.{u2} A) _inst_1 (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_4))
+Case conversion may be inaccurate. Consider using '#align power_series.algebra_polynomial' PowerSeries.algebraPolynomial'ₓ'. -/
 -- see Note [lower instance priority]
 instance (priority := 100) algebraPolynomial' {A : Type _} [CommSemiring A] [Algebra R A[X]] :
     Algebra R (PowerSeries A) :=
@@ -2604,10 +4212,22 @@ instance (priority := 100) algebraPolynomial' {A : Type _} [CommSemiring A] [Alg
 
 variable (A)
 
+/- warning: power_series.algebra_map_apply' -> PowerSeries.algebraMap_apply' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align power_series.algebra_map_apply' PowerSeries.algebraMap_apply'ₓ'. -/
 theorem algebraMap_apply' (p : R[X]) : algebraMap R[X] (PowerSeries A) p = map (algebraMap R A) p :=
   rfl
 #align power_series.algebra_map_apply' PowerSeries.algebraMap_apply'
 
+/- warning: power_series.algebra_map_apply'' -> PowerSeries.algebraMap_apply'' is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u1}} (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] (f : PowerSeries.{u1} R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u2} A) f) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u2} A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (PowerSeries.{u1} R) (PowerSeries.{u2} A) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (PowerSeries.{u2} A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (PowerSeries.{u1} R) (PowerSeries.{u2} A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (PowerSeries.{u1} R) (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} A) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (PowerSeries.algebraPowerSeries.{u1, u2} R A _inst_1 _inst_2 _inst_3)) f) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (PowerSeries.{u1} R) (fun (_x : PowerSeries.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => PowerSeries.{u2} A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (PowerSeries.{u1} R) (PowerSeries.{u2} A) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (PowerSeries.{u2} A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (PowerSeries.{u1} R) (PowerSeries.{u2} A) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (PowerSeries.{u1} R) (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} (PowerSeries.{u1} R) (PowerSeries.{u2} A) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (PowerSeries.{u2} A) (PowerSeries.instSemiringPowerSeries.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (PowerSeries.map.{u1, u2} R (CommSemiring.toSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u2} A _inst_2) (algebraMap.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) f)
+Case conversion may be inaccurate. Consider using '#align power_series.algebra_map_apply'' PowerSeries.algebraMap_apply''ₓ'. -/
 theorem algebraMap_apply'' :
     algebraMap (PowerSeries R) (PowerSeries A) f = map (algebraMap R A) f :=
   rfl

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

@@ -628,7 +628,7 @@ instance [Nonempty σ] [Nontrivial R] : Nontrivial (Subalgebra R (MvPowerSeries
       intro x
       rw [ext_iff, not_forall]
       refine' ⟨Finsupp.single default 1, _⟩
-      simp [algebra_map_apply, coeff_C]⟩⟩
+      simp [algebraMap_apply, coeff_C]⟩⟩
 
 end Algebra
 
@@ -1140,7 +1140,7 @@ as an algebra homomorphism.
 -/
 def coeToMvPowerSeries.algHom : MvPolynomial σ R →ₐ[R] MvPowerSeries σ A :=
   { (MvPowerSeries.map σ (algebraMap R A)).comp coeToMvPowerSeries.ringHom with
-    commutes' := fun r => by simp [algebra_map_apply, MvPowerSeries.algebraMap_apply] }
+    commutes' := fun r => by simp [algebraMap_apply, MvPowerSeries.algebraMap_apply] }
 #align mv_polynomial.coe_to_mv_power_series.alg_hom MvPolynomial.coeToMvPowerSeries.algHom
 
 @[simp]
@@ -2573,7 +2573,7 @@ as an algebra homomorphism.
 -/
 def coeToPowerSeries.algHom : R[X] →ₐ[R] PowerSeries A :=
   { (PowerSeries.map (algebraMap R A)).comp coeToPowerSeries.ringHom with
-    commutes' := fun r => by simp [algebra_map_apply, PowerSeries.algebraMap_apply] }
+    commutes' := fun r => by simp [algebraMap_apply, PowerSeries.algebraMap_apply] }
 #align polynomial.coe_to_power_series.alg_hom Polynomial.coeToPowerSeries.algHom
 
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -2117,7 +2117,7 @@ namespace PowerSeries
 
 variable {R : Type _}
 
-attribute [local instance] Classical.propDecidable
+attribute [local instance 1] Classical.propDecidable
 
 noncomputable section
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
 
 ! This file was ported from Lean 3 source module ring_theory.power_series.basic
-! leanprover-community/mathlib commit 7d6cd0411fa5334c211f4657e971f2666d08b15a
+! leanprover-community/mathlib commit 2d5739b61641ee4e7e53eca5688a08f66f2e6a60
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -697,9 +697,9 @@ theorem trunc_c (hnn : n ≠ 0) (a : R) : trunc R n (c σ R a) = MvPolynomial.C
 
 end Trunc
 
-section CommSemiring
+section Semiring
 
-variable [CommSemiring R]
+variable [Semiring R]
 
 theorem x_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
     (x s : MvPowerSeries σ R) ^ n ∣ φ ↔ ∀ m : σ →₀ ℕ, m s < n → coeff R m φ = 0 :=
@@ -766,7 +766,7 @@ theorem x_dvd_iff {s : σ} {φ : MvPowerSeries σ R} :
   · exact h m (Nat.eq_zero_of_le_zero <| Nat.le_of_succ_le_succ hm)
 #align mv_power_series.X_dvd_iff MvPowerSeries.x_dvd_iff
 
-end CommSemiring
+end Semiring
 
 section Ring
 
@@ -1135,10 +1135,6 @@ section Algebra
 
 variable (A : Type _) [CommSemiring A] [Algebra R A]
 
-theorem algebraMap_apply (r : R) : algebraMap R (MvPolynomial σ A) r = C (algebraMap R A r) :=
-  rfl
-#align mv_polynomial.algebra_map_apply MvPolynomial.algebraMap_apply
-
 /-- The coercion from multivariable polynomials to multivariable power series
 as an algebra homomorphism.
 -/
@@ -1611,12 +1607,6 @@ theorem map_x : map f x = x := by
 
 end Map
 
-end Semiring
-
-section CommSemiring
-
-variable [CommSemiring R]
-
 theorem x_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
     (x : PowerSeries R) ^ n ∣ φ ↔ ∀ m, m < n → coeff R m φ = 0 :=
   by
@@ -1638,6 +1628,12 @@ theorem x_dvd_iff {φ : PowerSeries R} : (x : PowerSeries R) ∣ φ ↔ constant
     rwa [Nat.eq_zero_of_le_zero (Nat.le_of_succ_le_succ hm)]
 #align power_series.X_dvd_iff PowerSeries.x_dvd_iff
 
+end Semiring
+
+section CommSemiring
+
+variable [CommSemiring R]
+
 open Finset Nat
 
 /-- The ring homomorphism taking a power series `f(X)` to `f(aX)`. -/

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

@@ -1620,7 +1620,7 @@ variable [CommSemiring R]
 theorem x_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
     (x : PowerSeries R) ^ n ∣ φ ↔ ∀ m, m < n → coeff R m φ = 0 :=
   by
-  convert @MvPowerSeries.x_pow_dvd_iff Unit R _ () n φ; apply propext
+  convert@MvPowerSeries.x_pow_dvd_iff Unit R _ () n φ; apply propext
   classical
     constructor <;> intro h m hm
     · rw [Finsupp.unique_single m]

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

@@ -687,10 +687,10 @@ theorem trunc_one (hnn : n ≠ 0) : trunc R n 1 = 1 :=
 #align mv_power_series.trunc_one MvPowerSeries.trunc_one
 
 @[simp]
-theorem trunc_c (hnn : n ≠ 0) (a : R) : trunc R n (c σ R a) = MvPolynomial.c a :=
+theorem trunc_c (hnn : n ≠ 0) (a : R) : trunc R n (c σ R a) = MvPolynomial.C a :=
   MvPolynomial.ext _ _ fun m =>
     by
-    rw [coeff_trunc, coeff_C, MvPolynomial.coeff_c]
+    rw [coeff_trunc, coeff_C, MvPolynomial.coeff_C]
     split_ifs with H <;> first |rfl|try simp_all
     exfalso; apply H; subst m; exact Ne.bot_lt hnn
 #align mv_power_series.trunc_C MvPowerSeries.trunc_c
@@ -1062,7 +1062,7 @@ theorem coe_mul : ((φ * ψ : MvPolynomial σ R) : MvPowerSeries σ R) = φ * ψ
 #align mv_polynomial.coe_mul MvPolynomial.coe_mul
 
 @[simp, norm_cast]
-theorem coe_c (a : R) : ((c a : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.c σ R a :=
+theorem coe_c (a : R) : ((C a : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.c σ R a :=
   coe_monomial _ _
 #align mv_polynomial.coe_C MvPolynomial.coe_c
 
@@ -1079,7 +1079,7 @@ theorem coe_bit1 :
 #align mv_polynomial.coe_bit1 MvPolynomial.coe_bit1
 
 @[simp, norm_cast]
-theorem coe_x (s : σ) : ((x s : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.x s :=
+theorem coe_x (s : σ) : ((X s : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.x s :=
   coe_monomial _ _
 #align mv_polynomial.coe_X MvPolynomial.coe_x
 
@@ -1135,7 +1135,7 @@ section Algebra
 
 variable (A : Type _) [CommSemiring A] [Algebra R A]
 
-theorem algebraMap_apply (r : R) : algebraMap R (MvPolynomial σ A) r = c (algebraMap R A r) :=
+theorem algebraMap_apply (r : R) : algebraMap R (MvPolynomial σ A) r = C (algebraMap R A r) :=
   rfl
 #align mv_polynomial.algebra_map_apply MvPolynomial.algebraMap_apply
 

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

@@ -343,7 +343,7 @@ theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
     exact (h₃ rfl).elim
   · rw [h₃, add_tsub_cancel_right] at h₂
     exact (h₂ rfl).elim
-  · exact zero_mul b
+  · exact MulZeroClass.zero_mul b
   · rw [h₂] at h₁
     exact (h₁ <| le_add_left le_rfl).elim
 #align mv_power_series.monomial_mul_monomial MvPowerSeries.monomial_mul_monomial
@@ -708,7 +708,7 @@ theorem x_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
   · rintro ⟨φ, rfl⟩ m h
     rw [coeff_mul, Finset.sum_eq_zero]
     rintro ⟨i, j⟩ hij
-    rw [coeff_X_pow, if_neg, zero_mul]
+    rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
     contrapose! h
     subst i
     rw [Finsupp.mem_antidiagonal] at hij
@@ -731,7 +731,7 @@ theorem x_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
           refine' ⟨rfl, _⟩
           ext t
           simp only [add_tsub_cancel_left, Finsupp.add_apply, Finsupp.tsub_apply]
-        · exact zero_mul _
+        · exact MulZeroClass.zero_mul _
       · intro hni
         exfalso
         apply hni
@@ -746,7 +746,7 @@ theorem x_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
           rw [← hij, hi]
           ext
           rw [coe_add, coe_add, Pi.add_apply, Pi.add_apply, add_tsub_cancel_left, add_comm]
-        · exact zero_mul _
+        · exact MulZeroClass.zero_mul _
       ·
         classical
           contrapose! H
@@ -924,7 +924,8 @@ theorem inv_eq_zero {φ : MvPowerSeries σ k} : φ⁻¹ = 0 ↔ constantCoeff σ
   ⟨fun h => by simpa using congr_arg (constant_coeff σ k) h, fun h =>
     ext fun n => by
       rw [coeff_inv]
-      split_ifs <;> simp only [h, MvPowerSeries.coeff_zero, zero_mul, inv_zero, neg_zero]⟩
+      split_ifs <;>
+        simp only [h, MvPowerSeries.coeff_zero, MulZeroClass.zero_mul, inv_zero, neg_zero]⟩
 #align mv_power_series.inv_eq_zero MvPowerSeries.inv_eq_zero
 
 @[simp]
@@ -1492,7 +1493,7 @@ theorem coeff_mul_x_pow (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (p * x
   by
   rw [coeff_mul, Finset.sum_eq_single (d, n), coeff_X_pow, if_pos rfl, mul_one]
   · rintro ⟨i, j⟩ h1 h2
-    rw [coeff_X_pow, if_neg, mul_zero]
+    rw [coeff_X_pow, if_neg, MulZeroClass.mul_zero]
     rintro rfl
     apply h2
     rw [Finset.Nat.mem_antidiagonal, add_right_cancel_iff] at h1
@@ -1505,7 +1506,7 @@ theorem coeff_x_pow_mul (p : PowerSeries R) (n d : ℕ) : coeff R (d + n) (x ^ n
   by
   rw [coeff_mul, Finset.sum_eq_single (n, d), coeff_X_pow, if_pos rfl, one_mul]
   · rintro ⟨i, j⟩ h1 h2
-    rw [coeff_X_pow, if_neg, zero_mul]
+    rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
     rintro rfl
     apply h2
     rw [Finset.Nat.mem_antidiagonal, add_comm, add_right_cancel_iff] at h1
@@ -1520,7 +1521,7 @@ theorem coeff_mul_x_pow' (p : PowerSeries R) (n d : ℕ) :
   split_ifs
   · rw [← tsub_add_cancel_of_le h, coeff_mul_X_pow, add_tsub_cancel_right]
   · refine' (coeff_mul _ _ _).trans (Finset.sum_eq_zero fun x hx => _)
-    rw [coeff_X_pow, if_neg, mul_zero]
+    rw [coeff_X_pow, if_neg, MulZeroClass.mul_zero]
     exact ((le_of_add_le_right (finset.nat.mem_antidiagonal.mp hx).le).trans_lt <| not_le.mp h).Ne
 #align power_series.coeff_mul_X_pow' PowerSeries.coeff_mul_x_pow'
 
@@ -1531,7 +1532,7 @@ theorem coeff_x_pow_mul' (p : PowerSeries R) (n d : ℕ) :
   · rw [← tsub_add_cancel_of_le h, coeff_X_pow_mul]
     simp
   · refine' (coeff_mul _ _ _).trans (Finset.sum_eq_zero fun x hx => _)
-    rw [coeff_X_pow, if_neg, zero_mul]
+    rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
     have := finset.nat.mem_antidiagonal.mp hx
     rw [add_comm] at this
     exact ((le_of_add_le_right this.le).trans_lt <| not_le.mp h).Ne
@@ -1551,7 +1552,7 @@ theorem eq_shift_mul_x_add_const (φ : PowerSeries R) :
   ext (_ | n)
   ·
     simp only [RingHom.map_add, constant_coeff_C, constant_coeff_X, coeff_zero_eq_constant_coeff,
-      zero_add, mul_zero, RingHom.map_mul]
+      zero_add, MulZeroClass.mul_zero, RingHom.map_mul]
   ·
     simp only [coeff_succ_mul_X, coeff_mk, LinearMap.map_add, coeff_C, n.succ_ne_zero, sub_zero,
       if_false, add_zero]
@@ -1564,7 +1565,7 @@ theorem eq_x_mul_shift_add_const (φ : PowerSeries R) :
   ext (_ | n)
   ·
     simp only [RingHom.map_add, constant_coeff_C, constant_coeff_X, coeff_zero_eq_constant_coeff,
-      zero_add, zero_mul, RingHom.map_mul]
+      zero_add, MulZeroClass.zero_mul, RingHom.map_mul]
   ·
     simp only [coeff_succ_X_mul, coeff_mk, LinearMap.map_add, coeff_C, n.succ_ne_zero, sub_zero,
       if_false, add_zero]
@@ -1645,7 +1646,7 @@ noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R
   toFun f := PowerSeries.mk fun n => a ^ n * PowerSeries.coeff R n f
   map_zero' := by
     ext
-    simp only [LinearMap.map_zero, PowerSeries.coeff_mk, mul_zero]
+    simp only [LinearMap.map_zero, PowerSeries.coeff_mk, MulZeroClass.mul_zero]
   map_one' := by
     ext1
     simp only [mul_boole, PowerSeries.coeff_mk, PowerSeries.coeff_one]
@@ -1679,7 +1680,7 @@ theorem rescale_zero : rescale 0 = (c R).comp (constantCoeff R) :=
     PowerSeries.coeff_mk _ _, coeff_C]
   split_ifs
   · simp only [h, one_mul, coeff_zero_eq_constant_coeff, pow_zero]
-  · rw [zero_pow' n h, zero_mul]
+  · rw [zero_pow' n h, MulZeroClass.zero_mul]
 #align power_series.rescale_zero PowerSeries.rescale_zero
 
 theorem rescale_zero_apply : rescale 0 x = c R (constantCoeff R x) := by simp
@@ -1913,11 +1914,11 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSerie
     exact h hm₁
   · rintro ⟨i, j⟩ hij hne
     by_cases hj : j < n
-    · rw [ih j hj, mul_zero]
+    · rw [ih j hj, MulZeroClass.mul_zero]
     by_cases hi : i < m
     · specialize hm₂ _ hi
       push_neg  at hm₂
-      rw [hm₂, zero_mul]
+      rw [hm₂, MulZeroClass.zero_mul]
     rw [Finset.Nat.mem_antidiagonal] at hij
     push_neg  at hi hj
     suffices m < i by
@@ -2300,9 +2301,9 @@ theorem order_mul_ge (φ ψ : PowerSeries R) : order φ + order ψ ≤ order (φ
   intro n hn; rw [coeff_mul, Finset.sum_eq_zero]
   rintro ⟨i, j⟩ hij
   by_cases hi : ↑i < order φ
-  · rw [coeff_of_lt_order i hi, zero_mul]
+  · rw [coeff_of_lt_order i hi, MulZeroClass.zero_mul]
   by_cases hj : ↑j < order ψ
-  · rw [coeff_of_lt_order j hj, mul_zero]
+  · rw [coeff_of_lt_order j hj, MulZeroClass.mul_zero]
   rw [not_lt] at hi hj; rw [Finset.Nat.mem_antidiagonal] at hij
   exfalso
   apply ne_of_lt (lt_of_lt_of_le hn <| add_le_add hi hj)

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

@@ -1313,7 +1313,7 @@ def x : PowerSeries R :=
 #align power_series.X PowerSeries.x
 
 theorem commute_x (φ : PowerSeries R) : Commute φ x :=
-  φ.commute_x _
+  φ.commute_X _
 #align power_series.commute_X PowerSeries.commute_x
 
 @[simp]
@@ -1749,9 +1749,9 @@ theorem trunc_one (n) : trunc (n + 1) (1 : PowerSeries R) = 1 :=
 #align power_series.trunc_one PowerSeries.trunc_one
 
 @[simp]
-theorem trunc_c (n) (a : R) : trunc (n + 1) (c R a) = Polynomial.c a :=
+theorem trunc_c (n) (a : R) : trunc (n + 1) (c R a) = Polynomial.C a :=
   Polynomial.ext fun m => by
-    rw [coeff_trunc, coeff_C, Polynomial.coeff_c]
+    rw [coeff_trunc, coeff_C, Polynomial.coeff_C]
     split_ifs with H <;> first |rfl|try simp_all
 #align power_series.trunc_C PowerSeries.trunc_c
 
@@ -2496,7 +2496,7 @@ theorem coe_mul : ((φ * ψ : R[X]) : PowerSeries R) = φ * ψ :=
 #align polynomial.coe_mul Polynomial.coe_mul
 
 @[simp, norm_cast]
-theorem coe_c (a : R) : ((c a : R[X]) : PowerSeries R) = PowerSeries.c R a :=
+theorem coe_c (a : R) : ((C a : R[X]) : PowerSeries R) = PowerSeries.c R a :=
   by
   have := coe_monomial 0 a
   rwa [PowerSeries.monomial_zero_eq_c_apply] at this
@@ -2513,7 +2513,7 @@ theorem coe_bit1 : ((bit1 φ : R[X]) : PowerSeries R) = bit1 (φ : PowerSeries R
 #align polynomial.coe_bit1 Polynomial.coe_bit1
 
 @[simp, norm_cast]
-theorem coe_x : ((x : R[X]) : PowerSeries R) = PowerSeries.x :=
+theorem coe_x : ((X : R[X]) : PowerSeries R) = PowerSeries.x :=
   coe_monomial _ _
 #align polynomial.coe_X Polynomial.coe_x
 

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

This PR was supposed to be simultaneous with #12090 but I got ill last week.

This is based on seeing the import Algebra.Algebra.Subalgebra.Basic → RingTheory.Ideal.Operations on the longest pole. It feels like Ideal.Operations should not be needed to define the notion of subalgebra, only to construct some interesting examples. So I removed the import and split off anything that wouldn't fit.

The following results and their corollaries were split off:

• Subalgebra.prod
• Subalgebra.iSupLift
• AlgHom.ker_rangeRestrict
• Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem

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

@@ -5,6 +5,7 @@ Authors: Johan Commelin, Kenny Lau
 -/
 import Mathlib.Algebra.Polynomial.AlgebraMap
 import Mathlib.Algebra.Polynomial.Basic
+import Mathlib.RingTheory.Ideal.Operations
 import Mathlib.RingTheory.MvPowerSeries.Basic
 
 #align_import ring_theory.power_series.basic from "leanprover-community/mathlib"@"2d5739b61641ee4e7e53eca5688a08f66f2e6a60"

Add some basic lemmas about (univariate) power series over fields and their inverses, aiming at proving that they form a DVR.

Co-authored-by: María Inés de Frutos Fernández @mariainesdff

@@ -20,6 +20,10 @@ We prove that if the commutative ring `R` of coefficients is an integral domain,
 then the ring `R⟦X⟧` of formal power series in one variable over `R`
 is an integral domain.
 
+Given a non-zero power series `f`, `divided_by_X_pow_order f` is the power series obtained by
+dividing out the largest power of X that divides `f`, that is its order. This is useful when
+proving that `R⟦X⟧` is a normalization monoid, which is done in `PowerSeries.Inverse`.
+
 -/
 noncomputable section
 
@@ -293,6 +297,16 @@ theorem order_eq_multiplicity_X {R : Type*} [Semiring R] [@DecidableRel R⟦X⟧
 set_option linter.uppercaseLean3 false in
 #align power_series.order_eq_multiplicity_X PowerSeries.order_eq_multiplicity_X
 
+/-- Given a non-zero power series `f`, `divided_by_X_pow_order f` is the power series obtained by
+  dividing out the largest power of X that divides `f`, that is its order-/
+def divided_by_X_pow_order {f : PowerSeries R} (hf : f ≠ 0) : R⟦X⟧ :=
+  (exists_eq_mul_right_of_dvd (X_pow_order_dvd (order_finite_iff_ne_zero.2 hf))).choose
+
+theorem self_eq_X_pow_order_mul_divided_by_X_pow_order {f : R⟦X⟧} (hf : f ≠ 0) :
+    X ^ f.order.get (order_finite_iff_ne_zero.mpr hf) * divided_by_X_pow_order hf = f :=
+  haveI dvd := X_pow_order_dvd (order_finite_iff_ne_zero.mpr hf)
+  (exists_eq_mul_right_of_dvd dvd).choose_spec.symm
+
 end OrderBasic
 
 section OrderZeroNeOne
@@ -305,6 +319,13 @@ theorem order_one : order (1 : R⟦X⟧) = 0 := by
   simpa using order_monomial_of_ne_zero 0 (1 : R) one_ne_zero
 #align power_series.order_one PowerSeries.order_one
 
+/-- The order of an invertible power series is `0`. -/
+theorem order_zero_of_unit {f : PowerSeries R} : IsUnit f → f.order = 0 := by
+  rintro ⟨⟨u, v, hu, hv⟩, hf⟩
+  apply And.left
+  rw [← add_eq_zero_iff, ← hf, ← nonpos_iff_eq_zero, ← @order_one R _ _, ← hu]
+  exact order_mul_ge _ _
+
 /-- The order of the formal power series `X` is `1`. -/
 @[simp]
 theorem order_X : order (X : R⟦X⟧) = 1 := by
@@ -335,6 +356,35 @@ theorem order_mul (φ ψ : R⟦X⟧) : order (φ * ψ) = order φ + order ψ :=
   exact multiplicity.mul X_prime
 #align power_series.order_mul PowerSeries.order_mul
 
+-- Dividing `X` by the maximal power of `X` dividing it leaves `1`.
+@[simp]
+theorem divided_by_X_pow_order_of_X_eq_one : divided_by_X_pow_order X_ne_zero = (1 : R⟦X⟧) := by
+  rw [← mul_eq_left₀ X_ne_zero]
+  simpa only [order_X, X_ne_zero, PartENat.get_one, pow_one, Ne.def,
+    not_false_iff] using self_eq_X_pow_order_mul_divided_by_X_pow_order (@X_ne_zero R _ _)
+
+-- Dividing a power series by the maximal power of `X` dividing it, respects multiplication.
+theorem divided_by_X_pow_orderMul {f g : R⟦X⟧} (hf : f ≠ 0) (hg : g ≠ 0) :
+    divided_by_X_pow_order hf * divided_by_X_pow_order hg =
+      divided_by_X_pow_order (mul_ne_zero hf hg) := by
+  set df := f.order.get (order_finite_iff_ne_zero.mpr hf)
+  set dg := g.order.get (order_finite_iff_ne_zero.mpr hg)
+  set dfg := (f * g).order.get (order_finite_iff_ne_zero.mpr (mul_ne_zero hf hg)) with hdfg
+  have H_add_d : df + dg = dfg := by simp_all only [PartENat.get_add, order_mul f g]
+  have H := self_eq_X_pow_order_mul_divided_by_X_pow_order (mul_ne_zero hf hg)
+  have : f * g = X ^ dfg * (divided_by_X_pow_order hf * divided_by_X_pow_order hg) := by
+    calc
+      f * g = X ^ df * divided_by_X_pow_order hf * (X ^ dg * divided_by_X_pow_order hg) := by
+        rw [self_eq_X_pow_order_mul_divided_by_X_pow_order,
+          self_eq_X_pow_order_mul_divided_by_X_pow_order]
+      _ = X ^ df * X ^ dg * divided_by_X_pow_order hf * divided_by_X_pow_order hg := by ring
+      _ = X ^ (df + dg) * divided_by_X_pow_order hf * divided_by_X_pow_order hg := by rw [pow_add]
+      _ = X ^ dfg * divided_by_X_pow_order hf * divided_by_X_pow_order hg := by rw [H_add_d]
+      _ = X ^ dfg * (divided_by_X_pow_order hf * divided_by_X_pow_order hg) := by rw [mul_assoc]
+  simp [← hdfg, this] at H
+  refine' (IsLeftCancelMulZero.mul_left_cancel_of_ne_zero (pow_ne_zero dfg X_ne_zero) _).symm
+  convert H
+
 end OrderIsDomain
 
 end PowerSeries

Add some basic lemmas about (univariate) power series over fields and their inverses, aiming at proving that they form a DVR.

Co-authored-by: María Inés de Frutos Fernández @mariainesdff

@@ -4,8 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
 -/
 
-import Mathlib.RingTheory.PowerSeries.Basic
+import Mathlib.RingTheory.DedekindDomain.Basic
+import Mathlib.RingTheory.DiscreteValuationRing.Basic
 import Mathlib.RingTheory.MvPowerSeries.Inverse
+import Mathlib.RingTheory.PowerSeries.Basic
+import Mathlib.RingTheory.PowerSeries.Order
+
+
 
 #align_import ring_theory.power_series.basic from "leanprover-community/mathlib"@"2d5739b61641ee4e7e53eca5688a08f66f2e6a60"
 
@@ -18,6 +23,9 @@ the construction.)
 
 Formal (univariate) power series over a local ring form a local ring.
 
+Formal (univariate) power series over a field form a discrete valuation ring, and a normalization
+monoid. The definition `residueFieldOfPowerSeries` provides the isomorphism between the residue
+field of `k⟦X⟧` and `k`, when `k` is a field.
 
 -/
 
@@ -120,18 +128,17 @@ section Field
 variable {k : Type*} [Field k]
 
 /-- The inverse 1/f of a power series f defined over a field -/
-protected def inv : PowerSeries k → PowerSeries k :=
+protected def inv : k⟦X⟧ → k⟦X⟧ :=
   MvPowerSeries.inv
 #align power_series.inv PowerSeries.inv
 
-instance : Inv (PowerSeries k) :=
-  ⟨PowerSeries.inv⟩
+instance : Inv k⟦X⟧ := ⟨PowerSeries.inv⟩
 
-theorem inv_eq_inv_aux (φ : PowerSeries k) : φ⁻¹ = inv.aux (constantCoeff k φ)⁻¹ φ :=
+theorem inv_eq_inv_aux (φ : k⟦X⟧) : φ⁻¹ = inv.aux (constantCoeff k φ)⁻¹ φ :=
   rfl
 #align power_series.inv_eq_inv_aux PowerSeries.inv_eq_inv_aux
 
-theorem coeff_inv (n) (φ : PowerSeries k) :
+theorem coeff_inv (n) (φ : k⟦X⟧) :
     coeff k n φ⁻¹ =
       if n = 0 then (constantCoeff k φ)⁻¹
       else
@@ -142,63 +149,63 @@ theorem coeff_inv (n) (φ : PowerSeries k) :
 #align power_series.coeff_inv PowerSeries.coeff_inv
 
 @[simp]
-theorem constantCoeff_inv (φ : PowerSeries k) : constantCoeff k φ⁻¹ = (constantCoeff k φ)⁻¹ :=
+theorem constantCoeff_inv (φ : k⟦X⟧) : constantCoeff k φ⁻¹ = (constantCoeff k φ)⁻¹ :=
   MvPowerSeries.constantCoeff_inv φ
 #align power_series.constant_coeff_inv PowerSeries.constantCoeff_inv
 
-theorem inv_eq_zero {φ : PowerSeries k} : φ⁻¹ = 0 ↔ constantCoeff k φ = 0 :=
+theorem inv_eq_zero {φ : k⟦X⟧} : φ⁻¹ = 0 ↔ constantCoeff k φ = 0 :=
   MvPowerSeries.inv_eq_zero
 #align power_series.inv_eq_zero PowerSeries.inv_eq_zero
 
 @[simp]
-theorem zero_inv : (0 : PowerSeries k)⁻¹ = 0 :=
+theorem zero_inv : (0 : k⟦X⟧)⁻¹ = 0 :=
   MvPowerSeries.zero_inv
 #align power_series.zero_inv PowerSeries.zero_inv
 
 -- Porting note (#10618): simp can prove this.
 -- @[simp]
-theorem invOfUnit_eq (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) :
+theorem invOfUnit_eq (φ : k⟦X⟧) (h : constantCoeff k φ ≠ 0) :
     invOfUnit φ (Units.mk0 _ h) = φ⁻¹ :=
   MvPowerSeries.invOfUnit_eq _ _
 #align power_series.inv_of_unit_eq PowerSeries.invOfUnit_eq
 
 @[simp]
-theorem invOfUnit_eq' (φ : PowerSeries k) (u : Units k) (h : constantCoeff k φ = u) :
+theorem invOfUnit_eq' (φ : k⟦X⟧) (u : Units k) (h : constantCoeff k φ = u) :
     invOfUnit φ u = φ⁻¹ :=
   MvPowerSeries.invOfUnit_eq' φ _ h
 #align power_series.inv_of_unit_eq' PowerSeries.invOfUnit_eq'
 
 @[simp]
-protected theorem mul_inv_cancel (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) : φ * φ⁻¹ = 1 :=
+protected theorem mul_inv_cancel (φ : k⟦X⟧) (h : constantCoeff k φ ≠ 0) : φ * φ⁻¹ = 1 :=
   MvPowerSeries.mul_inv_cancel φ h
 #align power_series.mul_inv_cancel PowerSeries.mul_inv_cancel
 
 @[simp]
-protected theorem inv_mul_cancel (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) : φ⁻¹ * φ = 1 :=
+protected theorem inv_mul_cancel (φ : k⟦X⟧) (h : constantCoeff k φ ≠ 0) : φ⁻¹ * φ = 1 :=
   MvPowerSeries.inv_mul_cancel φ h
 #align power_series.inv_mul_cancel PowerSeries.inv_mul_cancel
 
-theorem eq_mul_inv_iff_mul_eq {φ₁ φ₂ φ₃ : PowerSeries k} (h : constantCoeff k φ₃ ≠ 0) :
+theorem eq_mul_inv_iff_mul_eq {φ₁ φ₂ φ₃ : k⟦X⟧} (h : constantCoeff k φ₃ ≠ 0) :
     φ₁ = φ₂ * φ₃⁻¹ ↔ φ₁ * φ₃ = φ₂ :=
   MvPowerSeries.eq_mul_inv_iff_mul_eq h
 #align power_series.eq_mul_inv_iff_mul_eq PowerSeries.eq_mul_inv_iff_mul_eq
 
-theorem eq_inv_iff_mul_eq_one {φ ψ : PowerSeries k} (h : constantCoeff k ψ ≠ 0) :
+theorem eq_inv_iff_mul_eq_one {φ ψ : k⟦X⟧} (h : constantCoeff k ψ ≠ 0) :
     φ = ψ⁻¹ ↔ φ * ψ = 1 :=
   MvPowerSeries.eq_inv_iff_mul_eq_one h
 #align power_series.eq_inv_iff_mul_eq_one PowerSeries.eq_inv_iff_mul_eq_one
 
-theorem inv_eq_iff_mul_eq_one {φ ψ : PowerSeries k} (h : constantCoeff k ψ ≠ 0) :
+theorem inv_eq_iff_mul_eq_one {φ ψ : k⟦X⟧} (h : constantCoeff k ψ ≠ 0) :
     ψ⁻¹ = φ ↔ φ * ψ = 1 :=
   MvPowerSeries.inv_eq_iff_mul_eq_one h
 #align power_series.inv_eq_iff_mul_eq_one PowerSeries.inv_eq_iff_mul_eq_one
 
 @[simp]
-protected theorem mul_inv_rev (φ ψ : PowerSeries k) : (φ * ψ)⁻¹ = ψ⁻¹ * φ⁻¹ :=
+protected theorem mul_inv_rev (φ ψ : k⟦X⟧) : (φ * ψ)⁻¹ = ψ⁻¹ * φ⁻¹ :=
   MvPowerSeries.mul_inv_rev _ _
 #align power_series.mul_inv_rev PowerSeries.mul_inv_rev
 
-instance : InvOneClass (PowerSeries k) :=
+instance : InvOneClass k⟦X⟧ :=
   { inferInstanceAs <| InvOneClass <| MvPowerSeries Unit k with }
 
 @[simp]
@@ -208,16 +215,80 @@ set_option linter.uppercaseLean3 false in
 #align power_series.C_inv PowerSeries.C_inv
 
 @[simp]
-theorem X_inv : (X : PowerSeries k)⁻¹ = 0 :=
+theorem X_inv : (X : k⟦X⟧)⁻¹ = 0 :=
   MvPowerSeries.X_inv _
 set_option linter.uppercaseLean3 false in
 #align power_series.X_inv PowerSeries.X_inv
 
 @[simp]
-theorem smul_inv (r : k) (φ : PowerSeries k) : (r • φ)⁻¹ = r⁻¹ • φ⁻¹ :=
+theorem smul_inv (r : k) (φ : k⟦X⟧) : (r • φ)⁻¹ = r⁻¹ • φ⁻¹ :=
   MvPowerSeries.smul_inv _ _
 #align power_series.smul_inv PowerSeries.smul_inv
 
+/-- `firstUnitCoeff` is the non-zero coefficient whose index is `f.order`, seen as a unit of the
+  field. It is obtained using `divided_by_X_pow_order`, defined in `PowerSeries.Order`-/
+def firstUnitCoeff {f : k⟦X⟧} (hf : f ≠ 0) : kˣ :=
+  let d := f.order.get (order_finite_iff_ne_zero.mpr hf)
+  have f_const : coeff k d f ≠ 0 := by apply coeff_order
+  have : Invertible (constantCoeff k (divided_by_X_pow_order hf)) := by
+    apply invertibleOfNonzero
+    convert f_const using 1
+    rw [← coeff_zero_eq_constantCoeff, ← zero_add d]
+    convert (coeff_X_pow_mul (exists_eq_mul_right_of_dvd (X_pow_order_dvd
+      (order_finite_iff_ne_zero.mpr hf))).choose d 0).symm
+    exact (self_eq_X_pow_order_mul_divided_by_X_pow_order hf).symm
+  unitOfInvertible (constantCoeff k (divided_by_X_pow_order hf))
+
+/-- `Inv_divided_by_X_pow_order` is the inverse of the element obtained by diving a non-zero power
+series by the largest power of `X` dividing it. Useful to create a term of type `Units`, done in
+`Unit_divided_by_X_pow_order` -/
+def Inv_divided_by_X_pow_order {f : k⟦X⟧} (hf : f ≠ 0) : k⟦X⟧ :=
+  invOfUnit (divided_by_X_pow_order hf) (firstUnitCoeff hf)
+
+@[simp]
+theorem Inv_divided_by_X_pow_order_rightInv {f : k⟦X⟧} (hf : f ≠ 0) :
+    divided_by_X_pow_order hf * Inv_divided_by_X_pow_order hf = 1 :=
+  mul_invOfUnit (divided_by_X_pow_order hf) (firstUnitCoeff hf) rfl
+
+@[simp]
+theorem Inv_divided_by_X_pow_order_leftInv {f : k⟦X⟧} (hf : f ≠ 0) :
+    (Inv_divided_by_X_pow_order hf) * (divided_by_X_pow_order hf) = 1 := by
+  rw [mul_comm]
+  exact mul_invOfUnit (divided_by_X_pow_order hf) (firstUnitCoeff hf) rfl
+
+open scoped Classical
+
+/-- `Unit_of_divided_by_X_pow_order` is the unit power series obtained by dividing a non-zero
+power series by the largest power of `X` that divides it. -/
+def Unit_of_divided_by_X_pow_order (f : k⟦X⟧) : k⟦X⟧ˣ :=
+  if hf : f = 0 then 1
+  else
+    { val := divided_by_X_pow_order hf
+      inv := Inv_divided_by_X_pow_order hf
+      val_inv := Inv_divided_by_X_pow_order_rightInv hf
+      inv_val := Inv_divided_by_X_pow_order_leftInv hf }
+
+theorem isUnit_divided_by_X_pow_order {f : k⟦X⟧} (hf : f ≠ 0) :
+    IsUnit (divided_by_X_pow_order hf) :=
+  ⟨Unit_of_divided_by_X_pow_order f,
+    by simp only [Unit_of_divided_by_X_pow_order, dif_neg hf, Units.val_mk]⟩
+
+theorem Unit_of_divided_by_X_pow_order_nonzero {f : k⟦X⟧} (hf : f ≠ 0) :
+    ↑(Unit_of_divided_by_X_pow_order f) = divided_by_X_pow_order hf := by
+  simp only [Unit_of_divided_by_X_pow_order, dif_neg hf, Units.val_mk]
+
+@[simp]
+theorem Unit_of_divided_by_X_pow_order_zero : Unit_of_divided_by_X_pow_order (0 : k⟦X⟧) = 1 := by
+  simp only [Unit_of_divided_by_X_pow_order, dif_pos]
+
+theorem eq_divided_by_X_pow_order_Iff_Unit {f : k⟦X⟧} (hf : f ≠ 0) :
+    f = divided_by_X_pow_order hf ↔ IsUnit f :=
+  ⟨fun h => by rw [h]; exact isUnit_divided_by_X_pow_order hf, fun h => by
+    have : f.order.get (order_finite_iff_ne_zero.mpr hf) = 0 := by
+      simp only [order_zero_of_unit h, PartENat.get_zero]
+    convert (self_eq_X_pow_order_mul_divided_by_X_pow_order hf).symm
+    simp only [this, pow_zero, one_mul]⟩
+
 end Field
 
 section LocalRing
@@ -236,6 +307,81 @@ instance : LocalRing R⟦X⟧ :=
 
 end LocalRing
 
+section DiscreteValuationRing
+
+variable {k : Type*} [Field k]
+
+open DiscreteValuationRing
+
+theorem hasUnitMulPowIrreducibleFactorization :
+    HasUnitMulPowIrreducibleFactorization k⟦X⟧ :=
+  ⟨X, And.intro X_irreducible
+      (by
+        intro f hf
+        use f.order.get (order_finite_iff_ne_zero.mpr hf)
+        use Unit_of_divided_by_X_pow_order f
+        simp only [Unit_of_divided_by_X_pow_order_nonzero hf]
+        exact self_eq_X_pow_order_mul_divided_by_X_pow_order hf)⟩
+
+instance : UniqueFactorizationMonoid k⟦X⟧ :=
+  hasUnitMulPowIrreducibleFactorization.toUniqueFactorizationMonoid
+
+instance : DiscreteValuationRing k⟦X⟧ :=
+  ofHasUnitMulPowIrreducibleFactorization hasUnitMulPowIrreducibleFactorization
+
+instance isNoetherianRing : IsNoetherianRing k⟦X⟧ :=
+  PrincipalIdealRing.isNoetherianRing
+
+/-- The maximal ideal of `k⟦X⟧` is generated by `X`. -/
+theorem maximalIdeal_eq_span_X : LocalRing.maximalIdeal (k⟦X⟧) = Ideal.span {X} := by
+  have hX : (Ideal.span {(X : k⟦X⟧)}).IsMaximal := by
+    rw [Ideal.isMaximal_iff]
+    constructor
+    · rw [Ideal.mem_span_singleton]
+      exact Prime.not_dvd_one X_prime
+    · intro I f hI hfX hfI
+      rw [Ideal.mem_span_singleton, X_dvd_iff] at hfX
+      have hfI0 : C k (f 0) ∈ I := by
+        have : C k (f 0) = f - (f - C k (f 0)) := by rw [sub_sub_cancel]
+        rw [this]
+        apply Ideal.sub_mem I hfI
+        apply hI
+        rw [Ideal.mem_span_singleton, X_dvd_iff, map_sub, constantCoeff_C, ←
+          coeff_zero_eq_constantCoeff_apply, sub_eq_zero, coeff_zero_eq_constantCoeff]
+        rfl
+      rw [← Ideal.eq_top_iff_one]
+      apply Ideal.eq_top_of_isUnit_mem I hfI0 (IsUnit.map (C k) (Ne.isUnit hfX))
+  rw [LocalRing.eq_maximalIdeal hX]
+
+instance : NormalizationMonoid k⟦X⟧ where
+  normUnit f := (Unit_of_divided_by_X_pow_order f)⁻¹
+  normUnit_zero := by simp only [Unit_of_divided_by_X_pow_order_zero, inv_one]
+  normUnit_mul  := fun hf hg => by
+    simp only [← mul_inv, inv_inj]
+    simp only [Unit_of_divided_by_X_pow_order_nonzero (mul_ne_zero hf hg),
+      Unit_of_divided_by_X_pow_order_nonzero hf, Unit_of_divided_by_X_pow_order_nonzero hg,
+      Units.ext_iff, val_unitOfInvertible, Units.val_mul, divided_by_X_pow_orderMul]
+  normUnit_coe_units := by
+    intro u
+    set u₀ := u.1 with hu
+    have h₀ : IsUnit u₀ := ⟨u, hu.symm⟩
+    rw [inv_inj, Units.ext_iff, ← hu, Unit_of_divided_by_X_pow_order_nonzero h₀.ne_zero]
+    exact ((eq_divided_by_X_pow_order_Iff_Unit h₀.ne_zero).mpr h₀).symm
+
+open LocalRing
+
+theorem ker_coeff_eq_max_ideal : RingHom.ker (constantCoeff k) = maximalIdeal _ :=
+  Ideal.ext fun _ => by
+    rw [RingHom.mem_ker, maximalIdeal_eq_span_X, Ideal.mem_span_singleton, X_dvd_iff]
+
+/-- The ring isomorphism between the residue field of the ring of power series valued in a field `K`
+and `K` itself. -/
+def residueFieldOfPowerSeries : ResidueField k⟦X⟧ ≃+* k :=
+  (Ideal.quotEquivOfEq (ker_coeff_eq_max_ideal).symm).trans
+    (RingHom.quotientKerEquivOfSurjective PowerSeries.constantCoeff_surj)
+
+end DiscreteValuationRing
+
 
 end PowerSeries
 

Add some basic lemmas about (univariate) power series over fields and their inverses, aiming at proving that they form a DVR.

Co-authored-by: María Inés de Frutos Fernández @mariainesdff

@@ -166,6 +166,10 @@ theorem ext_iff {φ ψ : R⟦X⟧} : φ = ψ ↔ ∀ n, coeff R n φ = coeff R n
   ⟨fun h n => congr_arg (coeff R n) h, ext⟩
 #align power_series.ext_iff PowerSeries.ext_iff
 
+instance [Subsingleton R] : Subsingleton R⟦X⟧ := by
+  simp only [subsingleton_iff, ext_iff]
+  exact fun _ _ _ ↦ (subsingleton_iff).mp (by infer_instance) _ _
+
 /-- Constructor for formal power series. -/
 def mk {R} (f : ℕ → R) : R⟦X⟧ := fun s => f (s ())
 #align power_series.mk PowerSeries.mk
@@ -261,6 +265,16 @@ theorem coeff_ne_zero_C {a : R} {n : ℕ} (h : n ≠ 0) : coeff R n (C R a) = 0
 theorem coeff_succ_C {a : R} {n : ℕ} : coeff R (n + 1) (C R a) = 0 :=
   coeff_ne_zero_C n.succ_ne_zero
 
+theorem C_injective : Function.Injective (C R) := by
+  intro a b H
+  have := (ext_iff (φ := C R a) (ψ := C R b)).mp H 0
+  rwa [coeff_zero_C, coeff_zero_C] at this
+
+protected theorem subsingleton_iff : Subsingleton R⟦X⟧ ↔ Subsingleton R := by
+  refine ⟨fun h ↦ ?_, fun _ ↦ inferInstance⟩
+  rw [subsingleton_iff] at h ⊢
+  exact fun a b ↦ C_injective (h (C R a) (C R b))
+
 theorem X_eq : (X : R⟦X⟧) = monomial R 1 1 :=
   rfl
 set_option linter.uppercaseLean3 false in
@@ -400,6 +414,9 @@ theorem coeff_zero_X_mul (φ : R⟦X⟧) : coeff R 0 (X * φ) = 0 := by simp
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_zero_X_mul PowerSeries.coeff_zero_X_mul
 
+theorem constantCoeff_surj : Function.Surjective (constantCoeff R) :=
+  fun r => ⟨(C R) r, constantCoeff_C r⟩
+
 -- The following section duplicates the API of `Data.Polynomial.Coeff` and should attempt to keep
 -- up to date with that
 section
@@ -655,6 +672,19 @@ section CommRing
 
 variable {A : Type*} [CommRing A]
 
+theorem not_isField : ¬IsField A⟦X⟧ := by
+  by_cases hA : Subsingleton A
+  · exact not_isField_of_subsingleton _
+  · nontriviality A
+    rw [Ring.not_isField_iff_exists_ideal_bot_lt_and_lt_top]
+    use Ideal.span {X}
+    constructor
+    · rw [bot_lt_iff_ne_bot, Ne.def, Ideal.span_singleton_eq_bot]
+      exact X_ne_zero
+    · rw [lt_top_iff_ne_top, Ne.def, Ideal.eq_top_iff_one, Ideal.mem_span_singleton,
+        X_dvd_iff, constantCoeff_one]
+      exact one_ne_zero
+
 @[simp]
 theorem rescale_X (a : A) : rescale a X = C A a * X := by
   ext
@@ -758,6 +788,9 @@ theorem X_prime : Prime (X : R⟦X⟧) := by
 set_option linter.uppercaseLean3 false in
 #align power_series.X_prime PowerSeries.X_prime
 
+/-- The variable of the power series ring over an integral domain is irreducible. -/
+theorem X_irreducible : Irreducible (X : R⟦X⟧) := X_prime.irreducible
+
 theorem rescale_injective {a : R} (ha : a ≠ 0) : Function.Injective (rescale a) := by
   intro p q h
   rw [PowerSeries.ext_iff] at *

A mix of various changes; generated with a script and manually tweaked.

@@ -400,7 +400,7 @@ theorem coeff_zero_X_mul (φ : R⟦X⟧) : coeff R 0 (X * φ) = 0 := by simp
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_zero_X_mul PowerSeries.coeff_zero_X_mul
 
--- The following section duplicates the api of `data.polynomial.coeff` and should attempt to keep
+-- The following section duplicates the API of `Data.Polynomial.Coeff` and should attempt to keep
 -- up to date with that
 section
 

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -202,13 +202,13 @@ theorem trunc_coe_eq_self {n} {f : R[X]} (hn : natDegree f < n) : trunc n (f : R
     exact coeff_eq_zero_of_natDegree_lt <| lt_of_lt_of_le hn h
 
 /-- The function `coeff n : R⟦X⟧ → R` is continuous. I.e. `coeff n f` depends only on a sufficiently
-long truncation of the power series `f`.-/
+long truncation of the power series `f`. -/
 theorem coeff_coe_trunc_of_lt {n m} {f : R⟦X⟧} (h : n < m) :
     coeff R n (trunc m f) = coeff R n f := by
   rwa [coeff_coe, coeff_trunc, if_pos]
 
 /-- The `n`-th coefficient of `f*g` may be calculated
-from the truncations of `f` and `g`.-/
+from the truncations of `f` and `g`. -/
 theorem coeff_mul_eq_coeff_trunc_mul_trunc₂ {n a b} (f g) (ha : n < a) (hb : n < b) :
     coeff R n (f * g) = coeff R n (trunc a f * trunc b g) := by
   symm

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -54,7 +54,7 @@ def order (φ : R⟦X⟧) : PartENat :=
   if h : φ = 0 then ⊤ else Nat.find (exists_coeff_ne_zero_iff_ne_zero.mpr h)
 #align power_series.order PowerSeries.order
 
-/-- The order of the `0` power series is infinite.-/
+/-- The order of the `0` power series is infinite. -/
 @[simp]
 theorem order_zero : order (0 : R⟦X⟧) = ⊤ :=
   dif_pos rfl
@@ -71,7 +71,7 @@ theorem order_finite_iff_ne_zero : (order φ).Dom ↔ φ ≠ 0 := by
 #align power_series.order_finite_iff_ne_zero PowerSeries.order_finite_iff_ne_zero
 
 /-- If the order of a formal power series is finite,
-then the coefficient indexed by the order is nonzero.-/
+then the coefficient indexed by the order is nonzero. -/
 theorem coeff_order (h : (order φ).Dom) : coeff R (φ.order.get h) φ ≠ 0 := by
   classical
   simp only [order, order_finite_iff_ne_zero.mp h, not_false_iff, dif_neg, PartENat.get_natCast']
@@ -80,7 +80,7 @@ theorem coeff_order (h : (order φ).Dom) : coeff R (φ.order.get h) φ ≠ 0 :=
 #align power_series.coeff_order PowerSeries.coeff_order
 
 /-- If the `n`th coefficient of a formal power series is nonzero,
-then the order of the power series is less than or equal to `n`.-/
+then the order of the power series is less than or equal to `n`. -/
 theorem order_le (n : ℕ) (h : coeff R n φ ≠ 0) : order φ ≤ n := by
   classical
   rw [order, dif_neg]
@@ -90,20 +90,20 @@ theorem order_le (n : ℕ) (h : coeff R n φ ≠ 0) : order φ ≤ n := by
 #align power_series.order_le PowerSeries.order_le
 
 /-- The `n`th coefficient of a formal power series is `0` if `n` is strictly
-smaller than the order of the power series.-/
+smaller than the order of the power series. -/
 theorem coeff_of_lt_order (n : ℕ) (h : ↑n < order φ) : coeff R n φ = 0 := by
   contrapose! h
   exact order_le _ h
 #align power_series.coeff_of_lt_order PowerSeries.coeff_of_lt_order
 
-/-- The `0` power series is the unique power series with infinite order.-/
+/-- The `0` power series is the unique power series with infinite order. -/
 @[simp]
 theorem order_eq_top {φ : R⟦X⟧} : φ.order = ⊤ ↔ φ = 0 :=
   PartENat.not_dom_iff_eq_top.symm.trans order_finite_iff_ne_zero.not_left
 #align power_series.order_eq_top PowerSeries.order_eq_top
 
 /-- The order of a formal power series is at least `n` if
-the `i`th coefficient is `0` for all `i < n`.-/
+the `i`th coefficient is `0` for all `i < n`. -/
 theorem nat_le_order (φ : R⟦X⟧) (n : ℕ) (h : ∀ i < n, coeff R i φ = 0) : ↑n ≤ order φ := by
   by_contra H; rw [not_le] at H
   have : (order φ).Dom := PartENat.dom_of_le_natCast H.le
@@ -112,7 +112,7 @@ theorem nat_le_order (φ : R⟦X⟧) (n : ℕ) (h : ∀ i < n, coeff R i φ = 0)
 #align power_series.nat_le_order PowerSeries.nat_le_order
 
 /-- The order of a formal power series is at least `n` if
-the `i`th coefficient is `0` for all `i < n`.-/
+the `i`th coefficient is `0` for all `i < n`. -/
 theorem le_order (φ : R⟦X⟧) (n : PartENat) (h : ∀ i : ℕ, ↑i < n → coeff R i φ = 0) :
     n ≤ order φ := by
   induction n using PartENat.casesOn
@@ -125,7 +125,7 @@ theorem le_order (φ : R⟦X⟧) (n : PartENat) (h : ∀ i : ℕ, ↑i < n → c
 #align power_series.le_order PowerSeries.le_order
 
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
-and the `i`th coefficient is `0` for all `i < n`.-/
+and the `i`th coefficient is `0` for all `i < n`. -/
 theorem order_eq_nat {φ : R⟦X⟧} {n : ℕ} :
     order φ = n ↔ coeff R n φ ≠ 0 ∧ ∀ i, i < n → coeff R i φ = 0 := by
   classical
@@ -135,7 +135,7 @@ theorem order_eq_nat {φ : R⟦X⟧} {n : ℕ} :
 #align power_series.order_eq_nat PowerSeries.order_eq_nat
 
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
-and the `i`th coefficient is `0` for all `i < n`.-/
+and the `i`th coefficient is `0` for all `i < n`. -/
 theorem order_eq {φ : R⟦X⟧} {n : PartENat} :
     order φ = n ↔ (∀ i : ℕ, ↑i = n → coeff R i φ ≠ 0) ∧ ∀ i : ℕ, ↑i < n → coeff R i φ = 0 := by
   induction n using PartENat.casesOn
@@ -153,7 +153,7 @@ theorem order_eq {φ : R⟦X⟧} {n : PartENat} :
 #align power_series.order_eq PowerSeries.order_eq
 
 /-- The order of the sum of two formal power series
- is at least the minimum of their orders.-/
+ is at least the minimum of their orders. -/
 theorem le_order_add (φ ψ : R⟦X⟧) : min (order φ) (order ψ) ≤ order (φ + ψ) := by
   refine' le_order _ _ _
   simp (config := { contextual := true }) [coeff_of_lt_order]
@@ -176,7 +176,7 @@ private theorem order_add_of_order_eq.aux (φ ψ : R⟦X⟧) (_h : order φ ≠
 -- #align power_series.order_add_of_order_eq.aux power_series.order_add_of_order_eq.aux
 
 /-- The order of the sum of two formal power series
- is the minimum of their orders if their orders differ.-/
+ is the minimum of their orders if their orders differ. -/
 theorem order_add_of_order_eq (φ ψ : R⟦X⟧) (h : order φ ≠ order ψ) :
     order (φ + ψ) = order φ ⊓ order ψ := by
   refine' le_antisymm _ (le_order_add _ _)
@@ -188,7 +188,7 @@ theorem order_add_of_order_eq (φ ψ : R⟦X⟧) (h : order φ ≠ order ψ) :
 #align power_series.order_add_of_order_eq PowerSeries.order_add_of_order_eq
 
 /-- The order of the product of two formal power series
- is at least the sum of their orders.-/
+ is at least the sum of their orders. -/
 theorem order_mul_ge (φ ψ : R⟦X⟧) : order φ + order ψ ≤ order (φ * ψ) := by
   apply le_order
   intro n hn; rw [coeff_mul, Finset.sum_eq_zero]
@@ -203,7 +203,7 @@ theorem order_mul_ge (φ ψ : R⟦X⟧) : order φ + order ψ ≤ order (φ * ψ
   rw [← Nat.cast_add, hij]
 #align power_series.order_mul_ge PowerSeries.order_mul_ge
 
-/-- The order of the monomial `a*X^n` is infinite if `a = 0` and `n` otherwise.-/
+/-- The order of the monomial `a*X^n` is infinite if `a = 0` and `n` otherwise. -/
 theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
     order (monomial R n a) = if a = 0 then (⊤ : PartENat) else n := by
   split_ifs with h
@@ -217,7 +217,7 @@ theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
       exact ne_of_lt hi
 #align power_series.order_monomial PowerSeries.order_monomial
 
-/-- The order of the monomial `a*X^n` is `n` if `a ≠ 0`.-/
+/-- The order of the monomial `a*X^n` is `n` if `a ≠ 0`. -/
 theorem order_monomial_of_ne_zero (n : ℕ) (a : R) (h : a ≠ 0) : order (monomial R n a) = n := by
   classical
   rw [order_monomial, if_neg h]
@@ -299,20 +299,20 @@ section OrderZeroNeOne
 
 variable [Semiring R] [Nontrivial R]
 
-/-- The order of the formal power series `1` is `0`.-/
+/-- The order of the formal power series `1` is `0`. -/
 @[simp]
 theorem order_one : order (1 : R⟦X⟧) = 0 := by
   simpa using order_monomial_of_ne_zero 0 (1 : R) one_ne_zero
 #align power_series.order_one PowerSeries.order_one
 
-/-- The order of the formal power series `X` is `1`.-/
+/-- The order of the formal power series `X` is `1`. -/
 @[simp]
 theorem order_X : order (X : R⟦X⟧) = 1 := by
   simpa only [Nat.cast_one] using order_monomial_of_ne_zero 1 (1 : R) one_ne_zero
 set_option linter.uppercaseLean3 false in
 #align power_series.order_X PowerSeries.order_X
 
-/-- The order of the formal power series `X^n` is `n`.-/
+/-- The order of the formal power series `X^n` is `n`. -/
 @[simp]
 theorem order_X_pow (n : ℕ) : order ((X : R⟦X⟧) ^ n) = n := by
   rw [X_pow_eq, order_monomial_of_ne_zero]
@@ -328,7 +328,7 @@ section OrderIsDomain
 variable [CommRing R] [IsDomain R]
 
 /-- The order of the product of two formal power series over an integral domain
- is the sum of their orders.-/
+ is the sum of their orders. -/
 theorem order_mul (φ ψ : R⟦X⟧) : order (φ * ψ) = order φ + order ψ := by
   classical
   simp_rw [order_eq_multiplicity_X]

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -74,7 +74,7 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : R⟦X⟧) :
     · simpa [Finsupp.single_eq_same] using hh ()
 #align power_series.coeff_inv_aux PowerSeries.coeff_inv_aux
 
-/-- A formal power series is invertible if the constant coefficient is invertible.-/
+/-- A formal power series is invertible if the constant coefficient is invertible. -/
 def invOfUnit (φ : R⟦X⟧) (u : Rˣ) : R⟦X⟧ :=
   MvPowerSeries.invOfUnit φ u
 #align power_series.inv_of_unit PowerSeries.invOfUnit

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -136,12 +136,12 @@ section Semiring
 
 variable (R) [Semiring R]
 
-/-- The `n`th coefficient of a formal power series.-/
+/-- The `n`th coefficient of a formal power series. -/
 def coeff (n : ℕ) : R⟦X⟧ →ₗ[R] R :=
   MvPowerSeries.coeff R (single () n)
 #align power_series.coeff PowerSeries.coeff
 
-/-- The `n`th monomial with coefficient `a` as formal power series.-/
+/-- The `n`th monomial with coefficient `a` as formal power series. -/
 def monomial (n : ℕ) : R →ₗ[R] R⟦X⟧ :=
   MvPowerSeries.monomial R (single () n)
 #align power_series.monomial PowerSeries.monomial
@@ -152,7 +152,7 @@ theorem coeff_def {s : Unit →₀ ℕ} {n : ℕ} (h : s () = n) : coeff R n = M
   erw [coeff, ← h, ← Finsupp.unique_single s]
 #align power_series.coeff_def PowerSeries.coeff_def
 
-/-- Two formal power series are equal if all their coefficients are equal.-/
+/-- Two formal power series are equal if all their coefficients are equal. -/
 @[ext]
 theorem ext {φ ψ : R⟦X⟧} (h : ∀ n, coeff R n φ = coeff R n ψ) : φ = ψ :=
   MvPowerSeries.ext fun n => by
@@ -161,12 +161,12 @@ theorem ext {φ ψ : R⟦X⟧} (h : ∀ n, coeff R n φ = coeff R n ψ) : φ = 
     rfl
 #align power_series.ext PowerSeries.ext
 
-/-- Two formal power series are equal if all their coefficients are equal.-/
+/-- Two formal power series are equal if all their coefficients are equal. -/
 theorem ext_iff {φ ψ : R⟦X⟧} : φ = ψ ↔ ∀ n, coeff R n φ = coeff R n ψ :=
   ⟨fun h n => congr_arg (coeff R n) h, ext⟩
 #align power_series.ext_iff PowerSeries.ext_iff
 
-/-- Constructor for formal power series.-/
+/-- Constructor for formal power series. -/
 def mk {R} (f : ℕ → R) : R⟦X⟧ := fun s => f (s ())
 #align power_series.mk PowerSeries.mk
 
@@ -203,7 +203,7 @@ def constantCoeff : R⟦X⟧ →+* R :=
   MvPowerSeries.constantCoeff Unit R
 #align power_series.constant_coeff PowerSeries.constantCoeff
 
-/-- The constant formal power series.-/
+/-- The constant formal power series. -/
 def C : R →+* R⟦X⟧ :=
   MvPowerSeries.C Unit R
 set_option linter.uppercaseLean3 false in
@@ -211,7 +211,7 @@ set_option linter.uppercaseLean3 false in
 
 variable {R}
 
-/-- The variable of the formal power series ring.-/
+/-- The variable of the formal power series ring. -/
 def X : R⟦X⟧ :=
   MvPowerSeries.X ()
 set_option linter.uppercaseLean3 false in
@@ -466,7 +466,7 @@ set_option linter.uppercaseLean3 false in
 
 end
 
-/-- If a formal power series is invertible, then so is its constant coefficient.-/
+/-- If a formal power series is invertible, then so is its constant coefficient. -/
 theorem isUnit_constantCoeff (φ : R⟦X⟧) (h : IsUnit φ) : IsUnit (constantCoeff R φ) :=
   MvPowerSeries.isUnit_constantCoeff φ h
 #align power_series.is_unit_constant_coeff PowerSeries.isUnit_constantCoeff
@@ -498,7 +498,7 @@ section Map
 variable {S : Type*} {T : Type*} [Semiring S] [Semiring T]
 variable (f : R →+* S) (g : S →+* T)
 
-/-- The map between formal power series induced by a map on the coefficients.-/
+/-- The map between formal power series induced by a map on the coefficients. -/
 def map : R⟦X⟧ →+* S⟦X⟧ :=
   MvPowerSeries.map _ f
 #align power_series.map PowerSeries.map
@@ -738,7 +738,7 @@ section IsDomain
 variable [CommRing R] [IsDomain R]
 
 /-- The ideal spanned by the variable in the power series ring
- over an integral domain is a prime ideal.-/
+ over an integral domain is a prime ideal. -/
 theorem span_X_isPrime : (Ideal.span ({X} : Set R⟦X⟧)).IsPrime := by
   suffices Ideal.span ({X} : Set R⟦X⟧) = RingHom.ker (constantCoeff R) by
     rw [this]
@@ -749,7 +749,7 @@ theorem span_X_isPrime : (Ideal.span ({X} : Set R⟦X⟧)).IsPrime := by
 set_option linter.uppercaseLean3 false in
 #align power_series.span_X_is_prime PowerSeries.span_X_isPrime
 
-/-- The variable of the power series ring over an integral domain is prime.-/
+/-- The variable of the power series ring over an integral domain is prime. -/
 theorem X_prime : Prime (X : R⟦X⟧) := by
   rw [← Ideal.span_singleton_prime]
   · exact span_X_isPrime
@@ -798,12 +798,12 @@ open Finsupp Polynomial
 variable {σ : Type*} {R : Type*} [CommSemiring R] (φ ψ : R[X])
 
 -- Porting note: added so we can add the `@[coe]` attribute
-/-- The natural inclusion from polynomials into formal power series.-/
+/-- The natural inclusion from polynomials into formal power series. -/
 @[coe]
 def ToPowerSeries : R[X] → (PowerSeries R) := fun φ =>
   PowerSeries.mk fun n => coeff φ n
 
-/-- The natural inclusion from polynomials into formal power series.-/
+/-- The natural inclusion from polynomials into formal power series. -/
 instance coeToPowerSeries : Coe R[X] (PowerSeries R) :=
   ⟨ToPowerSeries⟩
 #align polynomial.coe_to_power_series Polynomial.coeToPowerSeries

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -61,7 +61,7 @@ well-founded recursion on the coefficients of the inverse.
 /-- Auxiliary definition that unifies
  the totalised inverse formal power series `(_)⁻¹` and
  the inverse formal power series that depends on
- an inverse of the constant coefficient `invOfUnit`.-/
+ an inverse of the constant coefficient `invOfUnit`. -/
 protected noncomputable def inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerSeries σ R
   | n =>
     letI := Classical.decEq σ
@@ -84,7 +84,7 @@ theorem coeff_inv_aux [DecidableEq σ] (n : σ →₀ ℕ) (a : R) (φ : MvPower
     rfl
 #align mv_power_series.coeff_inv_aux MvPowerSeries.coeff_inv_aux
 
-/-- A multivariate formal power series is invertible if the constant coefficient is invertible.-/
+/-- A multivariate formal power series is invertible if the constant coefficient is invertible. -/
 def invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) : MvPowerSeries σ R :=
   inv.aux (↑u⁻¹) φ
 #align mv_power_series.inv_of_unit MvPowerSeries.invOfUnit

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -54,7 +54,7 @@ open BigOperators
 open Finset (antidiagonal mem_antidiagonal)
 
 /-- Multivariate formal power series, where `σ` is the index set of the variables
-and `R` is the coefficient ring.-/
+and `R` is the coefficient ring. -/
 def MvPowerSeries (σ : Type*) (R : Type*) :=
   (σ →₀ ℕ) → R
 #align mv_power_series MvPowerSeries
@@ -107,21 +107,21 @@ def monomial (n : σ →₀ ℕ) : R →ₗ[R] MvPowerSeries σ R :=
   LinearMap.stdBasis R (fun _ ↦ R) n
 #align mv_power_series.monomial MvPowerSeries.monomial
 
-/-- The `n`th coefficient of a multivariate formal power series.-/
+/-- The `n`th coefficient of a multivariate formal power series. -/
 def coeff (n : σ →₀ ℕ) : MvPowerSeries σ R →ₗ[R] R :=
   LinearMap.proj n
 #align mv_power_series.coeff MvPowerSeries.coeff
 
 variable {R}
 
-/-- Two multivariate formal power series are equal if all their coefficients are equal.-/
+/-- Two multivariate formal power series are equal if all their coefficients are equal. -/
 @[ext]
 theorem ext {φ ψ} (h : ∀ n : σ →₀ ℕ, coeff R n φ = coeff R n ψ) : φ = ψ :=
   funext h
 #align mv_power_series.ext MvPowerSeries.ext
 
 /-- Two multivariate formal power series are equal
- if and only if all their coefficients are equal.-/
+ if and only if all their coefficients are equal. -/
 theorem ext_iff {φ ψ : MvPowerSeries σ R} : φ = ψ ↔ ∀ n : σ →₀ ℕ, coeff R n φ = coeff R n ψ :=
   Function.funext_iff
 #align mv_power_series.ext_iff MvPowerSeries.ext_iff
@@ -336,7 +336,7 @@ theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
 
 variable (σ) (R)
 
-/-- The constant multivariate formal power series.-/
+/-- The constant multivariate formal power series. -/
 def C : R →+* MvPowerSeries σ R :=
   { monomial R (0 : σ →₀ ℕ) with
     map_one' := rfl
@@ -369,7 +369,7 @@ theorem coeff_zero_C (a : R) : coeff R (0 : σ →₀ ℕ) (C σ R a) = a :=
 set_option linter.uppercaseLean3 false in
 #align mv_power_series.coeff_zero_C MvPowerSeries.coeff_zero_C
 
-/-- The variables of the multivariate formal power series ring.-/
+/-- The variables of the multivariate formal power series ring. -/
 def X (s : σ) : MvPowerSeries σ R :=
   monomial R (single s 1) 1
 set_option linter.uppercaseLean3 false in
@@ -449,7 +449,7 @@ set_option linter.uppercaseLean3 false in
 
 variable (σ) (R)
 
-/-- The constant coefficient of a formal power series.-/
+/-- The constant coefficient of a formal power series. -/
 def constantCoeff : MvPowerSeries σ R →+* R :=
   { coeff R (0 : σ →₀ ℕ) with
     toFun := coeff R (0 : σ →₀ ℕ)
@@ -501,7 +501,7 @@ set_option linter.uppercaseLean3 false in
 #align mv_power_series.constant_coeff_X MvPowerSeries.constantCoeff_X
 
 /-- If a multivariate formal power series is invertible,
- then so is its constant coefficient.-/
+ then so is its constant coefficient. -/
 theorem isUnit_constantCoeff (φ : MvPowerSeries σ R) (h : IsUnit φ) :
     IsUnit (constantCoeff σ R φ) :=
   h.map _
@@ -544,7 +544,7 @@ variable {S T : Type*} [Semiring R] [Semiring S] [Semiring T]
 variable (f : R →+* S) (g : S →+* T)
 variable (σ)
 
-/-- The map between multivariate formal power series induced by a map on the coefficients.-/
+/-- The map between multivariate formal power series induced by a map on the coefficients. -/
 def map : MvPowerSeries σ R →+* MvPowerSeries σ S where
   toFun φ n := f <| coeff R n φ
   map_zero' := ext fun _n => f.map_zero
@@ -774,12 +774,12 @@ open Finsupp
 variable {σ : Type*} {R : Type*} [CommSemiring R] (φ ψ : MvPolynomial σ R)
 
 -- Porting note: added so we can add the `@[coe]` attribute
-/-- The natural inclusion from multivariate polynomials into multivariate formal power series.-/
+/-- The natural inclusion from multivariate polynomials into multivariate formal power series. -/
 @[coe]
 def toMvPowerSeries : MvPolynomial σ R → MvPowerSeries σ R :=
   fun φ n => coeff n φ
 
-/-- The natural inclusion from multivariate polynomials into multivariate formal power series.-/
+/-- The natural inclusion from multivariate polynomials into multivariate formal power series. -/
 instance coeToMvPowerSeries : Coe (MvPolynomial σ R) (MvPowerSeries σ R) :=
   ⟨toMvPowerSeries⟩
 #align mv_polynomial.coe_to_mv_power_series MvPolynomial.coeToMvPowerSeries

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

@@ -3,10 +3,9 @@ Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
 -/
-
+import Mathlib.Algebra.Polynomial.Coeff
+import Mathlib.Algebra.Polynomial.Degree.Lemmas
 import Mathlib.RingTheory.PowerSeries.Basic
-import Mathlib.Data.Polynomial.Coeff
-import Mathlib.Data.Polynomial.Degree.Lemmas
 
 #align_import ring_theory.power_series.basic from "leanprover-community/mathlib"@"2d5739b61641ee4e7e53eca5688a08f66f2e6a60"
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
 -/
+import Mathlib.Algebra.Polynomial.AlgebraMap
+import Mathlib.Algebra.Polynomial.Basic
 import Mathlib.RingTheory.MvPowerSeries.Basic
-import Mathlib.Data.Polynomial.Basic
-import Mathlib.Data.Polynomial.AlgebraMap
 
 #align_import ring_theory.power_series.basic from "leanprover-community/mathlib"@"2d5739b61641ee4e7e53eca5688a08f66f2e6a60"
 

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

@@ -4,10 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
 -/
 
+import Mathlib.Algebra.MvPolynomial.Basic
+import Mathlib.Data.Finset.PiAntidiagonal
 import Mathlib.LinearAlgebra.StdBasis
 import Mathlib.Tactic.Linarith
-import Mathlib.Data.Finset.PiAntidiagonal
-import Mathlib.Data.MvPolynomial.Basic
 
 #align_import ring_theory.power_series.basic from "leanprover-community/mathlib"@"2d5739b61641ee4e7e53eca5688a08f66f2e6a60"
 

@@ -98,14 +98,8 @@ theorem coeff_of_lt_order (n : ℕ) (h : ↑n < order φ) : coeff R n φ = 0 :=
 
 /-- The `0` power series is the unique power series with infinite order.-/
 @[simp]
-theorem order_eq_top {φ : R⟦X⟧} : φ.order = ⊤ ↔ φ = 0 := by
-  constructor
-  · intro h
-    ext n
-    rw [(coeff R n).map_zero, coeff_of_lt_order]
-    simp [h]
-  · rintro rfl
-    exact order_zero
+theorem order_eq_top {φ : R⟦X⟧} : φ.order = ⊤ ↔ φ = 0 :=
+  PartENat.not_dom_iff_eq_top.symm.trans order_finite_iff_ne_zero.not_left
 #align power_series.order_eq_top PowerSeries.order_eq_top
 
 /-- The order of a formal power series is at least `n` if

@@ -719,7 +719,7 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : R⟦X⟧)
       exact ne_of_lt this hij.symm
     contrapose! hne
     obtain rfl := le_antisymm hi hne
-    simpa [Ne.def, Prod.mk.inj_iff] using (add_right_inj m).mp hij
+    simpa [Ne, Prod.mk.inj_iff] using (add_right_inj m).mp hij
   · contrapose!
     intro
     rw [mem_antidiagonal]

@@ -753,7 +753,7 @@ theorem algebraMap_apply {r : R} :
 instance [Nonempty σ] [Nontrivial R] : Nontrivial (Subalgebra R (MvPowerSeries σ R)) :=
   ⟨⟨⊥, ⊤, by
       classical
-      rw [Ne.def, SetLike.ext_iff, not_forall]
+      rw [Ne, SetLike.ext_iff, not_forall]
       inhabit σ
       refine' ⟨X default, _⟩
       simp only [Algebra.mem_bot, not_exists, Set.mem_range, iff_true_iff, Algebra.mem_top]

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -188,7 +188,8 @@ theorem trunc_trunc_mul_trunc {n} (f g : R⟦X⟧) :
   | zero =>
     rw [pow_zero, pow_zero]
   | succ a ih =>
-    rw [pow_succ, pow_succ, trunc_trunc_mul, ← trunc_trunc_mul_trunc, ih, trunc_trunc_mul_trunc]
+    rw [_root_.pow_succ', _root_.pow_succ', trunc_trunc_mul,
+      ← trunc_trunc_mul_trunc, ih, trunc_trunc_mul_trunc]
 
 theorem trunc_coe_eq_self {n} {f : R[X]} (hn : natDegree f < n) : trunc n (f : R⟦X⟧) = f := by
   rw [← Polynomial.coe_inj]

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -414,7 +414,7 @@ set_option linter.uppercaseLean3 false in
 theorem X_pow_eq (s : σ) (n : ℕ) : (X s : MvPowerSeries σ R) ^ n = monomial R (single s n) 1 := by
   induction' n with n ih
   · simp
-  · rw [pow_succ', ih, Nat.succ_eq_add_one, Finsupp.single_add, X, monomial_mul_monomial, one_mul]
+  · rw [pow_succ, ih, Nat.succ_eq_add_one, Finsupp.single_add, X, monomial_mul_monomial, one_mul]
 set_option linter.uppercaseLean3 false in
 #align mv_power_series.X_pow_eq MvPowerSeries.X_pow_eq
 

These will be caught by the linter in a future lean version.

@@ -64,9 +64,7 @@ theorem order_finite_iff_ne_zero : (order φ).Dom ↔ φ ≠ 0 := by
   simp only [order]
   constructor
   · split_ifs with h <;> intro H
-    · contrapose! H
-      simp only [← Part.eq_none_iff']
-      rfl
+    · simp only [PartENat.top_eq_none, Part.not_none_dom] at H
     · exact h
   · intro h
     simp [h]

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -496,7 +496,6 @@ set_option linter.uppercaseLean3 false in
 section Map
 
 variable {S : Type*} {T : Type*} [Semiring S] [Semiring T]
-
 variable (f : R →+* S) (g : S →+* T)
 
 /-- The map between formal power series induced by a map on the coefficients.-/

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -541,9 +541,7 @@ end Semiring
 section Map
 
 variable {S T : Type*} [Semiring R] [Semiring S] [Semiring T]
-
 variable (f : R →+* S) (g : S →+* T)
-
 variable (σ)
 
 /-- The map between multivariate formal power series induced by a map on the coefficients.-/

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

@@ -242,7 +242,7 @@ theorem coeff_mul_of_lt_order {φ ψ : R⟦X⟧} {n : ℕ} (h : ↑n < ψ.order)
   refine' mul_eq_zero_of_right (coeff R x.fst φ) (coeff_of_lt_order x.snd (lt_of_le_of_lt _ h))
   rw [mem_antidiagonal] at hx
   norm_cast
-  linarith
+  omega
 #align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_order
 
 theorem coeff_mul_one_sub_of_lt_order {R : Type*} [CommRing R] {φ ψ : R⟦X⟧} (n : ℕ)

This PR split the files devoted to power series (especially RingTheory/PowerSeries/Basic) into several ones:

• RingTheory/MvPowerSeries/Basic - initial definitions (multivariate)

• RingTheory/MvPowerSeries/Trunc - truncation

• RingTheory/MvPowerSeries/Inverse - stuff pertaining to inverses

• RingTheory/PowerSeries/Basic - initial definitions (univariate)

• RingTheory/PowerSeries/Trunc - truncation

• RingTheory/PowerSeries/Inverse - stuff pertaining to inverses

• RingTheory/PowerSeries/Order - stuff pertaining to order

it remains to adjust the other files (PowerSeries/Derivative and PowerSeries/WellKnown)

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: faenuccio <filippo.nuccio@univ-st-etienne.fr>

This PR split the files devoted to power series (especially RingTheory/PowerSeries/Basic) into several ones:

• RingTheory/MvPowerSeries/Basic - initial definitions (multivariate)

• RingTheory/MvPowerSeries/Trunc - truncation

• RingTheory/MvPowerSeries/Inverse - stuff pertaining to inverses

• RingTheory/PowerSeries/Basic - initial definitions (univariate)

• RingTheory/PowerSeries/Trunc - truncation

• RingTheory/PowerSeries/Inverse - stuff pertaining to inverses

• RingTheory/PowerSeries/Order - stuff pertaining to order

it remains to adjust the other files (PowerSeries/Derivative and PowerSeries/WellKnown)

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: faenuccio <filippo.nuccio@univ-st-etienne.fr>

This PR split the files devoted to power series (especially RingTheory/PowerSeries/Basic) into several ones:

• RingTheory/MvPowerSeries/Basic - initial definitions (multivariate)

• RingTheory/MvPowerSeries/Trunc - truncation

• RingTheory/MvPowerSeries/Inverse - stuff pertaining to inverses

• RingTheory/PowerSeries/Basic - initial definitions (univariate)

• RingTheory/PowerSeries/Trunc - truncation

• RingTheory/PowerSeries/Inverse - stuff pertaining to inverses

• RingTheory/PowerSeries/Order - stuff pertaining to order

it remains to adjust the other files (PowerSeries/Derivative and PowerSeries/WellKnown)

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: faenuccio <filippo.nuccio@univ-st-etienne.fr>

This PR split the files devoted to power series (especially RingTheory/PowerSeries/Basic) into several ones:

• RingTheory/MvPowerSeries/Basic - initial definitions (multivariate)

• RingTheory/MvPowerSeries/Trunc - truncation

• RingTheory/MvPowerSeries/Inverse - stuff pertaining to inverses

• RingTheory/PowerSeries/Basic - initial definitions (univariate)

• RingTheory/PowerSeries/Trunc - truncation

• RingTheory/PowerSeries/Inverse - stuff pertaining to inverses

• RingTheory/PowerSeries/Order - stuff pertaining to order

it remains to adjust the other files (PowerSeries/Derivative and PowerSeries/WellKnown)

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: faenuccio <filippo.nuccio@univ-st-etienne.fr>

@@ -3,1294 +3,55 @@ Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
 -/
-import Mathlib.Data.Finsupp.Interval
-import Mathlib.Data.MvPolynomial.Basic
+import Mathlib.RingTheory.MvPowerSeries.Basic
+import Mathlib.Data.Polynomial.Basic
 import Mathlib.Data.Polynomial.AlgebraMap
-import Mathlib.Data.Polynomial.Coeff
-import Mathlib.LinearAlgebra.StdBasis
-import Mathlib.RingTheory.Ideal.LocalRing
-import Mathlib.RingTheory.Multiplicity
-import Mathlib.Tactic.Linarith
-import Mathlib.Data.Finset.PiAntidiagonal
 
 #align_import ring_theory.power_series.basic from "leanprover-community/mathlib"@"2d5739b61641ee4e7e53eca5688a08f66f2e6a60"
 
 /-!
-# Formal power series
+# Formal power series (in one variable)
 
-This file defines (multivariate) formal power series
+This file defines (univariate) formal power series
 and develops the basic properties of these objects.
 
 A formal power series is to a polynomial like an infinite sum is to a finite sum.
 
-We provide the natural inclusion from polynomials to formal power series.
-
-## Generalities
-
-The file starts with setting up the (semi)ring structure on multivariate power series.
-
-`trunc n φ` truncates a formal power series to the polynomial
-that has the same coefficients as `φ`, for all `m < n`, and `0` otherwise.
-
-If the constant coefficient of a formal power series is invertible,
-then this formal power series is invertible.
-
-Formal power series over a local ring form a local ring.
-
-## Formal power series in one variable
-
-We prove that if the ring of coefficients is an integral domain,
-then formal power series in one variable form an integral domain.
-
-The `order` of a formal power series `φ` is the multiplicity of the variable `X` in `φ`.
-
-If the coefficients form an integral domain, then `order` is a valuation
-(`order_mul`, `le_order_add`).
-
-## Implementation notes
-
-In this file we define multivariate formal power series with
-variables indexed by `σ` and coefficients in `R` as
-`MvPowerSeries σ R := (σ →₀ ℕ) → R`.
-Unfortunately there is not yet enough API to show that they are the completion
-of the ring of multivariate polynomials. However, we provide most of the infrastructure
-that is needed to do this. Once I-adic completion (topological or algebraic) is available
-it should not be hard to fill in the details.
-
-Formal power series in one variable are defined as
-`PowerSeries R := MvPowerSeries Unit R`.
-
-This allows us to port a lot of proofs and properties
-from the multivariate case to the single variable case.
-However, it means that formal power series are indexed by `Unit →₀ ℕ`,
-which is of course canonically isomorphic to `ℕ`.
-We then build some glue to treat formal power series as if they are indexed by `ℕ`.
-Occasionally this leads to proofs that are uglier than expected.
--/
-
-
-noncomputable section
-
-open BigOperators Polynomial
-
-open Finset (antidiagonal mem_antidiagonal)
-
-/-- Multivariate formal power series, where `σ` is the index set of the variables
-and `R` is the coefficient ring.-/
-def MvPowerSeries (σ : Type*) (R : Type*) :=
-  (σ →₀ ℕ) → R
-#align mv_power_series MvPowerSeries
-
-namespace MvPowerSeries
-
-open Finsupp
-
-variable {σ R : Type*}
-
-instance [Inhabited R] : Inhabited (MvPowerSeries σ R) :=
-  ⟨fun _ => default⟩
-
-instance [Zero R] : Zero (MvPowerSeries σ R) :=
-  Pi.instZero
-
-instance [AddMonoid R] : AddMonoid (MvPowerSeries σ R) :=
-  Pi.addMonoid
-
-instance [AddGroup R] : AddGroup (MvPowerSeries σ R) :=
-  Pi.addGroup
-
-instance [AddCommMonoid R] : AddCommMonoid (MvPowerSeries σ R) :=
-  Pi.addCommMonoid
-
-instance [AddCommGroup R] : AddCommGroup (MvPowerSeries σ R) :=
-  Pi.addCommGroup
-
-instance [Nontrivial R] : Nontrivial (MvPowerSeries σ R) :=
-  Function.nontrivial
-
-instance {A} [Semiring R] [AddCommMonoid A] [Module R A] : Module R (MvPowerSeries σ A) :=
-  Pi.module _ _ _
-
-instance {A S} [Semiring R] [Semiring S] [AddCommMonoid A] [Module R A] [Module S A] [SMul R S]
-    [IsScalarTower R S A] : IsScalarTower R S (MvPowerSeries σ A) :=
-  Pi.isScalarTower
-
-section Semiring
-
-variable (R) [Semiring R]
-
-/-- The `n`th monomial with coefficient `a` as multivariate formal power series.-/
-def monomial (n : σ →₀ ℕ) : R →ₗ[R] MvPowerSeries σ R :=
-  letI := Classical.decEq σ
-  LinearMap.stdBasis R (fun _ ↦ R) n
-#align mv_power_series.monomial MvPowerSeries.monomial
-
-/-- The `n`th coefficient of a multivariate formal power series.-/
-def coeff (n : σ →₀ ℕ) : MvPowerSeries σ R →ₗ[R] R :=
-  LinearMap.proj n
-#align mv_power_series.coeff MvPowerSeries.coeff
-
-variable {R}
-
-/-- Two multivariate formal power series are equal if all their coefficients are equal.-/
-@[ext]
-theorem ext {φ ψ} (h : ∀ n : σ →₀ ℕ, coeff R n φ = coeff R n ψ) : φ = ψ :=
-  funext h
-#align mv_power_series.ext MvPowerSeries.ext
-
-/-- Two multivariate formal power series are equal
- if and only if all their coefficients are equal.-/
-theorem ext_iff {φ ψ : MvPowerSeries σ R} : φ = ψ ↔ ∀ n : σ →₀ ℕ, coeff R n φ = coeff R n ψ :=
-  Function.funext_iff
-#align mv_power_series.ext_iff MvPowerSeries.ext_iff
-
-theorem monomial_def [DecidableEq σ] (n : σ →₀ ℕ) :
-    (monomial R n) = LinearMap.stdBasis R (fun _ ↦ R) n := by
-  rw [monomial]
-  -- unify the `Decidable` arguments
-  convert rfl
-#align mv_power_series.monomial_def MvPowerSeries.monomial_def
-
-theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
-    coeff R m (monomial R n a) = if m = n then a else 0 := by
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [coeff, monomial_def, LinearMap.proj_apply (i := m)]
-  dsimp only
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [LinearMap.stdBasis_apply, Function.update_apply, Pi.zero_apply]
-#align mv_power_series.coeff_monomial MvPowerSeries.coeff_monomial
-
-@[simp]
-theorem coeff_monomial_same (n : σ →₀ ℕ) (a : R) : coeff R n (monomial R n a) = a := by
-  classical
-  rw [monomial_def]
-  exact LinearMap.stdBasis_same R (fun _ ↦ R) n a
-#align mv_power_series.coeff_monomial_same MvPowerSeries.coeff_monomial_same
-
-theorem coeff_monomial_ne {m n : σ →₀ ℕ} (h : m ≠ n) (a : R) : coeff R m (monomial R n a) = 0 := by
-  classical
-  rw [monomial_def]
-  exact LinearMap.stdBasis_ne R (fun _ ↦ R) _ _ h a
-#align mv_power_series.coeff_monomial_ne MvPowerSeries.coeff_monomial_ne
-
-theorem eq_of_coeff_monomial_ne_zero {m n : σ →₀ ℕ} {a : R} (h : coeff R m (monomial R n a) ≠ 0) :
-    m = n :=
-  by_contra fun h' => h <| coeff_monomial_ne h' a
-#align mv_power_series.eq_of_coeff_monomial_ne_zero MvPowerSeries.eq_of_coeff_monomial_ne_zero
-
-@[simp]
-theorem coeff_comp_monomial (n : σ →₀ ℕ) : (coeff R n).comp (monomial R n) = LinearMap.id :=
-  LinearMap.ext <| coeff_monomial_same n
-#align mv_power_series.coeff_comp_monomial MvPowerSeries.coeff_comp_monomial
-
--- Porting note (#10618): simp can prove this.
--- @[simp]
-theorem coeff_zero (n : σ →₀ ℕ) : coeff R n (0 : MvPowerSeries σ R) = 0 :=
-  rfl
-#align mv_power_series.coeff_zero MvPowerSeries.coeff_zero
-
-variable (m n : σ →₀ ℕ) (φ ψ : MvPowerSeries σ R)
-
-instance : One (MvPowerSeries σ R) :=
-  ⟨monomial R (0 : σ →₀ ℕ) 1⟩
-
-theorem coeff_one [DecidableEq σ] : coeff R n (1 : MvPowerSeries σ R) = if n = 0 then 1 else 0 :=
-  coeff_monomial _ _ _
-#align mv_power_series.coeff_one MvPowerSeries.coeff_one
-
-theorem coeff_zero_one : coeff R (0 : σ →₀ ℕ) 1 = 1 :=
-  coeff_monomial_same 0 1
-#align mv_power_series.coeff_zero_one MvPowerSeries.coeff_zero_one
-
-theorem monomial_zero_one : monomial R (0 : σ →₀ ℕ) 1 = 1 :=
-  rfl
-#align mv_power_series.monomial_zero_one MvPowerSeries.monomial_zero_one
-
-instance : AddMonoidWithOne (MvPowerSeries σ R) :=
-  { show AddMonoid (MvPowerSeries σ R) by infer_instance with
-    natCast := fun n => monomial R 0 n
-    natCast_zero := by simp [Nat.cast]
-    natCast_succ := by simp [Nat.cast, monomial_zero_one]
-    one := 1 }
-
-instance : Mul (MvPowerSeries σ R) :=
-  letI := Classical.decEq σ
-  ⟨fun φ ψ n => ∑ p in antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ⟩
-
-theorem coeff_mul [DecidableEq σ] :
-    coeff R n (φ * ψ) = ∑ p in antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ := by
-  refine Finset.sum_congr ?_ fun _ _ => rfl
-  rw [Subsingleton.elim (Classical.decEq σ) ‹DecidableEq σ›]
-#align mv_power_series.coeff_mul MvPowerSeries.coeff_mul
-
-protected theorem zero_mul : (0 : MvPowerSeries σ R) * φ = 0 :=
-  ext fun n => by classical simp [coeff_mul]
-#align mv_power_series.zero_mul MvPowerSeries.zero_mul
-
-protected theorem mul_zero : φ * 0 = 0 :=
-  ext fun n => by classical simp [coeff_mul]
-#align mv_power_series.mul_zero MvPowerSeries.mul_zero
-
-theorem coeff_monomial_mul (a : R) :
-    coeff R m (monomial R n a * φ) = if n ≤ m then a * coeff R (m - n) φ else 0 := by
-  classical
-  have :
-    ∀ p ∈ antidiagonal m,
-      coeff R (p : (σ →₀ ℕ) × (σ →₀ ℕ)).1 (monomial R n a) * coeff R p.2 φ ≠ 0 → p.1 = n :=
-    fun p _ hp => eq_of_coeff_monomial_ne_zero (left_ne_zero_of_mul hp)
-  rw [coeff_mul, ← Finset.sum_filter_of_ne this, Finset.filter_fst_eq_antidiagonal _ n,
-    Finset.sum_ite_index]
-  simp only [Finset.sum_singleton, coeff_monomial_same, Finset.sum_empty]
-#align mv_power_series.coeff_monomial_mul MvPowerSeries.coeff_monomial_mul
-
-theorem coeff_mul_monomial (a : R) :
-    coeff R m (φ * monomial R n a) = if n ≤ m then coeff R (m - n) φ * a else 0 := by
-  classical
-  have :
-    ∀ p ∈ antidiagonal m,
-      coeff R (p : (σ →₀ ℕ) × (σ →₀ ℕ)).1 φ * coeff R p.2 (monomial R n a) ≠ 0 → p.2 = n :=
-    fun p _ hp => eq_of_coeff_monomial_ne_zero (right_ne_zero_of_mul hp)
-  rw [coeff_mul, ← Finset.sum_filter_of_ne this, Finset.filter_snd_eq_antidiagonal _ n,
-    Finset.sum_ite_index]
-  simp only [Finset.sum_singleton, coeff_monomial_same, Finset.sum_empty]
-#align mv_power_series.coeff_mul_monomial MvPowerSeries.coeff_mul_monomial
-
-theorem coeff_add_monomial_mul (a : R) :
-    coeff R (m + n) (monomial R m a * φ) = a * coeff R n φ := by
-  rw [coeff_monomial_mul, if_pos, add_tsub_cancel_left]
-  exact le_add_right le_rfl
-#align mv_power_series.coeff_add_monomial_mul MvPowerSeries.coeff_add_monomial_mul
-
-theorem coeff_add_mul_monomial (a : R) :
-    coeff R (m + n) (φ * monomial R n a) = coeff R m φ * a := by
-  rw [coeff_mul_monomial, if_pos, add_tsub_cancel_right]
-  exact le_add_left le_rfl
-#align mv_power_series.coeff_add_mul_monomial MvPowerSeries.coeff_add_mul_monomial
-
-@[simp]
-theorem commute_monomial {a : R} {n} :
-    Commute φ (monomial R n a) ↔ ∀ m, Commute (coeff R m φ) a := by
-  refine' ext_iff.trans ⟨fun h m => _, fun h m => _⟩
-  · have := h (m + n)
-    rwa [coeff_add_mul_monomial, add_comm, coeff_add_monomial_mul] at this
-  · rw [coeff_mul_monomial, coeff_monomial_mul]
-    split_ifs <;> [apply h; rfl]
-#align mv_power_series.commute_monomial MvPowerSeries.commute_monomial
-
-protected theorem one_mul : (1 : MvPowerSeries σ R) * φ = φ :=
-  ext fun n => by simpa using coeff_add_monomial_mul 0 n φ 1
-#align mv_power_series.one_mul MvPowerSeries.one_mul
-
-protected theorem mul_one : φ * 1 = φ :=
-  ext fun n => by simpa using coeff_add_mul_monomial n 0 φ 1
-#align mv_power_series.mul_one MvPowerSeries.mul_one
-
-protected theorem mul_add (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : φ₁ * (φ₂ + φ₃) = φ₁ * φ₂ + φ₁ * φ₃ :=
-  ext fun n => by
-    classical simp only [coeff_mul, mul_add, Finset.sum_add_distrib, LinearMap.map_add]
-#align mv_power_series.mul_add MvPowerSeries.mul_add
-
-protected theorem add_mul (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : (φ₁ + φ₂) * φ₃ = φ₁ * φ₃ + φ₂ * φ₃ :=
-  ext fun n => by
-    classical simp only [coeff_mul, add_mul, Finset.sum_add_distrib, LinearMap.map_add]
-#align mv_power_series.add_mul MvPowerSeries.add_mul
-
-protected theorem mul_assoc (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : φ₁ * φ₂ * φ₃ = φ₁ * (φ₂ * φ₃) := by
-  ext1 n
-  classical
-  simp only [coeff_mul, Finset.sum_mul, Finset.mul_sum, Finset.sum_sigma']
-  apply Finset.sum_nbij' (fun ⟨⟨_i, j⟩, ⟨k, l⟩⟩ ↦ ⟨(k, l + j), (l, j)⟩)
-    (fun ⟨⟨i, _j⟩, ⟨k, l⟩⟩ ↦ ⟨(i + k, l), (i, k)⟩) <;> aesop (add simp [add_assoc, mul_assoc])
-#align mv_power_series.mul_assoc MvPowerSeries.mul_assoc
-
-instance : Semiring (MvPowerSeries σ R) :=
-  { inferInstanceAs (AddMonoidWithOne (MvPowerSeries σ R)),
-    inferInstanceAs (Mul (MvPowerSeries σ R)),
-    inferInstanceAs (AddCommMonoid (MvPowerSeries σ R)) with
-    mul_one := MvPowerSeries.mul_one
-    one_mul := MvPowerSeries.one_mul
-    mul_assoc := MvPowerSeries.mul_assoc
-    mul_zero := MvPowerSeries.mul_zero
-    zero_mul := MvPowerSeries.zero_mul
-    left_distrib := MvPowerSeries.mul_add
-    right_distrib := MvPowerSeries.add_mul }
-
-end Semiring
-
-instance [CommSemiring R] : CommSemiring (MvPowerSeries σ R) :=
-  { show Semiring (MvPowerSeries σ R) by infer_instance with
-    mul_comm := fun φ ψ =>
-      ext fun n => by
-        classical
-        simpa only [coeff_mul, mul_comm] using
-          sum_antidiagonal_swap n fun a b => coeff R a φ * coeff R b ψ }
-
-instance [Ring R] : Ring (MvPowerSeries σ R) :=
-  { inferInstanceAs (Semiring (MvPowerSeries σ R)),
-    inferInstanceAs (AddCommGroup (MvPowerSeries σ R)) with }
-
-instance [CommRing R] : CommRing (MvPowerSeries σ R) :=
-  { inferInstanceAs (CommSemiring (MvPowerSeries σ R)),
-    inferInstanceAs (AddCommGroup (MvPowerSeries σ R)) with }
-
-section Semiring
-
-variable [Semiring R]
-
-theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
-    monomial R m a * monomial R n b = monomial R (m + n) (a * b) := by
-  classical
-  ext k
-  simp only [coeff_mul_monomial, coeff_monomial]
-  split_ifs with h₁ h₂ h₃ h₃ h₂ <;> try rfl
-  · rw [← h₂, tsub_add_cancel_of_le h₁] at h₃
-    exact (h₃ rfl).elim
-  · rw [h₃, add_tsub_cancel_right] at h₂
-    exact (h₂ rfl).elim
-  · exact zero_mul b
-  · rw [h₂] at h₁
-    exact (h₁ <| le_add_left le_rfl).elim
-#align mv_power_series.monomial_mul_monomial MvPowerSeries.monomial_mul_monomial
-
-variable (σ) (R)
-
-/-- The constant multivariate formal power series.-/
-def C : R →+* MvPowerSeries σ R :=
-  { monomial R (0 : σ →₀ ℕ) with
-    map_one' := rfl
-    map_mul' := fun a b => (monomial_mul_monomial 0 0 a b).symm
-    map_zero' := (monomial R (0 : _)).map_zero }
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.C MvPowerSeries.C
-
-variable {σ} {R}
-
-@[simp]
-theorem monomial_zero_eq_C : ⇑(monomial R (0 : σ →₀ ℕ)) = C σ R :=
-  rfl
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.monomial_zero_eq_C MvPowerSeries.monomial_zero_eq_C
-
-theorem monomial_zero_eq_C_apply (a : R) : monomial R (0 : σ →₀ ℕ) a = C σ R a :=
-  rfl
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.monomial_zero_eq_C_apply MvPowerSeries.monomial_zero_eq_C_apply
-
-theorem coeff_C [DecidableEq σ] (n : σ →₀ ℕ) (a : R) :
-    coeff R n (C σ R a) = if n = 0 then a else 0 :=
-  coeff_monomial _ _ _
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.coeff_C MvPowerSeries.coeff_C
-
-theorem coeff_zero_C (a : R) : coeff R (0 : σ →₀ ℕ) (C σ R a) = a :=
-  coeff_monomial_same 0 a
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.coeff_zero_C MvPowerSeries.coeff_zero_C
-
-/-- The variables of the multivariate formal power series ring.-/
-def X (s : σ) : MvPowerSeries σ R :=
-  monomial R (single s 1) 1
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.X MvPowerSeries.X
-
-theorem coeff_X [DecidableEq σ] (n : σ →₀ ℕ) (s : σ) :
-    coeff R n (X s : MvPowerSeries σ R) = if n = single s 1 then 1 else 0 :=
-  coeff_monomial _ _ _
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.coeff_X MvPowerSeries.coeff_X
-
-theorem coeff_index_single_X [DecidableEq σ] (s t : σ) :
-    coeff R (single t 1) (X s : MvPowerSeries σ R) = if t = s then 1 else 0 := by
-  simp only [coeff_X, single_left_inj (one_ne_zero : (1 : ℕ) ≠ 0)]
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.coeff_index_single_X MvPowerSeries.coeff_index_single_X
-
-@[simp]
-theorem coeff_index_single_self_X (s : σ) : coeff R (single s 1) (X s : MvPowerSeries σ R) = 1 :=
-  coeff_monomial_same _ _
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.coeff_index_single_self_X MvPowerSeries.coeff_index_single_self_X
-
-theorem coeff_zero_X (s : σ) : coeff R (0 : σ →₀ ℕ) (X s : MvPowerSeries σ R) = 0 := by
-  classical
-  rw [coeff_X, if_neg]
-  intro h
-  exact one_ne_zero (single_eq_zero.mp h.symm)
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.coeff_zero_X MvPowerSeries.coeff_zero_X
-
-theorem commute_X (φ : MvPowerSeries σ R) (s : σ) : Commute φ (X s) :=
-  φ.commute_monomial.mpr fun _m => Commute.one_right _
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.commute_X MvPowerSeries.commute_X
-
-theorem X_def (s : σ) : X s = monomial R (single s 1) 1 :=
-  rfl
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.X_def MvPowerSeries.X_def
-
-theorem X_pow_eq (s : σ) (n : ℕ) : (X s : MvPowerSeries σ R) ^ n = monomial R (single s n) 1 := by
-  induction' n with n ih
-  · simp
-  · rw [pow_succ', ih, Nat.succ_eq_add_one, Finsupp.single_add, X, monomial_mul_monomial, one_mul]
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.X_pow_eq MvPowerSeries.X_pow_eq
-
-theorem coeff_X_pow [DecidableEq σ] (m : σ →₀ ℕ) (s : σ) (n : ℕ) :
-    coeff R m ((X s : MvPowerSeries σ R) ^ n) = if m = single s n then 1 else 0 := by
-  rw [X_pow_eq s n, coeff_monomial]
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.coeff_X_pow MvPowerSeries.coeff_X_pow
-
-@[simp]
-theorem coeff_mul_C (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
-    coeff R n (φ * C σ R a) = coeff R n φ * a := by simpa using coeff_add_mul_monomial n 0 φ a
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.coeff_mul_C MvPowerSeries.coeff_mul_C
-
-@[simp]
-theorem coeff_C_mul (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) :
-    coeff R n (C σ R a * φ) = a * coeff R n φ := by simpa using coeff_add_monomial_mul 0 n φ a
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.coeff_C_mul MvPowerSeries.coeff_C_mul
-
-theorem coeff_zero_mul_X (φ : MvPowerSeries σ R) (s : σ) : coeff R (0 : σ →₀ ℕ) (φ * X s) = 0 := by
-  have : ¬single s 1 ≤ 0 := fun h => by simpa using h s
-  simp only [X, coeff_mul_monomial, if_neg this]
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.coeff_zero_mul_X MvPowerSeries.coeff_zero_mul_X
-
-theorem coeff_zero_X_mul (φ : MvPowerSeries σ R) (s : σ) : coeff R (0 : σ →₀ ℕ) (X s * φ) = 0 := by
-  rw [← (φ.commute_X s).eq, coeff_zero_mul_X]
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.coeff_zero_X_mul MvPowerSeries.coeff_zero_X_mul
-
-variable (σ) (R)
-
-/-- The constant coefficient of a formal power series.-/
-def constantCoeff : MvPowerSeries σ R →+* R :=
-  { coeff R (0 : σ →₀ ℕ) with
-    toFun := coeff R (0 : σ →₀ ℕ)
-    map_one' := coeff_zero_one
-    map_mul' := fun φ ψ => by classical simp [coeff_mul, support_single_ne_zero]
-    map_zero' := LinearMap.map_zero _ }
-#align mv_power_series.constant_coeff MvPowerSeries.constantCoeff
-
-variable {σ} {R}
-
-@[simp]
-theorem coeff_zero_eq_constantCoeff : ⇑(coeff R (0 : σ →₀ ℕ)) = constantCoeff σ R :=
-  rfl
-#align mv_power_series.coeff_zero_eq_constant_coeff MvPowerSeries.coeff_zero_eq_constantCoeff
-
-theorem coeff_zero_eq_constantCoeff_apply (φ : MvPowerSeries σ R) :
-    coeff R (0 : σ →₀ ℕ) φ = constantCoeff σ R φ :=
-  rfl
-#align mv_power_series.coeff_zero_eq_constant_coeff_apply MvPowerSeries.coeff_zero_eq_constantCoeff_apply
-
-@[simp]
-theorem constantCoeff_C (a : R) : constantCoeff σ R (C σ R a) = a :=
-  rfl
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.constant_coeff_C MvPowerSeries.constantCoeff_C
-
-@[simp]
-theorem constantCoeff_comp_C : (constantCoeff σ R).comp (C σ R) = RingHom.id R :=
-  rfl
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.constant_coeff_comp_C MvPowerSeries.constantCoeff_comp_C
-
--- Porting note (#10618): simp can prove this.
--- @[simp]
-theorem constantCoeff_zero : constantCoeff σ R 0 = 0 :=
-  rfl
-#align mv_power_series.constant_coeff_zero MvPowerSeries.constantCoeff_zero
-
--- Porting note (#10618): simp can prove this.
--- @[simp]
-theorem constantCoeff_one : constantCoeff σ R 1 = 1 :=
-  rfl
-#align mv_power_series.constant_coeff_one MvPowerSeries.constantCoeff_one
-
-@[simp]
-theorem constantCoeff_X (s : σ) : constantCoeff σ R (X s) = 0 :=
-  coeff_zero_X s
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.constant_coeff_X MvPowerSeries.constantCoeff_X
-
-/-- If a multivariate formal power series is invertible,
- then so is its constant coefficient.-/
-theorem isUnit_constantCoeff (φ : MvPowerSeries σ R) (h : IsUnit φ) :
-    IsUnit (constantCoeff σ R φ) :=
-  h.map _
-#align mv_power_series.is_unit_constant_coeff MvPowerSeries.isUnit_constantCoeff
-
--- Porting note (#10618): simp can prove this.
--- @[simp]
-theorem coeff_smul (f : MvPowerSeries σ R) (n) (a : R) : coeff _ n (a • f) = a * coeff _ n f :=
-  rfl
-#align mv_power_series.coeff_smul MvPowerSeries.coeff_smul
-
-theorem smul_eq_C_mul (f : MvPowerSeries σ R) (a : R) : a • f = C σ R a * f := by
-  ext
-  simp
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.smul_eq_C_mul MvPowerSeries.smul_eq_C_mul
-
-theorem X_inj [Nontrivial R] {s t : σ} : (X s : MvPowerSeries σ R) = X t ↔ s = t :=
-  ⟨by
-    classical
-    intro h
-    replace h := congr_arg (coeff R (single s 1)) h
-    rw [coeff_X, if_pos rfl, coeff_X] at h
-    split_ifs at h with H
-    · rw [Finsupp.single_eq_single_iff] at H
-      cases' H with H H
-      · exact H.1
-      · exfalso
-        exact one_ne_zero H.1
-    · exfalso
-      exact one_ne_zero h, congr_arg X⟩
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.X_inj MvPowerSeries.X_inj
-
-end Semiring
-
-section Map
-
-variable {S T : Type*} [Semiring R] [Semiring S] [Semiring T]
-
-variable (f : R →+* S) (g : S →+* T)
-
-variable (σ)
-
-/-- The map between multivariate formal power series induced by a map on the coefficients.-/
-def map : MvPowerSeries σ R →+* MvPowerSeries σ S where
-  toFun φ n := f <| coeff R n φ
-  map_zero' := ext fun _n => f.map_zero
-  map_one' :=
-    ext fun n =>
-      show f ((coeff R n) 1) = (coeff S n) 1 by
-        classical
-        rw [coeff_one, coeff_one]
-        split_ifs with h
-        · simp only [RingHom.map_ite_one_zero, ite_true, map_one, h]
-        · simp only [RingHom.map_ite_one_zero, ite_false, map_zero, h]
-  map_add' φ ψ :=
-    ext fun n => show f ((coeff R n) (φ + ψ)) = f ((coeff R n) φ) + f ((coeff R n) ψ) by simp
-  map_mul' φ ψ :=
-    ext fun n =>
-      show f _ = _ by
-        classical
-        rw [coeff_mul, map_sum, coeff_mul]
-        apply Finset.sum_congr rfl
-        rintro ⟨i, j⟩ _; rw [f.map_mul]; rfl
-#align mv_power_series.map MvPowerSeries.map
-
-variable {σ}
-
-@[simp]
-theorem map_id : map σ (RingHom.id R) = RingHom.id _ :=
-  rfl
-#align mv_power_series.map_id MvPowerSeries.map_id
-
-theorem map_comp : map σ (g.comp f) = (map σ g).comp (map σ f) :=
-  rfl
-#align mv_power_series.map_comp MvPowerSeries.map_comp
-
-@[simp]
-theorem coeff_map (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) : coeff S n (map σ f φ) = f (coeff R n φ) :=
-  rfl
-#align mv_power_series.coeff_map MvPowerSeries.coeff_map
-
-@[simp]
-theorem constantCoeff_map (φ : MvPowerSeries σ R) :
-    constantCoeff σ S (map σ f φ) = f (constantCoeff σ R φ) :=
-  rfl
-#align mv_power_series.constant_coeff_map MvPowerSeries.constantCoeff_map
-
-@[simp]
-theorem map_monomial (n : σ →₀ ℕ) (a : R) : map σ f (monomial R n a) = monomial S n (f a) := by
-  classical
-  ext m
-  simp [coeff_monomial, apply_ite f]
-#align mv_power_series.map_monomial MvPowerSeries.map_monomial
-
-@[simp]
-theorem map_C (a : R) : map σ f (C σ R a) = C σ S (f a) :=
-  map_monomial _ _ _
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.map_C MvPowerSeries.map_C
-
-@[simp]
-theorem map_X (s : σ) : map σ f (X s) = X s := by simp [MvPowerSeries.X]
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.map_X MvPowerSeries.map_X
-
-end Map
-
-section Algebra
-
-variable {A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
-
-instance : Algebra R (MvPowerSeries σ A) :=
-  {
-    show Module R (MvPowerSeries σ A) by infer_instance with
-    commutes' := fun a φ => by
-      ext n
-      simp [Algebra.commutes]
-    smul_def' := fun a σ => by
-      ext n
-      simp [(coeff A n).map_smul_of_tower a, Algebra.smul_def]
-    toRingHom := (MvPowerSeries.map σ (algebraMap R A)).comp (C σ R) }
-
-theorem c_eq_algebraMap : C σ R = algebraMap R (MvPowerSeries σ R) :=
-  rfl
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.C_eq_algebra_map MvPowerSeries.c_eq_algebraMap
-
-theorem algebraMap_apply {r : R} :
-    algebraMap R (MvPowerSeries σ A) r = C σ A (algebraMap R A r) := by
-  change (MvPowerSeries.map σ (algebraMap R A)).comp (C σ R) r = _
-  simp
-#align mv_power_series.algebra_map_apply MvPowerSeries.algebraMap_apply
-
-instance [Nonempty σ] [Nontrivial R] : Nontrivial (Subalgebra R (MvPowerSeries σ R)) :=
-  ⟨⟨⊥, ⊤, by
-      classical
-      rw [Ne.def, SetLike.ext_iff, not_forall]
-      inhabit σ
-      refine' ⟨X default, _⟩
-      simp only [Algebra.mem_bot, not_exists, Set.mem_range, iff_true_iff, Algebra.mem_top]
-      intro x
-      rw [ext_iff, not_forall]
-      refine' ⟨Finsupp.single default 1, _⟩
-      simp [algebraMap_apply, coeff_C]⟩⟩
-
-end Algebra
-
-section Trunc
-
-variable [CommSemiring R] (n : σ →₀ ℕ)
-
-/-- Auxiliary definition for the truncation function. -/
-def truncFun (φ : MvPowerSeries σ R) : MvPolynomial σ R :=
-  ∑ m in Finset.Iio n, MvPolynomial.monomial m (coeff R m φ)
-#align mv_power_series.trunc_fun MvPowerSeries.truncFun
-
-theorem coeff_truncFun (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
-    (truncFun n φ).coeff m = if m < n then coeff R m φ else 0 := by
-  classical
-  simp [truncFun, MvPolynomial.coeff_sum]
-#align mv_power_series.coeff_trunc_fun MvPowerSeries.coeff_truncFun
-
-variable (R)
-
-/-- The `n`th truncation of a multivariate formal power series to a multivariate polynomial -/
-def trunc : MvPowerSeries σ R →+ MvPolynomial σ R where
-  toFun := truncFun n
-  map_zero' := by
-    classical
-    ext
-    simp [coeff_truncFun]
-  map_add' := by
-    classical
-    intros x y
-    ext m
-    simp only [coeff_truncFun, MvPolynomial.coeff_add]
-    split_ifs
-    · rw [map_add]
-    · rw [zero_add]
-
-#align mv_power_series.trunc MvPowerSeries.trunc
-
-variable {R}
-
-theorem coeff_trunc (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
-    (trunc R n φ).coeff m = if m < n then coeff R m φ else 0 := by
-  classical simp [trunc, coeff_truncFun]
-#align mv_power_series.coeff_trunc MvPowerSeries.coeff_trunc
-
-@[simp]
-theorem trunc_one (n : σ →₀ ℕ) (hnn : n ≠ 0) : trunc R n 1 = 1 :=
-  MvPolynomial.ext _ _ fun m => by
-    classical
-    rw [coeff_trunc, coeff_one]
-    split_ifs with H H'
-    · subst m
-      simp
-    · symm
-      rw [MvPolynomial.coeff_one]
-      exact if_neg (Ne.symm H')
-    · symm
-      rw [MvPolynomial.coeff_one]
-      refine' if_neg _
-      rintro rfl
-      apply H
-      exact Ne.bot_lt hnn
-#align mv_power_series.trunc_one MvPowerSeries.trunc_one
-
-@[simp]
-theorem trunc_c (n : σ →₀ ℕ) (hnn : n ≠ 0) (a : R) : trunc R n (C σ R a) = MvPolynomial.C a :=
-  MvPolynomial.ext _ _ fun m => by
-    classical
-    rw [coeff_trunc, coeff_C, MvPolynomial.coeff_C]
-    split_ifs with H <;> first |rfl|try simp_all
-    exfalso; apply H; subst m; exact Ne.bot_lt hnn
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.trunc_C MvPowerSeries.trunc_c
-
-end Trunc
-
-section Semiring
-
-variable [Semiring R]
-
-theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
-    (X s : MvPowerSeries σ R) ^ n ∣ φ ↔ ∀ m : σ →₀ ℕ, m s < n → coeff R m φ = 0 := by
-  classical
-  constructor
-  · rintro ⟨φ, rfl⟩ m h
-    rw [coeff_mul, Finset.sum_eq_zero]
-    rintro ⟨i, j⟩ hij
-    rw [coeff_X_pow, if_neg, zero_mul]
-    contrapose! h
-    dsimp at h
-    subst i
-    rw [mem_antidiagonal] at hij
-    rw [← hij, Finsupp.add_apply, Finsupp.single_eq_same]
-    exact Nat.le_add_right n _
-  · intro h
-    refine' ⟨fun m => coeff R (m + single s n) φ, _⟩
-    ext m
-    by_cases H : m - single s n + single s n = m
-    · rw [coeff_mul, Finset.sum_eq_single (single s n, m - single s n)]
-      · rw [coeff_X_pow, if_pos rfl, one_mul]
-        simpa using congr_arg (fun m : σ →₀ ℕ => coeff R m φ) H.symm
-      · rintro ⟨i, j⟩ hij hne
-        rw [mem_antidiagonal] at hij
-        rw [coeff_X_pow]
-        split_ifs with hi
-        · exfalso
-          apply hne
-          rw [← hij, ← hi, Prod.mk.inj_iff]
-          refine' ⟨rfl, _⟩
-          ext t
-          simp only [add_tsub_cancel_left, Finsupp.add_apply, Finsupp.tsub_apply]
-        · exact zero_mul _
-      · intro hni
-        exfalso
-        apply hni
-        rwa [mem_antidiagonal, add_comm]
-    · rw [h, coeff_mul, Finset.sum_eq_zero]
-      · rintro ⟨i, j⟩ hij
-        rw [mem_antidiagonal] at hij
-        rw [coeff_X_pow]
-        split_ifs with hi
-        · exfalso
-          apply H
-          rw [← hij, hi]
-          ext
-          rw [coe_add, coe_add, Pi.add_apply, Pi.add_apply, add_tsub_cancel_left, add_comm]
-        · exact zero_mul _
-      · contrapose! H
-        ext t
-        by_cases hst : s = t
-        · subst t
-          simpa using tsub_add_cancel_of_le H
-        · simp [Finsupp.single_apply, hst]
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.X_pow_dvd_iff MvPowerSeries.X_pow_dvd_iff
-
-theorem X_dvd_iff {s : σ} {φ : MvPowerSeries σ R} :
-    (X s : MvPowerSeries σ R) ∣ φ ↔ ∀ m : σ →₀ ℕ, m s = 0 → coeff R m φ = 0 := by
-  rw [← pow_one (X s : MvPowerSeries σ R), X_pow_dvd_iff]
-  constructor <;> intro h m hm
-  · exact h m (hm.symm ▸ zero_lt_one)
-  · exact h m (Nat.eq_zero_of_le_zero <| Nat.le_of_succ_le_succ hm)
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.X_dvd_iff MvPowerSeries.X_dvd_iff
-
-end Semiring
-
-section CommSemiring
-
-open Finset.HasAntidiagonal Finset
-
-variable {R : Type*} [CommSemiring R] {ι : Type*} [DecidableEq ι]
-
-/-- Coefficients of a product of power series -/
-theorem coeff_prod [DecidableEq σ]
-    (f : ι → MvPowerSeries σ R) (d : σ →₀ ℕ) (s : Finset ι) :
-    coeff R d (∏ j in s, f j) =
-      ∑ l in piAntidiagonal s d,
-        ∏ i in s, coeff R (l i) (f i) := by
-  induction s using Finset.induction_on generalizing d with
-  | empty =>
-    simp only [prod_empty, sum_const, nsmul_eq_mul, mul_one, coeff_one, piAntidiagonal_empty]
-    split_ifs
-    · simp only [card_singleton, Nat.cast_one]
-    · simp only [card_empty, Nat.cast_zero]
-  | @insert a s ha ih =>
-    rw [piAntidiagonal_insert ha, prod_insert ha, coeff_mul, sum_biUnion]
-    · apply Finset.sum_congr rfl
-      · simp only [mem_antidiagonal, sum_map, Function.Embedding.coeFn_mk, coe_update, Prod.forall]
-        rintro u v rfl
-        rw [ih, Finset.mul_sum, ← Finset.sum_attach]
-        apply Finset.sum_congr rfl
-        simp only [mem_attach, Finset.prod_insert ha, Function.update_same, forall_true_left,
-          Subtype.forall]
-        rintro x -
-        rw [Finset.prod_congr rfl]
-        intro i hi
-        rw [Function.update_noteq]
-        exact ne_of_mem_of_not_mem hi ha
-    · simp only [Set.PairwiseDisjoint, Set.Pairwise, mem_coe, mem_antidiagonal, ne_eq,
-        disjoint_left, mem_map, mem_attach, Function.Embedding.coeFn_mk, true_and, Subtype.exists,
-        exists_prop, not_exists, not_and, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂,
-        Prod.forall, Prod.mk.injEq]
-      rintro u v rfl u' v' huv h k - l - hkl
-      obtain rfl : u' = u := by
-        simpa only [Finsupp.coe_update, Function.update_same] using DFunLike.congr_fun hkl a
-      simp only [add_right_inj] at huv
-      exact h rfl huv.symm
-
-end CommSemiring
-
-section Ring
-
-variable [Ring R]
-
-/-
-The inverse of a multivariate formal power series is defined by
-well-founded recursion on the coefficients of the inverse.
--/
-/-- Auxiliary definition that unifies
- the totalised inverse formal power series `(_)⁻¹` and
- the inverse formal power series that depends on
- an inverse of the constant coefficient `invOfUnit`.-/
-protected noncomputable def inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerSeries σ R
-  | n =>
-    letI := Classical.decEq σ
-    if n = 0 then a
-    else
-      -a *
-        ∑ x in antidiagonal n, if _ : x.2 < n then coeff R x.1 φ * inv.aux a φ x.2 else 0
-termination_by n => n
-#align mv_power_series.inv.aux MvPowerSeries.inv.aux
-
-theorem coeff_inv_aux [DecidableEq σ] (n : σ →₀ ℕ) (a : R) (φ : MvPowerSeries σ R) :
-    coeff R n (inv.aux a φ) =
-      if n = 0 then a
-      else
-        -a *
-          ∑ x in antidiagonal n, if x.2 < n then coeff R x.1 φ * coeff R x.2 (inv.aux a φ) else 0 :=
-  show inv.aux a φ n = _ by
-    cases Subsingleton.elim ‹DecidableEq σ› (Classical.decEq σ)
-    rw [inv.aux]
-    rfl
-#align mv_power_series.coeff_inv_aux MvPowerSeries.coeff_inv_aux
-
-/-- A multivariate formal power series is invertible if the constant coefficient is invertible.-/
-def invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) : MvPowerSeries σ R :=
-  inv.aux (↑u⁻¹) φ
-#align mv_power_series.inv_of_unit MvPowerSeries.invOfUnit
-
-theorem coeff_invOfUnit [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (u : Rˣ) :
-    coeff R n (invOfUnit φ u) =
-      if n = 0 then ↑u⁻¹
-      else
-        -↑u⁻¹ *
-          ∑ x in antidiagonal n,
-            if x.2 < n then coeff R x.1 φ * coeff R x.2 (invOfUnit φ u) else 0 := by
-  convert coeff_inv_aux n (↑u⁻¹) φ
-#align mv_power_series.coeff_inv_of_unit MvPowerSeries.coeff_invOfUnit
-
-@[simp]
-theorem constantCoeff_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) :
-    constantCoeff σ R (invOfUnit φ u) = ↑u⁻¹ := by
-  classical
-  rw [← coeff_zero_eq_constantCoeff_apply, coeff_invOfUnit, if_pos rfl]
-#align mv_power_series.constant_coeff_inv_of_unit MvPowerSeries.constantCoeff_invOfUnit
-
-theorem mul_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) (h : constantCoeff σ R φ = u) :
-    φ * invOfUnit φ u = 1 :=
-  ext fun n =>
-    letI := Classical.decEq (σ →₀ ℕ)
-    if H : n = 0 then by
-      rw [H]
-      simp [coeff_mul, support_single_ne_zero, h]
-    else by
-      classical
-      have : ((0 : σ →₀ ℕ), n) ∈ antidiagonal n := by rw [mem_antidiagonal, zero_add]
-      rw [coeff_one, if_neg H, coeff_mul, ← Finset.insert_erase this,
-        Finset.sum_insert (Finset.not_mem_erase _ _), coeff_zero_eq_constantCoeff_apply, h,
-        coeff_invOfUnit, if_neg H, neg_mul, mul_neg, Units.mul_inv_cancel_left, ←
-        Finset.insert_erase this, Finset.sum_insert (Finset.not_mem_erase _ _),
-        Finset.insert_erase this, if_neg (not_lt_of_ge <| le_rfl), zero_add, add_comm, ←
-        sub_eq_add_neg, sub_eq_zero, Finset.sum_congr rfl]
-      rintro ⟨i, j⟩ hij
-      rw [Finset.mem_erase, mem_antidiagonal] at hij
-      cases' hij with h₁ h₂
-      subst n
-      rw [if_pos]
-      suffices (0 : _) + j < i + j by simpa
-      apply add_lt_add_right
-      constructor
-      · intro s
-        exact Nat.zero_le _
-      · intro H
-        apply h₁
-        suffices i = 0 by simp [this]
-        ext1 s
-        exact Nat.eq_zero_of_le_zero (H s)
-#align mv_power_series.mul_inv_of_unit MvPowerSeries.mul_invOfUnit
-
-end Ring
-
-section CommRing
-
-variable [CommRing R]
-
-/-- Multivariate formal power series over a local ring form a local ring. -/
-instance [LocalRing R] : LocalRing (MvPowerSeries σ R) :=
-  LocalRing.of_isUnit_or_isUnit_one_sub_self <| by
-    intro φ
-    rcases LocalRing.isUnit_or_isUnit_one_sub_self (constantCoeff σ R φ) with (⟨u, h⟩ | ⟨u, h⟩) <;>
-        [left; right] <;>
-      · refine' isUnit_of_mul_eq_one _ _ (mul_invOfUnit _ u _)
-        simpa using h.symm
-
--- TODO(jmc): once adic topology lands, show that this is complete
-end CommRing
+Formal power series in one variable are defined from multivariate
+power series as `PowerSeries R := MvPowerSeries Unit R`.
 
-section LocalRing
+The file sets up the (semi)ring structure on univariate power series.
 
-variable {S : Type*} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalRingHom f]
-
--- Thanks to the linter for informing us that this instance does
--- not actually need R and S to be local rings!
-/-- The map `A[[X]] → B[[X]]` induced by a local ring hom `A → B` is local -/
-instance map.isLocalRingHom : IsLocalRingHom (map σ f) :=
-  ⟨by
-    rintro φ ⟨ψ, h⟩
-    replace h := congr_arg (constantCoeff σ S) h
-    rw [constantCoeff_map] at h
-    have : IsUnit (constantCoeff σ S ↑ψ) := isUnit_constantCoeff (↑ψ) ψ.isUnit
-    rw [h] at this
-    rcases isUnit_of_map_unit f _ this with ⟨c, hc⟩
-    exact isUnit_of_mul_eq_one φ (invOfUnit φ c) (mul_invOfUnit φ c hc.symm)⟩
-#align mv_power_series.map.is_local_ring_hom MvPowerSeries.map.isLocalRingHom
-
-end LocalRing
-
-section Field
-
-variable {k : Type*} [Field k]
-
-/-- The inverse `1/f` of a multivariable power series `f` over a field -/
-protected def inv (φ : MvPowerSeries σ k) : MvPowerSeries σ k :=
-  inv.aux (constantCoeff σ k φ)⁻¹ φ
-#align mv_power_series.inv MvPowerSeries.inv
-
-instance : Inv (MvPowerSeries σ k) :=
-  ⟨MvPowerSeries.inv⟩
-
-theorem coeff_inv [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ k) :
-    coeff k n φ⁻¹ =
-      if n = 0 then (constantCoeff σ k φ)⁻¹
-      else
-        -(constantCoeff σ k φ)⁻¹ *
-          ∑ x in antidiagonal n, if x.2 < n then coeff k x.1 φ * coeff k x.2 φ⁻¹ else 0 :=
-  coeff_inv_aux n _ φ
-#align mv_power_series.coeff_inv MvPowerSeries.coeff_inv
-
-@[simp]
-theorem constantCoeff_inv (φ : MvPowerSeries σ k) :
-    constantCoeff σ k φ⁻¹ = (constantCoeff σ k φ)⁻¹ := by
-  classical
-  rw [← coeff_zero_eq_constantCoeff_apply, coeff_inv, if_pos rfl]
-#align mv_power_series.constant_coeff_inv MvPowerSeries.constantCoeff_inv
-
-theorem inv_eq_zero {φ : MvPowerSeries σ k} : φ⁻¹ = 0 ↔ constantCoeff σ k φ = 0 :=
-  ⟨fun h => by simpa using congr_arg (constantCoeff σ k) h, fun h =>
-    ext fun n => by
-      classical
-      rw [coeff_inv]
-      split_ifs <;>
-        simp only [h, map_zero, zero_mul, inv_zero, neg_zero]⟩
-#align mv_power_series.inv_eq_zero MvPowerSeries.inv_eq_zero
-
-@[simp]
-theorem zero_inv : (0 : MvPowerSeries σ k)⁻¹ = 0 := by
-  rw [inv_eq_zero, constantCoeff_zero]
-#align mv_power_series.zero_inv MvPowerSeries.zero_inv
-
--- Porting note (#10618): simp can prove this.
--- @[simp]
-theorem invOfUnit_eq (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
-    invOfUnit φ (Units.mk0 _ h) = φ⁻¹ :=
-  rfl
-#align mv_power_series.inv_of_unit_eq MvPowerSeries.invOfUnit_eq
-
-@[simp]
-theorem invOfUnit_eq' (φ : MvPowerSeries σ k) (u : Units k) (h : constantCoeff σ k φ = u) :
-    invOfUnit φ u = φ⁻¹ := by
-  rw [← invOfUnit_eq φ (h.symm ▸ u.ne_zero)]
-  apply congrArg (invOfUnit φ)
-  rw [Units.ext_iff]
-  exact h.symm
-#align mv_power_series.inv_of_unit_eq' MvPowerSeries.invOfUnit_eq'
-
-@[simp]
-protected theorem mul_inv_cancel (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
-    φ * φ⁻¹ = 1 := by rw [← invOfUnit_eq φ h, mul_invOfUnit φ (Units.mk0 _ h) rfl]
-#align mv_power_series.mul_inv_cancel MvPowerSeries.mul_inv_cancel
-
-@[simp]
-protected theorem inv_mul_cancel (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
-    φ⁻¹ * φ = 1 := by rw [mul_comm, φ.mul_inv_cancel h]
-#align mv_power_series.inv_mul_cancel MvPowerSeries.inv_mul_cancel
-
-protected theorem eq_mul_inv_iff_mul_eq {φ₁ φ₂ φ₃ : MvPowerSeries σ k}
-    (h : constantCoeff σ k φ₃ ≠ 0) : φ₁ = φ₂ * φ₃⁻¹ ↔ φ₁ * φ₃ = φ₂ :=
-  ⟨fun k => by simp [k, mul_assoc, MvPowerSeries.inv_mul_cancel _ h], fun k => by
-    simp [← k, mul_assoc, MvPowerSeries.mul_inv_cancel _ h]⟩
-#align mv_power_series.eq_mul_inv_iff_mul_eq MvPowerSeries.eq_mul_inv_iff_mul_eq
-
-protected theorem eq_inv_iff_mul_eq_one {φ ψ : MvPowerSeries σ k} (h : constantCoeff σ k ψ ≠ 0) :
-    φ = ψ⁻¹ ↔ φ * ψ = 1 := by rw [← MvPowerSeries.eq_mul_inv_iff_mul_eq h, one_mul]
-#align mv_power_series.eq_inv_iff_mul_eq_one MvPowerSeries.eq_inv_iff_mul_eq_one
-
-protected theorem inv_eq_iff_mul_eq_one {φ ψ : MvPowerSeries σ k} (h : constantCoeff σ k ψ ≠ 0) :
-    ψ⁻¹ = φ ↔ φ * ψ = 1 := by rw [eq_comm, MvPowerSeries.eq_inv_iff_mul_eq_one h]
-#align mv_power_series.inv_eq_iff_mul_eq_one MvPowerSeries.inv_eq_iff_mul_eq_one
-
-@[simp]
-protected theorem mul_inv_rev (φ ψ : MvPowerSeries σ k) :
-    (φ * ψ)⁻¹ = ψ⁻¹ * φ⁻¹ := by
-  by_cases h : constantCoeff σ k (φ * ψ) = 0
-  · rw [inv_eq_zero.mpr h]
-    simp only [map_mul, mul_eq_zero] at h
-    -- we don't have `NoZeroDivisors (MvPowerSeries σ k)` yet,
-    cases' h with h h <;> simp [inv_eq_zero.mpr h]
-  · rw [MvPowerSeries.inv_eq_iff_mul_eq_one h]
-    simp only [not_or, map_mul, mul_eq_zero] at h
-    rw [← mul_assoc, mul_assoc _⁻¹, MvPowerSeries.inv_mul_cancel _ h.left, mul_one,
-      MvPowerSeries.inv_mul_cancel _ h.right]
-#align mv_power_series.mul_inv_rev MvPowerSeries.mul_inv_rev
-
-instance : InvOneClass (MvPowerSeries σ k) :=
-  { inferInstanceAs (One (MvPowerSeries σ k)),
-    inferInstanceAs (Inv (MvPowerSeries σ k)) with
-    inv_one := by
-      rw [MvPowerSeries.inv_eq_iff_mul_eq_one, mul_one]
-      simp }
-
-@[simp]
-theorem C_inv (r : k) : (C σ k r)⁻¹ = C σ k r⁻¹ := by
-  rcases eq_or_ne r 0 with (rfl | hr)
-  · simp
-  rw [MvPowerSeries.inv_eq_iff_mul_eq_one, ← map_mul, inv_mul_cancel hr, map_one]
-  simpa using hr
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.C_inv MvPowerSeries.C_inv
-
-@[simp]
-theorem X_inv (s : σ) : (X s : MvPowerSeries σ k)⁻¹ = 0 := by
-  rw [inv_eq_zero, constantCoeff_X]
-set_option linter.uppercaseLean3 false in
-#align mv_power_series.X_inv MvPowerSeries.X_inv
-
-@[simp]
-theorem smul_inv (r : k) (φ : MvPowerSeries σ k) : (r • φ)⁻¹ = r⁻¹ • φ⁻¹ := by
-  simp [smul_eq_C_mul, mul_comm]
-#align mv_power_series.smul_inv MvPowerSeries.smul_inv
-
-end Field
-
-end MvPowerSeries
-
-namespace MvPolynomial
-
-open Finsupp
-
-variable {σ : Type*} {R : Type*} [CommSemiring R] (φ ψ : MvPolynomial σ R)
-
--- Porting note: added so we can add the `@[coe]` attribute
-/-- The natural inclusion from multivariate polynomials into multivariate formal power series.-/
-@[coe]
-def toMvPowerSeries : MvPolynomial σ R → MvPowerSeries σ R :=
-  fun φ n => coeff n φ
-
-/-- The natural inclusion from multivariate polynomials into multivariate formal power series.-/
-instance coeToMvPowerSeries : Coe (MvPolynomial σ R) (MvPowerSeries σ R) :=
-  ⟨toMvPowerSeries⟩
-#align mv_polynomial.coe_to_mv_power_series MvPolynomial.coeToMvPowerSeries
-
-theorem coe_def : (φ : MvPowerSeries σ R) = fun n => coeff n φ :=
-  rfl
-#align mv_polynomial.coe_def MvPolynomial.coe_def
-
-@[simp, norm_cast]
-theorem coeff_coe (n : σ →₀ ℕ) : MvPowerSeries.coeff R n ↑φ = coeff n φ :=
-  rfl
-#align mv_polynomial.coeff_coe MvPolynomial.coeff_coe
-
-@[simp, norm_cast]
-theorem coe_monomial (n : σ →₀ ℕ) (a : R) :
-    (monomial n a : MvPowerSeries σ R) = MvPowerSeries.monomial R n a :=
-  MvPowerSeries.ext fun m => by
-    classical
-    rw [coeff_coe, coeff_monomial, MvPowerSeries.coeff_monomial]
-    split_ifs with h₁ h₂ <;> first |rfl|subst m; contradiction
-#align mv_polynomial.coe_monomial MvPolynomial.coe_monomial
-
-@[simp, norm_cast]
-theorem coe_zero : ((0 : MvPolynomial σ R) : MvPowerSeries σ R) = 0 :=
-  rfl
-#align mv_polynomial.coe_zero MvPolynomial.coe_zero
-
-@[simp, norm_cast]
-theorem coe_one : ((1 : MvPolynomial σ R) : MvPowerSeries σ R) = 1 :=
-    coe_monomial _ _
-#align mv_polynomial.coe_one MvPolynomial.coe_one
-
-@[simp, norm_cast]
-theorem coe_add : ((φ + ψ : MvPolynomial σ R) : MvPowerSeries σ R) = φ + ψ :=
-  rfl
-#align mv_polynomial.coe_add MvPolynomial.coe_add
-
-@[simp, norm_cast]
-theorem coe_mul : ((φ * ψ : MvPolynomial σ R) : MvPowerSeries σ R) = φ * ψ :=
-  MvPowerSeries.ext fun n => by
-    classical
-    simp only [coeff_coe, MvPowerSeries.coeff_mul, coeff_mul]
-#align mv_polynomial.coe_mul MvPolynomial.coe_mul
-
-@[simp, norm_cast]
-theorem coe_C (a : R) : ((C a : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.C σ R a :=
-  coe_monomial _ _
-set_option linter.uppercaseLean3 false in
-#align mv_polynomial.coe_C MvPolynomial.coe_C
-
-set_option linter.deprecated false in
-@[simp, norm_cast]
-theorem coe_bit0 :
-    ((bit0 φ : MvPolynomial σ R) : MvPowerSeries σ R) = bit0 (φ : MvPowerSeries σ R) :=
-  coe_add _ _
-#align mv_polynomial.coe_bit0 MvPolynomial.coe_bit0
-
-set_option linter.deprecated false in
-@[simp, norm_cast]
-theorem coe_bit1 :
-    ((bit1 φ : MvPolynomial σ R) : MvPowerSeries σ R) = bit1 (φ : MvPowerSeries σ R) := by
-  rw [bit1, bit1, coe_add, coe_one, coe_bit0]
-#align mv_polynomial.coe_bit1 MvPolynomial.coe_bit1
-
-@[simp, norm_cast]
-theorem coe_X (s : σ) : ((X s : MvPolynomial σ R) : MvPowerSeries σ R) = MvPowerSeries.X s :=
-  coe_monomial _ _
-set_option linter.uppercaseLean3 false in
-#align mv_polynomial.coe_X MvPolynomial.coe_X
-
-variable (σ R)
-
-theorem coe_injective : Function.Injective (Coe.coe : MvPolynomial σ R → MvPowerSeries σ R) :=
-    fun x y h => by
-  ext
-  simp_rw [← coeff_coe]
-  congr
-#align mv_polynomial.coe_injective MvPolynomial.coe_injective
-
-variable {σ R φ ψ}
-
-@[simp, norm_cast]
-theorem coe_inj : (φ : MvPowerSeries σ R) = ψ ↔ φ = ψ :=
-  (coe_injective σ R).eq_iff
-#align mv_polynomial.coe_inj MvPolynomial.coe_inj
-
-@[simp]
-theorem coe_eq_zero_iff : (φ : MvPowerSeries σ R) = 0 ↔ φ = 0 := by rw [← coe_zero, coe_inj]
-#align mv_polynomial.coe_eq_zero_iff MvPolynomial.coe_eq_zero_iff
-
-@[simp]
-theorem coe_eq_one_iff : (φ : MvPowerSeries σ R) = 1 ↔ φ = 1 := by rw [← coe_one, coe_inj]
-#align mv_polynomial.coe_eq_one_iff MvPolynomial.coe_eq_one_iff
-
-/-- The coercion from multivariable polynomials to multivariable power series
-as a ring homomorphism.
--/
-def coeToMvPowerSeries.ringHom : MvPolynomial σ R →+* MvPowerSeries σ R where
-  toFun := (Coe.coe : MvPolynomial σ R → MvPowerSeries σ R)
-  map_zero' := coe_zero
-  map_one' := coe_one
-  map_add' := coe_add
-  map_mul' := coe_mul
-#align mv_polynomial.coe_to_mv_power_series.ring_hom MvPolynomial.coeToMvPowerSeries.ringHom
-
-@[simp, norm_cast]
-theorem coe_pow (n : ℕ) :
-    ((φ ^ n : MvPolynomial σ R) : MvPowerSeries σ R) = (φ : MvPowerSeries σ R) ^ n :=
-  coeToMvPowerSeries.ringHom.map_pow _ _
-#align mv_polynomial.coe_pow MvPolynomial.coe_pow
-
-variable (φ ψ)
+We provide the natural inclusion from polynomials to formal power series.
 
-@[simp]
-theorem coeToMvPowerSeries.ringHom_apply : coeToMvPowerSeries.ringHom φ = φ :=
-  rfl
-#align mv_polynomial.coe_to_mv_power_series.ring_hom_apply MvPolynomial.coeToMvPowerSeries.ringHom_apply
+Additional results can be found in:
+* `Mathlib.RingTheory.PowerSeries.Trunc`, truncation of power series;
+* `Mathlib.RingTheory.PowerSeries.Inverse`, about inverses of power series,
+and the fact that power series over a local ring form a local ring;
+* `Mathlib.RingTheory.PowerSeries.Order`, the order of a power series at 0,
+and application to the fact that power series over an integral domain
+form an integral domain.
 
-section Algebra
+## Implementation notes
 
-variable (A : Type*) [CommSemiring A] [Algebra R A]
+Because of its definition,
+  `PowerSeries R := MvPowerSeries Unit R`.
+a lot of proofs and properties from the multivariate case
+can be ported to the single variable case.
+However, it means that formal power series are indexed by `Unit →₀ ℕ`,
+which is of course canonically isomorphic to `ℕ`.
+We then build some glue to treat formal power series as if they were indexed by `ℕ`.
+Occasionally this leads to proofs that are uglier than expected.
 
-/-- The coercion from multivariable polynomials to multivariable power series
-as an algebra homomorphism.
 -/
-def coeToMvPowerSeries.algHom : MvPolynomial σ R →ₐ[R] MvPowerSeries σ A :=
-  { (MvPowerSeries.map σ (algebraMap R A)).comp coeToMvPowerSeries.ringHom with
-    commutes' := fun r => by simp [algebraMap_apply, MvPowerSeries.algebraMap_apply] }
-#align mv_polynomial.coe_to_mv_power_series.alg_hom MvPolynomial.coeToMvPowerSeries.algHom
-
-@[simp]
-theorem coeToMvPowerSeries.algHom_apply :
-    coeToMvPowerSeries.algHom A φ = MvPowerSeries.map σ (algebraMap R A) ↑φ :=
-  rfl
-#align mv_polynomial.coe_to_mv_power_series.alg_hom_apply MvPolynomial.coeToMvPowerSeries.algHom_apply
 
-end Algebra
-
-end MvPolynomial
-
-namespace MvPowerSeries
-
-variable {σ R A : Type*} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : MvPowerSeries σ R)
-
-instance algebraMvPolynomial : Algebra (MvPolynomial σ R) (MvPowerSeries σ A) :=
-  RingHom.toAlgebra (MvPolynomial.coeToMvPowerSeries.algHom A).toRingHom
-#align mv_power_series.algebra_mv_polynomial MvPowerSeries.algebraMvPolynomial
-
-instance algebraMvPowerSeries : Algebra (MvPowerSeries σ R) (MvPowerSeries σ A) :=
-  (map σ (algebraMap R A)).toAlgebra
-#align mv_power_series.algebra_mv_power_series MvPowerSeries.algebraMvPowerSeries
-
-variable (A)
-
-theorem algebraMap_apply' (p : MvPolynomial σ R) :
-    algebraMap (MvPolynomial σ R) (MvPowerSeries σ A) p = map σ (algebraMap R A) p :=
-  rfl
-#align mv_power_series.algebra_map_apply' MvPowerSeries.algebraMap_apply'
+noncomputable section
 
-theorem algebraMap_apply'' :
-    algebraMap (MvPowerSeries σ R) (MvPowerSeries σ A) f = map σ (algebraMap R A) f :=
-  rfl
-#align mv_power_series.algebra_map_apply'' MvPowerSeries.algebraMap_apply''
+open BigOperators
 
-end MvPowerSeries
+open Finset (antidiagonal mem_antidiagonal)
 
-/-- Formal power series over the coefficient ring `R`.-/
+/-- Formal power series over a coefficient type `R` -/
 def PowerSeries (R : Type*) :=
   MvPowerSeries Unit R
 #align power_series PowerSeries
@@ -1869,196 +630,6 @@ theorem rescale_mul (a b : R) : rescale (a * b) = (rescale b).comp (rescale a) :
 
 end CommSemiring
 
-section Trunc
-variable [Semiring R]
-open Finset Nat
-
-/-- The `n`th truncation of a formal power series to a polynomial -/
-def trunc (n : ℕ) (φ : R⟦X⟧) : R[X] :=
-  ∑ m in Ico 0 n, Polynomial.monomial m (coeff R m φ)
-#align power_series.trunc PowerSeries.trunc
-
-theorem coeff_trunc (m) (n) (φ : R⟦X⟧) :
-    (trunc n φ).coeff m = if m < n then coeff R m φ else 0 := by
-  simp [trunc, Polynomial.coeff_sum, Polynomial.coeff_monomial, Nat.lt_succ_iff]
-#align power_series.coeff_trunc PowerSeries.coeff_trunc
-
-@[simp]
-theorem trunc_zero (n) : trunc n (0 : R⟦X⟧) = 0 :=
-  Polynomial.ext fun m => by
-    rw [coeff_trunc, LinearMap.map_zero, Polynomial.coeff_zero]
-    split_ifs <;> rfl
-#align power_series.trunc_zero PowerSeries.trunc_zero
-
-@[simp]
-theorem trunc_one (n) : trunc (n + 1) (1 : R⟦X⟧) = 1 :=
-  Polynomial.ext fun m => by
-    rw [coeff_trunc, coeff_one, Polynomial.coeff_one]
-    split_ifs with h _ h'
-    · rfl
-    · rfl
-    · subst h'; simp at h
-    · rfl
-#align power_series.trunc_one PowerSeries.trunc_one
-
-@[simp]
-theorem trunc_C (n) (a : R) : trunc (n + 1) (C R a) = Polynomial.C a :=
-  Polynomial.ext fun m => by
-    rw [coeff_trunc, coeff_C, Polynomial.coeff_C]
-    split_ifs with H <;> first |rfl|try simp_all
-set_option linter.uppercaseLean3 false in
-#align power_series.trunc_C PowerSeries.trunc_C
-
-@[simp]
-theorem trunc_add (n) (φ ψ : R⟦X⟧) : trunc n (φ + ψ) = trunc n φ + trunc n ψ :=
-  Polynomial.ext fun m => by
-    simp only [coeff_trunc, AddMonoidHom.map_add, Polynomial.coeff_add]
-    split_ifs with H
-    · rfl
-    · rw [zero_add]
-#align power_series.trunc_add PowerSeries.trunc_add
-
-theorem trunc_succ (f : R⟦X⟧) (n : ℕ) :
-    trunc n.succ f = trunc n f + Polynomial.monomial n (coeff R n f) := by
-  rw [trunc, Ico_zero_eq_range, sum_range_succ, trunc, Ico_zero_eq_range]
-
-theorem natDegree_trunc_lt (f : R⟦X⟧) (n) : (trunc (n + 1) f).natDegree < n + 1 := by
-  rw [Nat.lt_succ_iff, natDegree_le_iff_coeff_eq_zero]
-  intros
-  rw [coeff_trunc]
-  split_ifs with h
-  · rw [lt_succ, ← not_lt] at h
-    contradiction
-  · rfl
-
-@[simp] lemma trunc_zero' {f : R⟦X⟧} : trunc 0 f = 0 := rfl
-
-theorem degree_trunc_lt (f : R⟦X⟧) (n) : (trunc n f).degree < n := by
-  rw [degree_lt_iff_coeff_zero]
-  intros
-  rw [coeff_trunc]
-  split_ifs with h
-  · rw [← not_le] at h
-    contradiction
-  · rfl
-
-theorem eval₂_trunc_eq_sum_range {S : Type*} [Semiring S] (s : S) (G : R →+* S) (n) (f : R⟦X⟧) :
-    (trunc n f).eval₂ G s = ∑ i in range n, G (coeff R i f) * s ^ i := by
-  cases n with
-  | zero =>
-    rw [trunc_zero', range_zero, sum_empty, eval₂_zero]
-  | succ n =>
-    have := natDegree_trunc_lt f n
-    rw [eval₂_eq_sum_range' (hn := this)]
-    apply sum_congr rfl
-    intro _ h
-    rw [mem_range] at h
-    congr
-    rw [coeff_trunc, if_pos h]
-
-@[simp] theorem trunc_X (n) : trunc (n + 2) X = (Polynomial.X : R[X]) := by
-  ext d
-  rw [coeff_trunc, coeff_X]
-  split_ifs with h₁ h₂
-  · rw [h₂, coeff_X_one]
-  · rw [coeff_X_of_ne_one h₂]
-  · rw [coeff_X_of_ne_one]
-    intro hd
-    apply h₁
-    rw [hd]
-    exact n.one_lt_succ_succ
-
-lemma trunc_X_of {n : ℕ} (hn : 2 ≤ n) : trunc n X = (Polynomial.X : R[X]) := by
-  cases n with
-  | zero => contradiction
-  | succ n =>
-    cases n with
-    | zero => contradiction
-    | succ n => exact trunc_X n
-
-end Trunc
-
-
-section Ring
-
-variable [Ring R]
-
-/-- Auxiliary function used for computing inverse of a power series -/
-protected def inv.aux : R → R⟦X⟧ → R⟦X⟧ :=
-  MvPowerSeries.inv.aux
-#align power_series.inv.aux PowerSeries.inv.aux
-
-theorem coeff_inv_aux (n : ℕ) (a : R) (φ : R⟦X⟧) :
-    coeff R n (inv.aux a φ) =
-      if n = 0 then a
-      else
-        -a *
-          ∑ x in antidiagonal n,
-            if x.2 < n then coeff R x.1 φ * coeff R x.2 (inv.aux a φ) else 0 := by
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [coeff, inv.aux, MvPowerSeries.coeff_inv_aux]
-  simp only [Finsupp.single_eq_zero]
-  split_ifs; · rfl
-  congr 1
-  symm
-  apply Finset.sum_nbij' (fun (a, b) ↦ (single () a, single () b))
-    fun (f, g) ↦ (f (), g ())
-  · aesop
-  · aesop
-  · aesop
-  · aesop
-  · rintro ⟨i, j⟩ _hij
-    obtain H | H := le_or_lt n j
-    · aesop
-    rw [if_pos H, if_pos]
-    · rfl
-    refine ⟨?_, fun hh ↦ H.not_le ?_⟩
-    · rintro ⟨⟩
-      simpa [Finsupp.single_eq_same] using le_of_lt H
-    · simpa [Finsupp.single_eq_same] using hh ()
-#align power_series.coeff_inv_aux PowerSeries.coeff_inv_aux
-
-/-- A formal power series is invertible if the constant coefficient is invertible.-/
-def invOfUnit (φ : R⟦X⟧) (u : Rˣ) : R⟦X⟧ :=
-  MvPowerSeries.invOfUnit φ u
-#align power_series.inv_of_unit PowerSeries.invOfUnit
-
-theorem coeff_invOfUnit (n : ℕ) (φ : R⟦X⟧) (u : Rˣ) :
-    coeff R n (invOfUnit φ u) =
-      if n = 0 then ↑u⁻¹
-      else
-        -↑u⁻¹ *
-          ∑ x in antidiagonal n,
-            if x.2 < n then coeff R x.1 φ * coeff R x.2 (invOfUnit φ u) else 0 :=
-  coeff_inv_aux n (↑u⁻¹ : R) φ
-#align power_series.coeff_inv_of_unit PowerSeries.coeff_invOfUnit
-
-@[simp]
-theorem constantCoeff_invOfUnit (φ : R⟦X⟧) (u : Rˣ) :
-    constantCoeff R (invOfUnit φ u) = ↑u⁻¹ := by
-  rw [← coeff_zero_eq_constantCoeff_apply, coeff_invOfUnit, if_pos rfl]
-#align power_series.constant_coeff_inv_of_unit PowerSeries.constantCoeff_invOfUnit
-
-theorem mul_invOfUnit (φ : R⟦X⟧) (u : Rˣ) (h : constantCoeff R φ = u) :
-    φ * invOfUnit φ u = 1 :=
-  MvPowerSeries.mul_invOfUnit φ u <| h
-#align power_series.mul_inv_of_unit PowerSeries.mul_invOfUnit
-
-/-- Two ways of removing the constant coefficient of a power series are the same. -/
-theorem sub_const_eq_shift_mul_X (φ : R⟦X⟧) :
-    φ - C R (constantCoeff R φ) = (PowerSeries.mk fun p => coeff R (p + 1) φ) * X :=
-  sub_eq_iff_eq_add.mpr (eq_shift_mul_X_add_const φ)
-set_option linter.uppercaseLean3 false in
-#align power_series.sub_const_eq_shift_mul_X PowerSeries.sub_const_eq_shift_mul_X
-
-theorem sub_const_eq_X_mul_shift (φ : R⟦X⟧) :
-    φ - C R (constantCoeff R φ) = X * PowerSeries.mk fun p => coeff R (p + 1) φ :=
-  sub_eq_iff_eq_add.mpr (eq_X_mul_shift_add_const φ)
-set_option linter.uppercaseLean3 false in
-#align power_series.sub_const_eq_X_mul_shift PowerSeries.sub_const_eq_X_mul_shift
-
-end Ring
-
 section CommSemiring
 
 open Finset.HasAntidiagonal Finset
@@ -2201,22 +772,6 @@ theorem rescale_injective {a : R} (ha : a ≠ 0) : Function.Injective (rescale a
 
 end IsDomain
 
-section LocalRing
-
-variable {S : Type*} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalRingHom f]
-
-instance map.isLocalRingHom : IsLocalRingHom (map f) :=
-  MvPowerSeries.map.isLocalRingHom f
-#align power_series.map.is_local_ring_hom PowerSeries.map.isLocalRingHom
-
-variable [LocalRing R] [LocalRing S]
-
-instance : LocalRing R⟦X⟧ :=
-  { inferInstanceAs <| LocalRing <| MvPowerSeries Unit R with }
-
-
-end LocalRing
-
 section Algebra
 
 variable {A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
@@ -2235,434 +790,11 @@ instance [Nontrivial R] : Nontrivial (Subalgebra R R⟦X⟧) :=
 
 end Algebra
 
-section Field
-
-variable {k : Type*} [Field k]
-
-/-- The inverse 1/f of a power series f defined over a field -/
-protected def inv : PowerSeries k → PowerSeries k :=
-  MvPowerSeries.inv
-#align power_series.inv PowerSeries.inv
-
-instance : Inv (PowerSeries k) :=
-  ⟨PowerSeries.inv⟩
-
-theorem inv_eq_inv_aux (φ : PowerSeries k) : φ⁻¹ = inv.aux (constantCoeff k φ)⁻¹ φ :=
-  rfl
-#align power_series.inv_eq_inv_aux PowerSeries.inv_eq_inv_aux
-
-theorem coeff_inv (n) (φ : PowerSeries k) :
-    coeff k n φ⁻¹ =
-      if n = 0 then (constantCoeff k φ)⁻¹
-      else
-        -(constantCoeff k φ)⁻¹ *
-          ∑ x in antidiagonal n,
-            if x.2 < n then coeff k x.1 φ * coeff k x.2 φ⁻¹ else 0 :=
-  by rw [inv_eq_inv_aux, coeff_inv_aux n (constantCoeff k φ)⁻¹ φ]
-#align power_series.coeff_inv PowerSeries.coeff_inv
-
-@[simp]
-theorem constantCoeff_inv (φ : PowerSeries k) : constantCoeff k φ⁻¹ = (constantCoeff k φ)⁻¹ :=
-  MvPowerSeries.constantCoeff_inv φ
-#align power_series.constant_coeff_inv PowerSeries.constantCoeff_inv
-
-theorem inv_eq_zero {φ : PowerSeries k} : φ⁻¹ = 0 ↔ constantCoeff k φ = 0 :=
-  MvPowerSeries.inv_eq_zero
-#align power_series.inv_eq_zero PowerSeries.inv_eq_zero
-
-@[simp]
-theorem zero_inv : (0 : PowerSeries k)⁻¹ = 0 :=
-  MvPowerSeries.zero_inv
-#align power_series.zero_inv PowerSeries.zero_inv
-
--- Porting note (#10618): simp can prove this.
--- @[simp]
-theorem invOfUnit_eq (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) :
-    invOfUnit φ (Units.mk0 _ h) = φ⁻¹ :=
-  MvPowerSeries.invOfUnit_eq _ _
-#align power_series.inv_of_unit_eq PowerSeries.invOfUnit_eq
-
-@[simp]
-theorem invOfUnit_eq' (φ : PowerSeries k) (u : Units k) (h : constantCoeff k φ = u) :
-    invOfUnit φ u = φ⁻¹ :=
-  MvPowerSeries.invOfUnit_eq' φ _ h
-#align power_series.inv_of_unit_eq' PowerSeries.invOfUnit_eq'
-
-@[simp]
-protected theorem mul_inv_cancel (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) : φ * φ⁻¹ = 1 :=
-  MvPowerSeries.mul_inv_cancel φ h
-#align power_series.mul_inv_cancel PowerSeries.mul_inv_cancel
-
-@[simp]
-protected theorem inv_mul_cancel (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) : φ⁻¹ * φ = 1 :=
-  MvPowerSeries.inv_mul_cancel φ h
-#align power_series.inv_mul_cancel PowerSeries.inv_mul_cancel
-
-theorem eq_mul_inv_iff_mul_eq {φ₁ φ₂ φ₃ : PowerSeries k} (h : constantCoeff k φ₃ ≠ 0) :
-    φ₁ = φ₂ * φ₃⁻¹ ↔ φ₁ * φ₃ = φ₂ :=
-  MvPowerSeries.eq_mul_inv_iff_mul_eq h
-#align power_series.eq_mul_inv_iff_mul_eq PowerSeries.eq_mul_inv_iff_mul_eq
-
-theorem eq_inv_iff_mul_eq_one {φ ψ : PowerSeries k} (h : constantCoeff k ψ ≠ 0) :
-    φ = ψ⁻¹ ↔ φ * ψ = 1 :=
-  MvPowerSeries.eq_inv_iff_mul_eq_one h
-#align power_series.eq_inv_iff_mul_eq_one PowerSeries.eq_inv_iff_mul_eq_one
-
-theorem inv_eq_iff_mul_eq_one {φ ψ : PowerSeries k} (h : constantCoeff k ψ ≠ 0) :
-    ψ⁻¹ = φ ↔ φ * ψ = 1 :=
-  MvPowerSeries.inv_eq_iff_mul_eq_one h
-#align power_series.inv_eq_iff_mul_eq_one PowerSeries.inv_eq_iff_mul_eq_one
-
-@[simp]
-protected theorem mul_inv_rev (φ ψ : PowerSeries k) : (φ * ψ)⁻¹ = ψ⁻¹ * φ⁻¹ :=
-  MvPowerSeries.mul_inv_rev _ _
-#align power_series.mul_inv_rev PowerSeries.mul_inv_rev
-
-instance : InvOneClass (PowerSeries k) :=
-  { inferInstanceAs <| InvOneClass <| MvPowerSeries Unit k with }
-
-@[simp]
-theorem C_inv (r : k) : (C k r)⁻¹ = C k r⁻¹ :=
-  MvPowerSeries.C_inv _
-set_option linter.uppercaseLean3 false in
-#align power_series.C_inv PowerSeries.C_inv
-
-@[simp]
-theorem X_inv : (X : PowerSeries k)⁻¹ = 0 :=
-  MvPowerSeries.X_inv _
-set_option linter.uppercaseLean3 false in
-#align power_series.X_inv PowerSeries.X_inv
-
-@[simp]
-theorem smul_inv (r : k) (φ : PowerSeries k) : (r • φ)⁻¹ = r⁻¹ • φ⁻¹ :=
-  MvPowerSeries.smul_inv _ _
-#align power_series.smul_inv PowerSeries.smul_inv
-
-end Field
-
-end PowerSeries
-
-namespace PowerSeries
-
-variable {R : Type*}
-
-section OrderBasic
-
-open multiplicity
-
-variable [Semiring R] {φ : R⟦X⟧}
-
-theorem exists_coeff_ne_zero_iff_ne_zero : (∃ n : ℕ, coeff R n φ ≠ 0) ↔ φ ≠ 0 := by
-  refine' not_iff_not.mp _
-  push_neg
-  -- FIXME: the `FunLike.coe` doesn't seem to be picked up in the expression after #8386?
-  simp [PowerSeries.ext_iff, (coeff R _).map_zero]
-#align power_series.exists_coeff_ne_zero_iff_ne_zero PowerSeries.exists_coeff_ne_zero_iff_ne_zero
-
-/-- The order of a formal power series `φ` is the greatest `n : PartENat`
-such that `X^n` divides `φ`. The order is `⊤` if and only if `φ = 0`. -/
-def order (φ : R⟦X⟧) : PartENat :=
-  letI := Classical.decEq R
-  letI := Classical.decEq R⟦X⟧
-  if h : φ = 0 then ⊤ else Nat.find (exists_coeff_ne_zero_iff_ne_zero.mpr h)
-#align power_series.order PowerSeries.order
-
-/-- The order of the `0` power series is infinite.-/
-@[simp]
-theorem order_zero : order (0 : R⟦X⟧) = ⊤ :=
-  dif_pos rfl
-#align power_series.order_zero PowerSeries.order_zero
-
-theorem order_finite_iff_ne_zero : (order φ).Dom ↔ φ ≠ 0 := by
-  simp only [order]
-  constructor
-  · split_ifs with h <;> intro H
-    · contrapose! H
-      simp only [← Part.eq_none_iff']
-      rfl
-    · exact h
-  · intro h
-    simp [h]
-#align power_series.order_finite_iff_ne_zero PowerSeries.order_finite_iff_ne_zero
-
-/-- If the order of a formal power series is finite,
-then the coefficient indexed by the order is nonzero.-/
-theorem coeff_order (h : (order φ).Dom) : coeff R (φ.order.get h) φ ≠ 0 := by
-  classical
-  simp only [order, order_finite_iff_ne_zero.mp h, not_false_iff, dif_neg, PartENat.get_natCast']
-  generalize_proofs h
-  exact Nat.find_spec h
-#align power_series.coeff_order PowerSeries.coeff_order
-
-/-- If the `n`th coefficient of a formal power series is nonzero,
-then the order of the power series is less than or equal to `n`.-/
-theorem order_le (n : ℕ) (h : coeff R n φ ≠ 0) : order φ ≤ n := by
-  classical
-  rw [order, dif_neg]
-  · simp only [PartENat.coe_le_coe]
-    exact Nat.find_le h
-  · exact exists_coeff_ne_zero_iff_ne_zero.mp ⟨n, h⟩
-#align power_series.order_le PowerSeries.order_le
-
-/-- The `n`th coefficient of a formal power series is `0` if `n` is strictly
-smaller than the order of the power series.-/
-theorem coeff_of_lt_order (n : ℕ) (h : ↑n < order φ) : coeff R n φ = 0 := by
-  contrapose! h
-  exact order_le _ h
-#align power_series.coeff_of_lt_order PowerSeries.coeff_of_lt_order
-
-/-- The `0` power series is the unique power series with infinite order.-/
-@[simp]
-theorem order_eq_top {φ : R⟦X⟧} : φ.order = ⊤ ↔ φ = 0 := by
-  constructor
-  · intro h
-    ext n
-    rw [(coeff R n).map_zero, coeff_of_lt_order]
-    simp [h]
-  · rintro rfl
-    exact order_zero
-#align power_series.order_eq_top PowerSeries.order_eq_top
-
-/-- The order of a formal power series is at least `n` if
-the `i`th coefficient is `0` for all `i < n`.-/
-theorem nat_le_order (φ : R⟦X⟧) (n : ℕ) (h : ∀ i < n, coeff R i φ = 0) : ↑n ≤ order φ := by
-  by_contra H; rw [not_le] at H
-  have : (order φ).Dom := PartENat.dom_of_le_natCast H.le
-  rw [← PartENat.natCast_get this, PartENat.coe_lt_coe] at H
-  exact coeff_order this (h _ H)
-#align power_series.nat_le_order PowerSeries.nat_le_order
-
-/-- The order of a formal power series is at least `n` if
-the `i`th coefficient is `0` for all `i < n`.-/
-theorem le_order (φ : R⟦X⟧) (n : PartENat) (h : ∀ i : ℕ, ↑i < n → coeff R i φ = 0) :
-    n ≤ order φ := by
-  induction n using PartENat.casesOn
-  · show _ ≤ _
-    rw [top_le_iff, order_eq_top]
-    ext i
-    exact h _ (PartENat.natCast_lt_top i)
-  · apply nat_le_order
-    simpa only [PartENat.coe_lt_coe] using h
-#align power_series.le_order PowerSeries.le_order
-
-/-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
-and the `i`th coefficient is `0` for all `i < n`.-/
-theorem order_eq_nat {φ : R⟦X⟧} {n : ℕ} :
-    order φ = n ↔ coeff R n φ ≠ 0 ∧ ∀ i, i < n → coeff R i φ = 0 := by
-  classical
-  rcases eq_or_ne φ 0 with (rfl | hφ)
-  · simpa [(coeff R _).map_zero] using (PartENat.natCast_ne_top _).symm
-  simp [order, dif_neg hφ, Nat.find_eq_iff]
-#align power_series.order_eq_nat PowerSeries.order_eq_nat
-
-/-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
-and the `i`th coefficient is `0` for all `i < n`.-/
-theorem order_eq {φ : R⟦X⟧} {n : PartENat} :
-    order φ = n ↔ (∀ i : ℕ, ↑i = n → coeff R i φ ≠ 0) ∧ ∀ i : ℕ, ↑i < n → coeff R i φ = 0 := by
-  induction n using PartENat.casesOn
-  · rw [order_eq_top]
-    constructor
-    · rintro rfl
-      constructor <;> intros
-      · exfalso
-        exact PartENat.natCast_ne_top ‹_› ‹_›
-      · exact (coeff _ _).map_zero
-    · rintro ⟨_h₁, h₂⟩
-      ext i
-      exact h₂ i (PartENat.natCast_lt_top i)
-  · simpa [PartENat.natCast_inj] using order_eq_nat
-#align power_series.order_eq PowerSeries.order_eq
-
-/-- The order of the sum of two formal power series
- is at least the minimum of their orders.-/
-theorem le_order_add (φ ψ : R⟦X⟧) : min (order φ) (order ψ) ≤ order (φ + ψ) := by
-  refine' le_order _ _ _
-  simp (config := { contextual := true }) [coeff_of_lt_order]
-#align power_series.le_order_add PowerSeries.le_order_add
-
-private theorem order_add_of_order_eq.aux (φ ψ : R⟦X⟧) (_h : order φ ≠ order ψ)
-    (H : order φ < order ψ) : order (φ + ψ) ≤ order φ ⊓ order ψ := by
-  suffices order (φ + ψ) = order φ by
-    rw [le_inf_iff, this]
-    exact ⟨le_rfl, le_of_lt H⟩
-  · rw [order_eq]
-    constructor
-    · intro i hi
-      rw [← hi] at H
-      rw [(coeff _ _).map_add, coeff_of_lt_order i H, add_zero]
-      exact (order_eq_nat.1 hi.symm).1
-    · intro i hi
-      rw [(coeff _ _).map_add, coeff_of_lt_order i hi, coeff_of_lt_order i (lt_trans hi H),
-        zero_add]
--- #align power_series.order_add_of_order_eq.aux power_series.order_add_of_order_eq.aux
-
-/-- The order of the sum of two formal power series
- is the minimum of their orders if their orders differ.-/
-theorem order_add_of_order_eq (φ ψ : R⟦X⟧) (h : order φ ≠ order ψ) :
-    order (φ + ψ) = order φ ⊓ order ψ := by
-  refine' le_antisymm _ (le_order_add _ _)
-  by_cases H₁ : order φ < order ψ
-  · apply order_add_of_order_eq.aux _ _ h H₁
-  by_cases H₂ : order ψ < order φ
-  · simpa only [add_comm, inf_comm] using order_add_of_order_eq.aux _ _ h.symm H₂
-  exfalso; exact h (le_antisymm (not_lt.1 H₂) (not_lt.1 H₁))
-#align power_series.order_add_of_order_eq PowerSeries.order_add_of_order_eq
-
-/-- The order of the product of two formal power series
- is at least the sum of their orders.-/
-theorem order_mul_ge (φ ψ : R⟦X⟧) : order φ + order ψ ≤ order (φ * ψ) := by
-  apply le_order
-  intro n hn; rw [coeff_mul, Finset.sum_eq_zero]
-  rintro ⟨i, j⟩ hij
-  by_cases hi : ↑i < order φ
-  · rw [coeff_of_lt_order i hi, zero_mul]
-  by_cases hj : ↑j < order ψ
-  · rw [coeff_of_lt_order j hj, mul_zero]
-  rw [not_lt] at hi hj; rw [mem_antidiagonal] at hij
-  exfalso
-  apply ne_of_lt (lt_of_lt_of_le hn <| add_le_add hi hj)
-  rw [← Nat.cast_add, hij]
-#align power_series.order_mul_ge PowerSeries.order_mul_ge
-
-/-- The order of the monomial `a*X^n` is infinite if `a = 0` and `n` otherwise.-/
-theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
-    order (monomial R n a) = if a = 0 then (⊤ : PartENat) else n := by
-  split_ifs with h
-  · rw [h, order_eq_top, LinearMap.map_zero]
-  · rw [order_eq]
-    constructor <;> intro i hi
-    · rw [PartENat.natCast_inj] at hi
-      rwa [hi, coeff_monomial_same]
-    · rw [PartENat.coe_lt_coe] at hi
-      rw [coeff_monomial, if_neg]
-      exact ne_of_lt hi
-#align power_series.order_monomial PowerSeries.order_monomial
-
-/-- The order of the monomial `a*X^n` is `n` if `a ≠ 0`.-/
-theorem order_monomial_of_ne_zero (n : ℕ) (a : R) (h : a ≠ 0) : order (monomial R n a) = n := by
-  classical
-  rw [order_monomial, if_neg h]
-#align power_series.order_monomial_of_ne_zero PowerSeries.order_monomial_of_ne_zero
-
-/-- If `n` is strictly smaller than the order of `ψ`, then the `n`th coefficient of its product
-with any other power series is `0`. -/
-theorem coeff_mul_of_lt_order {φ ψ : R⟦X⟧} {n : ℕ} (h : ↑n < ψ.order) :
-    coeff R n (φ * ψ) = 0 := by
-  suffices coeff R n (φ * ψ) = ∑ p in antidiagonal n, 0 by rw [this, Finset.sum_const_zero]
-  rw [coeff_mul]
-  apply Finset.sum_congr rfl
-  intro x hx
-  refine' mul_eq_zero_of_right (coeff R x.fst φ) (coeff_of_lt_order x.snd (lt_of_le_of_lt _ h))
-  rw [mem_antidiagonal] at hx
-  norm_cast
-  linarith
-#align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_order
-
-theorem coeff_mul_one_sub_of_lt_order {R : Type*} [CommRing R] {φ ψ : R⟦X⟧} (n : ℕ)
-    (h : ↑n < ψ.order) : coeff R n (φ * (1 - ψ)) = coeff R n φ := by
-  simp [coeff_mul_of_lt_order h, mul_sub]
-#align power_series.coeff_mul_one_sub_of_lt_order PowerSeries.coeff_mul_one_sub_of_lt_order
-
-theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type*} [CommRing R] (k : ℕ) (s : Finset ι)
-    (φ : R⟦X⟧) (f : ι → R⟦X⟧) :
-    (∀ i ∈ s, ↑k < (f i).order) → coeff R k (φ * ∏ i in s, (1 - f i)) = coeff R k φ := by
-  classical
-  induction' s using Finset.induction_on with a s ha ih t
-  · simp
-  · intro t
-    simp only [Finset.mem_insert, forall_eq_or_imp] at t
-    rw [Finset.prod_insert ha, ← mul_assoc, mul_right_comm, coeff_mul_one_sub_of_lt_order _ t.1]
-    exact ih t.2
-#align power_series.coeff_mul_prod_one_sub_of_lt_order PowerSeries.coeff_mul_prod_one_sub_of_lt_order
-
--- TODO: link with `X_pow_dvd_iff`
-theorem X_pow_order_dvd (h : (order φ).Dom) : X ^ (order φ).get h ∣ φ := by
-  refine' ⟨PowerSeries.mk fun n => coeff R (n + (order φ).get h) φ, _⟩
-  ext n
-  simp only [coeff_mul, coeff_X_pow, coeff_mk, boole_mul, Finset.sum_ite,
-    Finset.sum_const_zero, add_zero]
-  rw [Finset.filter_fst_eq_antidiagonal n (Part.get (order φ) h)]
-  split_ifs with hn
-  · simp [tsub_add_cancel_of_le hn]
-  · simp only [Finset.sum_empty]
-    refine' coeff_of_lt_order _ _
-    simpa [PartENat.coe_lt_iff] using fun _ => hn
-set_option linter.uppercaseLean3 false in
-#align power_series.X_pow_order_dvd PowerSeries.X_pow_order_dvd
-
-theorem order_eq_multiplicity_X {R : Type*} [Semiring R] [@DecidableRel R⟦X⟧ (· ∣ ·)] (φ : R⟦X⟧) :
-    order φ = multiplicity X φ := by
-  classical
-  rcases eq_or_ne φ 0 with (rfl | hφ)
-  · simp
-  induction' ho : order φ using PartENat.casesOn with n
-  · simp [hφ] at ho
-  have hn : φ.order.get (order_finite_iff_ne_zero.mpr hφ) = n := by simp [ho]
-  rw [← hn]
-  refine'
-    le_antisymm (le_multiplicity_of_pow_dvd <| X_pow_order_dvd (order_finite_iff_ne_zero.mpr hφ))
-      (PartENat.find_le _ _ _)
-  rintro ⟨ψ, H⟩
-  have := congr_arg (coeff R n) H
-  rw [← (ψ.commute_X.pow_right _).eq, coeff_mul_of_lt_order, ← hn] at this
-  · exact coeff_order _ this
-  · rw [X_pow_eq, order_monomial]
-    split_ifs
-    · exact PartENat.natCast_lt_top _
-    · rw [← hn, PartENat.coe_lt_coe]
-      exact Nat.lt_succ_self _
-set_option linter.uppercaseLean3 false in
-#align power_series.order_eq_multiplicity_X PowerSeries.order_eq_multiplicity_X
-
-end OrderBasic
-
-section OrderZeroNeOne
-
-variable [Semiring R] [Nontrivial R]
-
-/-- The order of the formal power series `1` is `0`.-/
-@[simp]
-theorem order_one : order (1 : R⟦X⟧) = 0 := by
-  simpa using order_monomial_of_ne_zero 0 (1 : R) one_ne_zero
-#align power_series.order_one PowerSeries.order_one
-
-/-- The order of the formal power series `X` is `1`.-/
-@[simp]
-theorem order_X : order (X : R⟦X⟧) = 1 := by
-  simpa only [Nat.cast_one] using order_monomial_of_ne_zero 1 (1 : R) one_ne_zero
-set_option linter.uppercaseLean3 false in
-#align power_series.order_X PowerSeries.order_X
-
-/-- The order of the formal power series `X^n` is `n`.-/
-@[simp]
-theorem order_X_pow (n : ℕ) : order ((X : R⟦X⟧) ^ n) = n := by
-  rw [X_pow_eq, order_monomial_of_ne_zero]
-  exact one_ne_zero
-set_option linter.uppercaseLean3 false in
-#align power_series.order_X_pow PowerSeries.order_X_pow
-
-end OrderZeroNeOne
-
-section OrderIsDomain
-
--- TODO: generalize to `[Semiring R] [NoZeroDivisors R]`
-variable [CommRing R] [IsDomain R]
-
-/-- The order of the product of two formal power series over an integral domain
- is the sum of their orders.-/
-theorem order_mul (φ ψ : R⟦X⟧) : order (φ * ψ) = order φ + order ψ := by
-  classical
-  simp_rw [order_eq_multiplicity_X]
-  exact multiplicity.mul X_prime
-#align power_series.order_mul PowerSeries.order_mul
-
-end OrderIsDomain
-
 end PowerSeries
 
 namespace Polynomial
 
-open Finsupp
+open Finsupp Polynomial
 
 variable {σ : Type*} {R : Type*} [CommSemiring R] (φ ψ : R[X])
 
@@ -2822,6 +954,8 @@ namespace PowerSeries
 
 section Algebra
 
+open Polynomial
+
 variable {R A : Type*} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : R⟦X⟧)
 
 instance algebraPolynomial : Algebra R[X] A⟦X⟧ :=
@@ -2851,82 +985,6 @@ theorem algebraMap_apply'' :
 
 end Algebra
 
-section Trunc
-/-
-Lemmas in this section involve the coercion `R[X] → R⟦X⟧`, so they may only be stated in the case
-`R` is commutative. This is because the coercion is an `R`-algebra map.
--/
-variable {R : Type*} [CommSemiring R]
-
-open Nat hiding pow_succ pow_zero
-open Polynomial BigOperators Finset Finset.Nat
-
-theorem trunc_trunc_of_le {n m} (f : R⟦X⟧) (hnm : n ≤ m := by rfl) :
-    trunc n ↑(trunc m f) = trunc n f := by
-  ext d
-  rw [coeff_trunc, coeff_trunc, coeff_coe]
-  split_ifs with h
-  · rw [coeff_trunc, if_pos <| lt_of_lt_of_le h hnm]
-  · rfl
-
-@[simp] theorem trunc_trunc {n} (f : R⟦X⟧) : trunc n ↑(trunc n f) = trunc n f :=
-  trunc_trunc_of_le f
-
-@[simp] theorem trunc_trunc_mul {n} (f g : R ⟦X⟧) :
-    trunc n ((trunc n f) * g : R⟦X⟧) = trunc n (f * g) := by
-  ext m
-  rw [coeff_trunc, coeff_trunc]
-  split_ifs with h
-  · rw [coeff_mul, coeff_mul, sum_congr rfl]
-    intro _ hab
-    have ha := lt_of_le_of_lt (antidiagonal.fst_le hab) h
-    rw [coeff_coe, coeff_trunc, if_pos ha]
-  · rfl
-
-@[simp] theorem trunc_mul_trunc {n} (f g : R ⟦X⟧) :
-    trunc n (f * (trunc n g) : R⟦X⟧) = trunc n (f * g) := by
-  rw [mul_comm, trunc_trunc_mul, mul_comm]
-
-theorem trunc_trunc_mul_trunc {n} (f g : R⟦X⟧) :
-    trunc n (trunc n f * trunc n g : R⟦X⟧) = trunc n (f * g) := by
-  rw [trunc_trunc_mul, trunc_mul_trunc]
-
-@[simp] theorem trunc_trunc_pow (f : R⟦X⟧) (n a : ℕ) :
-    trunc n ((trunc n f : R⟦X⟧) ^ a) = trunc n (f ^ a) := by
-  induction a with
-  | zero =>
-    rw [pow_zero, pow_zero]
-  | succ a ih =>
-    rw [pow_succ, pow_succ, trunc_trunc_mul, ← trunc_trunc_mul_trunc, ih, trunc_trunc_mul_trunc]
-
-theorem trunc_coe_eq_self {n} {f : R[X]} (hn : natDegree f < n) : trunc n (f : R⟦X⟧) = f := by
-  rw [← Polynomial.coe_inj]
-  ext m
-  rw [coeff_coe, coeff_trunc]
-  split
-  case inl h => rfl
-  case inr h =>
-    rw [not_lt] at h
-    rw [coeff_coe]; symm
-    exact coeff_eq_zero_of_natDegree_lt <| lt_of_lt_of_le hn h
-
-/-- The function `coeff n : R⟦X⟧ → R` is continuous. I.e. `coeff n f` depends only on a sufficiently
-long truncation of the power series `f`.-/
-theorem coeff_coe_trunc_of_lt {n m} {f : R⟦X⟧} (h : n < m) :
-    coeff R n (trunc m f) = coeff R n f := by
-  rwa [coeff_coe, coeff_trunc, if_pos]
-
-/-- The `n`-th coefficient of `f*g` may be calculated
-from the truncations of `f` and `g`.-/
-theorem coeff_mul_eq_coeff_trunc_mul_trunc₂ {n a b} (f g) (ha : n < a) (hb : n < b) :
-    coeff R n (f * g) = coeff R n (trunc a f * trunc b g) := by
-  symm
-  rw [← coeff_coe_trunc_of_lt n.lt_succ_self, ← trunc_trunc_mul_trunc, trunc_trunc_of_le f ha,
-    trunc_trunc_of_le g hb, trunc_trunc_mul_trunc, coeff_coe_trunc_of_lt n.lt_succ_self]
-
-theorem coeff_mul_eq_coeff_trunc_mul_trunc {d n} (f g) (h : d < n) :
-    coeff R d (f * g) = coeff R d (trunc n f * trunc n g) :=
-  coeff_mul_eq_coeff_trunc_mul_trunc₂ f g h h
-
-end Trunc
 end PowerSeries
+
+end

This PR split the files devoted to power series (especially RingTheory/PowerSeries/Basic) into several ones:

• RingTheory/MvPowerSeries/Basic - initial definitions (multivariate)

• RingTheory/MvPowerSeries/Trunc - truncation

• RingTheory/MvPowerSeries/Inverse - stuff pertaining to inverses

• RingTheory/PowerSeries/Basic - initial definitions (univariate)

• RingTheory/PowerSeries/Trunc - truncation

• RingTheory/PowerSeries/Inverse - stuff pertaining to inverses

• RingTheory/PowerSeries/Order - stuff pertaining to order

it remains to adjust the other files (PowerSeries/Derivative and PowerSeries/WellKnown)

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: faenuccio <filippo.nuccio@univ-st-etienne.fr>

This PR split the files devoted to power series (especially RingTheory/PowerSeries/Basic) into several ones:

• RingTheory/MvPowerSeries/Basic - initial definitions (multivariate)

• RingTheory/MvPowerSeries/Trunc - truncation

• RingTheory/MvPowerSeries/Inverse - stuff pertaining to inverses

• RingTheory/PowerSeries/Basic - initial definitions (univariate)

• RingTheory/PowerSeries/Trunc - truncation

• RingTheory/PowerSeries/Inverse - stuff pertaining to inverses

• RingTheory/PowerSeries/Order - stuff pertaining to order

it remains to adjust the other files (PowerSeries/Derivative and PowerSeries/WellKnown)

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: faenuccio <filippo.nuccio@univ-st-etienne.fr>

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

@@ -183,7 +183,7 @@ theorem coeff_comp_monomial (n : σ →₀ ℕ) : (coeff R n).comp (monomial R n
   LinearMap.ext <| coeff_monomial_same n
 #align mv_power_series.coeff_comp_monomial MvPowerSeries.coeff_comp_monomial
 
--- Porting note: simp can prove this.
+-- Porting note (#10618): simp can prove this.
 -- @[simp]
 theorem coeff_zero (n : σ →₀ ℕ) : coeff R n (0 : MvPowerSeries σ R) = 0 :=
   rfl
@@ -500,13 +500,13 @@ theorem constantCoeff_comp_C : (constantCoeff σ R).comp (C σ R) = RingHom.id R
 set_option linter.uppercaseLean3 false in
 #align mv_power_series.constant_coeff_comp_C MvPowerSeries.constantCoeff_comp_C
 
--- Porting note: simp can prove this.
+-- Porting note (#10618): simp can prove this.
 -- @[simp]
 theorem constantCoeff_zero : constantCoeff σ R 0 = 0 :=
   rfl
 #align mv_power_series.constant_coeff_zero MvPowerSeries.constantCoeff_zero
 
--- Porting note: simp can prove this.
+-- Porting note (#10618): simp can prove this.
 -- @[simp]
 theorem constantCoeff_one : constantCoeff σ R 1 = 1 :=
   rfl
@@ -525,7 +525,7 @@ theorem isUnit_constantCoeff (φ : MvPowerSeries σ R) (h : IsUnit φ) :
   h.map _
 #align mv_power_series.is_unit_constant_coeff MvPowerSeries.isUnit_constantCoeff
 
--- Porting note: simp can prove this.
+-- Porting note (#10618): simp can prove this.
 -- @[simp]
 theorem coeff_smul (f : MvPowerSeries σ R) (n) (a : R) : coeff _ n (a • f) = a * coeff _ n f :=
   rfl
@@ -1026,7 +1026,7 @@ theorem zero_inv : (0 : MvPowerSeries σ k)⁻¹ = 0 := by
   rw [inv_eq_zero, constantCoeff_zero]
 #align mv_power_series.zero_inv MvPowerSeries.zero_inv
 
--- Porting note: simp can prove this.
+-- Porting note (#10618): simp can prove this.
 -- @[simp]
 theorem invOfUnit_eq (φ : MvPowerSeries σ k) (h : constantCoeff σ k φ ≠ 0) :
     invOfUnit φ (Units.mk0 _ h) = φ⁻¹ :=
@@ -1613,13 +1613,13 @@ theorem constantCoeff_comp_C : (constantCoeff R).comp (C R) = RingHom.id R :=
 set_option linter.uppercaseLean3 false in
 #align power_series.constant_coeff_comp_C PowerSeries.constantCoeff_comp_C
 
--- Porting note: simp can prove this.
+-- Porting note (#10618): simp can prove this.
 -- @[simp]
 theorem constantCoeff_zero : constantCoeff R 0 = 0 :=
   rfl
 #align power_series.constant_coeff_zero PowerSeries.constantCoeff_zero
 
--- Porting note: simp can prove this.
+-- Porting note (#10618): simp can prove this.
 -- @[simp]
 theorem constantCoeff_one : constantCoeff R 1 = 1 :=
   rfl
@@ -2275,7 +2275,7 @@ theorem zero_inv : (0 : PowerSeries k)⁻¹ = 0 :=
   MvPowerSeries.zero_inv
 #align power_series.zero_inv PowerSeries.zero_inv
 
--- Porting note: simp can prove this.
+-- Porting note (#10618): simp can prove this.
 -- @[simp]
 theorem invOfUnit_eq (φ : PowerSeries k) (h : constantCoeff k φ ≠ 0) :
     invOfUnit φ (Units.mk0 _ h) = φ⁻¹ :=

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -2548,8 +2548,7 @@ theorem order_monomial_of_ne_zero (n : ℕ) (a : R) (h : a ≠ 0) : order (monom
 with any other power series is `0`. -/
 theorem coeff_mul_of_lt_order {φ ψ : R⟦X⟧} {n : ℕ} (h : ↑n < ψ.order) :
     coeff R n (φ * ψ) = 0 := by
-  suffices : coeff R n (φ * ψ) = ∑ p in antidiagonal n, 0
-  rw [this, Finset.sum_const_zero]
+  suffices coeff R n (φ * ψ) = ∑ p in antidiagonal n, 0 by rw [this, Finset.sum_const_zero]
   rw [coeff_mul]
   apply Finset.sum_congr rfl
   intro x hx

• Use the class HasPiAntidiagonal defined in PR #7904 to compute the coefficients of products of power series (in several or one variable) : MvPowerSeries.coeff_prod and PowerSeries.coeff_prod
• Update the file Archive/Partition.lean accordingly

Co-author : Maria Ines de Frutos Fernandez

Based on work of Bhavik Mehta in Archive/Partition.lean

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: mariainesdff <mariaines.dff@gmail.com>

@@ -11,6 +11,7 @@ import Mathlib.LinearAlgebra.StdBasis
 import Mathlib.RingTheory.Ideal.LocalRing
 import Mathlib.RingTheory.Multiplicity
 import Mathlib.Tactic.Linarith
+import Mathlib.Data.Finset.PiAntidiagonal
 
 #align_import ring_theory.power_series.basic from "leanprover-community/mathlib"@"2d5739b61641ee4e7e53eca5688a08f66f2e6a60"
 
@@ -812,6 +813,50 @@ set_option linter.uppercaseLean3 false in
 
 end Semiring
 
+section CommSemiring
+
+open Finset.HasAntidiagonal Finset
+
+variable {R : Type*} [CommSemiring R] {ι : Type*} [DecidableEq ι]
+
+/-- Coefficients of a product of power series -/
+theorem coeff_prod [DecidableEq σ]
+    (f : ι → MvPowerSeries σ R) (d : σ →₀ ℕ) (s : Finset ι) :
+    coeff R d (∏ j in s, f j) =
+      ∑ l in piAntidiagonal s d,
+        ∏ i in s, coeff R (l i) (f i) := by
+  induction s using Finset.induction_on generalizing d with
+  | empty =>
+    simp only [prod_empty, sum_const, nsmul_eq_mul, mul_one, coeff_one, piAntidiagonal_empty]
+    split_ifs
+    · simp only [card_singleton, Nat.cast_one]
+    · simp only [card_empty, Nat.cast_zero]
+  | @insert a s ha ih =>
+    rw [piAntidiagonal_insert ha, prod_insert ha, coeff_mul, sum_biUnion]
+    · apply Finset.sum_congr rfl
+      · simp only [mem_antidiagonal, sum_map, Function.Embedding.coeFn_mk, coe_update, Prod.forall]
+        rintro u v rfl
+        rw [ih, Finset.mul_sum, ← Finset.sum_attach]
+        apply Finset.sum_congr rfl
+        simp only [mem_attach, Finset.prod_insert ha, Function.update_same, forall_true_left,
+          Subtype.forall]
+        rintro x -
+        rw [Finset.prod_congr rfl]
+        intro i hi
+        rw [Function.update_noteq]
+        exact ne_of_mem_of_not_mem hi ha
+    · simp only [Set.PairwiseDisjoint, Set.Pairwise, mem_coe, mem_antidiagonal, ne_eq,
+        disjoint_left, mem_map, mem_attach, Function.Embedding.coeFn_mk, true_and, Subtype.exists,
+        exists_prop, not_exists, not_and, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂,
+        Prod.forall, Prod.mk.injEq]
+      rintro u v rfl u' v' huv h k - l - hkl
+      obtain rfl : u' = u := by
+        simpa only [Finsupp.coe_update, Function.update_same] using DFunLike.congr_fun hkl a
+      simp only [add_right_inj] at huv
+      exact h rfl huv.symm
+
+end CommSemiring
+
 section Ring
 
 variable [Ring R]
@@ -2014,6 +2059,28 @@ set_option linter.uppercaseLean3 false in
 
 end Ring
 
+section CommSemiring
+
+open Finset.HasAntidiagonal Finset
+
+variable {R : Type*} [CommSemiring R] {ι : Type*} [DecidableEq ι]
+
+/-- Coefficients of a product of power series -/
+theorem coeff_prod (f : ι → PowerSeries R) (d : ℕ) (s : Finset ι) :
+    coeff R d (∏ j in s, f j) = ∑ l in piAntidiagonal s d, ∏ i in s, coeff R (l i) (f i) := by
+  simp only [coeff]
+  convert MvPowerSeries.coeff_prod _ _ _
+  rw [← AddEquiv.finsuppUnique_symm d, ← mapRange_piAntidiagonal_eq, sum_map, sum_congr rfl]
+  intro x _
+  apply prod_congr rfl
+  intro i _
+  congr 2
+  simp only [AddEquiv.toEquiv_eq_coe, Finsupp.mapRange.addEquiv_toEquiv, AddEquiv.toEquiv_symm,
+    Equiv.coe_toEmbedding, Finsupp.mapRange.equiv_apply, AddEquiv.coe_toEquiv_symm,
+    Finsupp.mapRange_apply, AddEquiv.finsuppUnique_symm]
+
+end CommSemiring
+
 section CommRing
 
 variable {A : Type*} [CommRing A]

@@ -677,7 +677,7 @@ def truncFun (φ : MvPowerSeries σ R) : MvPolynomial σ R :=
   ∑ m in Finset.Iio n, MvPolynomial.monomial m (coeff R m φ)
 #align mv_power_series.trunc_fun MvPowerSeries.truncFun
 
-theorem coeff_truncFun [DecidableEq σ] (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
+theorem coeff_truncFun (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
     (truncFun n φ).coeff m = if m < n then coeff R m φ else 0 := by
   classical
   simp [truncFun, MvPolynomial.coeff_sum]

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

@@ -1878,7 +1878,7 @@ theorem trunc_succ (f : R⟦X⟧) (n : ℕ) :
   rw [trunc, Ico_zero_eq_range, sum_range_succ, trunc, Ico_zero_eq_range]
 
 theorem natDegree_trunc_lt (f : R⟦X⟧) (n) : (trunc (n + 1) f).natDegree < n + 1 := by
-  rw [lt_succ_iff, natDegree_le_iff_coeff_eq_zero]
+  rw [Nat.lt_succ_iff, natDegree_le_iff_coeff_eq_zero]
   intros
   rw [coeff_trunc]
   split_ifs with h

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

Zulip thread

Important changes

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

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

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

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

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

Similarly, MyEquivClass should take EquivLike as a parameter.

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

Remaining issues

Slower (failing) search

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

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

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

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

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

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

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

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

simp not firing sometimes

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

Missing instances due to unification failing

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

Workaround for issues

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

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

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

@@ -2288,7 +2288,8 @@ variable [Semiring R] {φ : R⟦X⟧}
 theorem exists_coeff_ne_zero_iff_ne_zero : (∃ n : ℕ, coeff R n φ ≠ 0) ↔ φ ≠ 0 := by
   refine' not_iff_not.mp _
   push_neg
-  simp [PowerSeries.ext_iff]
+  -- FIXME: the `FunLike.coe` doesn't seem to be picked up in the expression after #8386?
+  simp [PowerSeries.ext_iff, (coeff R _).map_zero]
 #align power_series.exists_coeff_ne_zero_iff_ne_zero PowerSeries.exists_coeff_ne_zero_iff_ne_zero
 
 /-- The order of a formal power series `φ` is the greatest `n : PartENat`
@@ -2383,7 +2384,7 @@ theorem order_eq_nat {φ : R⟦X⟧} {n : ℕ} :
     order φ = n ↔ coeff R n φ ≠ 0 ∧ ∀ i, i < n → coeff R i φ = 0 := by
   classical
   rcases eq_or_ne φ 0 with (rfl | hφ)
-  · simpa using (PartENat.natCast_ne_top _).symm
+  · simpa [(coeff R _).map_zero] using (PartENat.natCast_ne_top _).symm
   simp [order, dif_neg hφ, Nat.find_eq_iff]
 #align power_series.order_eq_nat PowerSeries.order_eq_nat
 

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

@@ -831,7 +831,7 @@ protected noncomputable def inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerS
     else
       -a *
         ∑ x in antidiagonal n, if _ : x.2 < n then coeff R x.1 φ * inv.aux a φ x.2 else 0
-termination_by _ n => n
+termination_by n => n
 #align mv_power_series.inv.aux MvPowerSeries.inv.aux
 
 theorem coeff_inv_aux [DecidableEq σ] (n : σ →₀ ℕ) (a : R) (φ : MvPowerSeries σ R) :

Lemmas around this were a mess, throth in terms of names, statement and location. This PR standardises everything to be in Algebra.BigOperators.Basic and changes the lemmas to take in InjOn and SurjOn assumptions where possible (and where impossible make sure the hypotheses are taken in the correct order) and moves the equality of functions hypothesis last.

Also add a few lemmas that help fix downstream uses by golfing.

From LeanAPAP and LeanCamCombi

@@ -298,27 +298,8 @@ protected theorem mul_assoc (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : φ₁ * 
   ext1 n
   classical
   simp only [coeff_mul, Finset.sum_mul, Finset.mul_sum, Finset.sum_sigma']
-  refine' Finset.sum_bij (fun p _ => ⟨(p.2.1, p.2.2 + p.1.2), (p.2.2, p.1.2)⟩) _ _ _ _ <;>
-    simp only [mem_antidiagonal, Finset.mem_sigma, heq_iff_eq, Prod.mk.inj_iff, and_imp,
-      exists_prop]
-  · rintro ⟨⟨i, j⟩, ⟨k, l⟩⟩
-    dsimp only
-    rintro rfl rfl
-    simp [add_assoc]
-  · rintro ⟨⟨a, b⟩, ⟨c, d⟩⟩
-    dsimp only
-    rintro rfl rfl
-    apply mul_assoc
-  · rintro ⟨⟨a, b⟩, ⟨c, d⟩⟩ ⟨⟨i, j⟩, ⟨k, l⟩⟩
-    dsimp only
-    rintro rfl rfl - rfl
-    simp only [Sigma.mk.inj_iff, Prod.mk.injEq, heq_iff_eq, and_imp]
-    rintro rfl - rfl rfl
-    simp only [and_self]
-  · rintro ⟨⟨i, j⟩, ⟨k, l⟩⟩
-    dsimp only
-    rintro rfl rfl
-    refine' ⟨⟨(i + k, l), (i, k)⟩, _, _⟩ <;> simp [add_assoc]
+  apply Finset.sum_nbij' (fun ⟨⟨_i, j⟩, ⟨k, l⟩⟩ ↦ ⟨(k, l + j), (l, j)⟩)
+    (fun ⟨⟨i, _j⟩, ⟨k, l⟩⟩ ↦ ⟨(i + k, l), (i, k)⟩) <;> aesop (add simp [add_assoc, mul_assoc])
 #align mv_power_series.mul_assoc MvPowerSeries.mul_assoc
 
 instance : Semiring (MvPowerSeries σ R) :=
@@ -1975,35 +1956,21 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : R⟦X⟧) :
   split_ifs; · rfl
   congr 1
   symm
-  apply Finset.sum_bij fun (p : ℕ × ℕ) _h => (single () p.1, single () p.2)
-  · rintro ⟨i, j⟩ hij
-    rw [mem_antidiagonal] at hij
-    rw [mem_antidiagonal, ← Finsupp.single_add, hij]
+  apply Finset.sum_nbij' (fun (a, b) ↦ (single () a, single () b))
+    fun (f, g) ↦ (f (), g ())
+  · aesop
+  · aesop
+  · aesop
+  · aesop
   · rintro ⟨i, j⟩ _hij
-    by_cases H : j < n
-    · rw [if_pos H, if_pos]
-      · rfl
-      constructor
-      · rintro ⟨⟩
-        simpa [Finsupp.single_eq_same] using le_of_lt H
-      · intro hh
-        rw [lt_iff_not_ge] at H
-        apply H
-        simpa [Finsupp.single_eq_same] using hh ()
-    · rw [if_neg H, if_neg]
-      rintro ⟨_h₁, h₂⟩
-      apply h₂
-      rintro ⟨⟩
-      simpa [Finsupp.single_eq_same] using not_lt.1 H
-  · rintro ⟨i, j⟩ ⟨k, l⟩ _hij _hkl
-    simpa only [Prod.mk.inj_iff, Finsupp.unique_single_eq_iff] using id
-  · rintro ⟨f, g⟩ hfg
-    refine' ⟨(f (), g ()), _, _⟩
-    · rw [mem_antidiagonal] at hfg
-      rw [mem_antidiagonal, ← Finsupp.add_apply, hfg, Finsupp.single_eq_same]
-    · rw [Prod.mk.inj_iff]
-      dsimp
-      exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
+    obtain H | H := le_or_lt n j
+    · aesop
+    rw [if_pos H, if_pos]
+    · rfl
+    refine ⟨?_, fun hh ↦ H.not_le ?_⟩
+    · rintro ⟨⟩
+      simpa [Finsupp.single_eq_same] using le_of_lt H
+    · simpa [Finsupp.single_eq_same] using hh ()
 #align power_series.coeff_inv_aux PowerSeries.coeff_inv_aux
 
 /-- A formal power series is invertible if the constant coefficient is invertible.-/

@@ -2363,10 +2363,9 @@ theorem coeff_order (h : (order φ).Dom) : coeff R (φ.order.get h) φ ≠ 0 :=
 then the order of the power series is less than or equal to `n`.-/
 theorem order_le (n : ℕ) (h : coeff R n φ ≠ 0) : order φ ≤ n := by
   classical
-  have _ :  ∃ n, coeff R n φ ≠ 0 := Exists.intro n h
   rw [order, dif_neg]
-  · simp only [PartENat.coe_le_coe, Nat.find_le_iff]
-    exact ⟨n, le_rfl, h⟩
+  · simp only [PartENat.coe_le_coe]
+    exact Nat.find_le h
   · exact exists_coeff_ne_zero_iff_ne_zero.mp ⟨n, h⟩
 #align power_series.order_le PowerSeries.order_le
 

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

@@ -1901,7 +1901,7 @@ theorem natDegree_trunc_lt (f : R⟦X⟧) (n) : (trunc (n + 1) f).natDegree < n
   intros
   rw [coeff_trunc]
   split_ifs with h
-  · rw [lt_succ, ←not_lt] at h
+  · rw [lt_succ, ← not_lt] at h
     contradiction
   · rfl
 
@@ -1912,7 +1912,7 @@ theorem degree_trunc_lt (f : R⟦X⟧) (n) : (trunc n f).degree < n := by
   intros
   rw [coeff_trunc]
   split_ifs with h
-  · rw [←not_le] at h
+  · rw [← not_le] at h
     contradiction
   · rfl
 
@@ -2760,8 +2760,8 @@ theorem coe_pow (n : ℕ) : ((φ ^ n : R[X]) : PowerSeries R) = (φ : PowerSerie
 #align polynomial.coe_pow Polynomial.coe_pow
 
 theorem eval₂_C_X_eq_coe : φ.eval₂ (PowerSeries.C R) PowerSeries.X = ↑φ := by
-  nth_rw 2 [←eval₂_C_X (p := φ)]
-  rw [←coeToPowerSeries.ringHom_apply, eval₂_eq_sum_range, eval₂_eq_sum_range, map_sum]
+  nth_rw 2 [← eval₂_C_X (p := φ)]
+  rw [← coeToPowerSeries.ringHom_apply, eval₂_eq_sum_range, eval₂_eq_sum_range, map_sum]
   apply Finset.sum_congr rfl
   intros
   rw [map_mul, map_pow, coeToPowerSeries.ringHom_apply,
@@ -2864,10 +2864,10 @@ theorem trunc_trunc_mul_trunc {n} (f g : R⟦X⟧) :
   | zero =>
     rw [pow_zero, pow_zero]
   | succ a ih =>
-    rw [pow_succ, pow_succ, trunc_trunc_mul, ←trunc_trunc_mul_trunc, ih, trunc_trunc_mul_trunc]
+    rw [pow_succ, pow_succ, trunc_trunc_mul, ← trunc_trunc_mul_trunc, ih, trunc_trunc_mul_trunc]
 
 theorem trunc_coe_eq_self {n} {f : R[X]} (hn : natDegree f < n) : trunc n (f : R⟦X⟧) = f := by
-  rw [←Polynomial.coe_inj]
+  rw [← Polynomial.coe_inj]
   ext m
   rw [coeff_coe, coeff_trunc]
   split
@@ -2888,7 +2888,7 @@ from the truncations of `f` and `g`.-/
 theorem coeff_mul_eq_coeff_trunc_mul_trunc₂ {n a b} (f g) (ha : n < a) (hb : n < b) :
     coeff R n (f * g) = coeff R n (trunc a f * trunc b g) := by
   symm
-  rw [←coeff_coe_trunc_of_lt n.lt_succ_self, ←trunc_trunc_mul_trunc, trunc_trunc_of_le f ha,
+  rw [← coeff_coe_trunc_of_lt n.lt_succ_self, ← trunc_trunc_mul_trunc, trunc_trunc_of_le f ha,
     trunc_trunc_of_le g hb, trunc_trunc_mul_trunc, coeff_coe_trunc_of_lt n.lt_succ_self]
 
 theorem coeff_mul_eq_coeff_trunc_mul_trunc {d n} (f g) (h : d < n) :

These parallel the lemmas for Polynomial

@@ -1463,10 +1463,17 @@ set_option linter.uppercaseLean3 false in
 
 @[simp]
 theorem coeff_zero_C (a : R) : coeff R 0 (C R a) = a := by
-  rw [← monomial_zero_eq_C_apply, coeff_monomial_same 0 a]
+  rw [coeff_C, if_pos rfl]
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_zero_C PowerSeries.coeff_zero_C
 
+theorem coeff_ne_zero_C {a : R} {n : ℕ} (h : n ≠ 0) : coeff R n (C R a) = 0 := by
+  rw [coeff_C, if_neg h]
+
+@[simp]
+theorem coeff_succ_C {a : R} {n : ℕ} : coeff R (n + 1) (C R a) = 0 :=
+  coeff_ne_zero_C n.succ_ne_zero
+
 theorem X_eq : (X : R⟦X⟧) = monomial R 1 1 :=
   rfl
 set_option linter.uppercaseLean3 false in

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>

@@ -72,6 +72,8 @@ noncomputable section
 
 open BigOperators Polynomial
 
+open Finset (antidiagonal mem_antidiagonal)
+
 /-- Multivariate formal power series, where `σ` is the index set of the variables
 and `R` is the coefficient ring.-/
 def MvPowerSeries (σ : Type*) (R : Type*) :=
@@ -212,10 +214,10 @@ instance : AddMonoidWithOne (MvPowerSeries σ R) :=
 
 instance : Mul (MvPowerSeries σ R) :=
   letI := Classical.decEq σ
-  ⟨fun φ ψ n => ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ⟩
+  ⟨fun φ ψ n => ∑ p in antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ⟩
 
 theorem coeff_mul [DecidableEq σ] :
-    coeff R n (φ * ψ) = ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ := by
+    coeff R n (φ * ψ) = ∑ p in antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ := by
   refine Finset.sum_congr ?_ fun _ _ => rfl
   rw [Subsingleton.elim (Classical.decEq σ) ‹DecidableEq σ›]
 #align mv_power_series.coeff_mul MvPowerSeries.coeff_mul
@@ -235,7 +237,8 @@ theorem coeff_monomial_mul (a : R) :
     ∀ p ∈ antidiagonal m,
       coeff R (p : (σ →₀ ℕ) × (σ →₀ ℕ)).1 (monomial R n a) * coeff R p.2 φ ≠ 0 → p.1 = n :=
     fun p _ hp => eq_of_coeff_monomial_ne_zero (left_ne_zero_of_mul hp)
-  rw [coeff_mul, ← Finset.sum_filter_of_ne this, antidiagonal_filter_fst_eq, Finset.sum_ite_index]
+  rw [coeff_mul, ← Finset.sum_filter_of_ne this, Finset.filter_fst_eq_antidiagonal _ n,
+    Finset.sum_ite_index]
   simp only [Finset.sum_singleton, coeff_monomial_same, Finset.sum_empty]
 #align mv_power_series.coeff_monomial_mul MvPowerSeries.coeff_monomial_mul
 
@@ -246,7 +249,8 @@ theorem coeff_mul_monomial (a : R) :
     ∀ p ∈ antidiagonal m,
       coeff R (p : (σ →₀ ℕ) × (σ →₀ ℕ)).1 φ * coeff R p.2 (monomial R n a) ≠ 0 → p.2 = n :=
     fun p _ hp => eq_of_coeff_monomial_ne_zero (right_ne_zero_of_mul hp)
-  rw [coeff_mul, ← Finset.sum_filter_of_ne this, antidiagonal_filter_snd_eq, Finset.sum_ite_index]
+  rw [coeff_mul, ← Finset.sum_filter_of_ne this, Finset.filter_snd_eq_antidiagonal _ n,
+    Finset.sum_ite_index]
   simp only [Finset.sum_singleton, coeff_monomial_same, Finset.sum_empty]
 #align mv_power_series.coeff_mul_monomial MvPowerSeries.coeff_mul_monomial
 
@@ -771,7 +775,7 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
     contrapose! h
     dsimp at h
     subst i
-    rw [Finsupp.mem_antidiagonal] at hij
+    rw [mem_antidiagonal] at hij
     rw [← hij, Finsupp.add_apply, Finsupp.single_eq_same]
     exact Nat.le_add_right n _
   · intro h
@@ -782,7 +786,7 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
       · rw [coeff_X_pow, if_pos rfl, one_mul]
         simpa using congr_arg (fun m : σ →₀ ℕ => coeff R m φ) H.symm
       · rintro ⟨i, j⟩ hij hne
-        rw [Finsupp.mem_antidiagonal] at hij
+        rw [mem_antidiagonal] at hij
         rw [coeff_X_pow]
         split_ifs with hi
         · exfalso
@@ -795,10 +799,10 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
       · intro hni
         exfalso
         apply hni
-        rwa [Finsupp.mem_antidiagonal, add_comm]
+        rwa [mem_antidiagonal, add_comm]
     · rw [h, coeff_mul, Finset.sum_eq_zero]
       · rintro ⟨i, j⟩ hij
-        rw [Finsupp.mem_antidiagonal] at hij
+        rw [mem_antidiagonal] at hij
         rw [coeff_X_pow]
         split_ifs with hi
         · exfalso
@@ -845,7 +849,7 @@ protected noncomputable def inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerS
     if n = 0 then a
     else
       -a *
-        ∑ x in n.antidiagonal, if _ : x.2 < n then coeff R x.1 φ * inv.aux a φ x.2 else 0
+        ∑ x in antidiagonal n, if _ : x.2 < n then coeff R x.1 φ * inv.aux a φ x.2 else 0
 termination_by _ n => n
 #align mv_power_series.inv.aux MvPowerSeries.inv.aux
 
@@ -854,11 +858,11 @@ theorem coeff_inv_aux [DecidableEq σ] (n : σ →₀ ℕ) (a : R) (φ : MvPower
       if n = 0 then a
       else
         -a *
-          ∑ x in n.antidiagonal, if x.2 < n then coeff R x.1 φ * coeff R x.2 (inv.aux a φ) else 0 :=
+          ∑ x in antidiagonal n, if x.2 < n then coeff R x.1 φ * coeff R x.2 (inv.aux a φ) else 0 :=
   show inv.aux a φ n = _ by
+    cases Subsingleton.elim ‹DecidableEq σ› (Classical.decEq σ)
     rw [inv.aux]
-    -- unify `Decidable` instances
-    convert rfl
+    rfl
 #align mv_power_series.coeff_inv_aux MvPowerSeries.coeff_inv_aux
 
 /-- A multivariate formal power series is invertible if the constant coefficient is invertible.-/
@@ -871,7 +875,7 @@ theorem coeff_invOfUnit [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries
       if n = 0 then ↑u⁻¹
       else
         -↑u⁻¹ *
-          ∑ x in n.antidiagonal,
+          ∑ x in antidiagonal n,
             if x.2 < n then coeff R x.1 φ * coeff R x.2 (invOfUnit φ u) else 0 := by
   convert coeff_inv_aux n (↑u⁻¹) φ
 #align mv_power_series.coeff_inv_of_unit MvPowerSeries.coeff_invOfUnit
@@ -892,7 +896,7 @@ theorem mul_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) (h : constantCoeff σ
       simp [coeff_mul, support_single_ne_zero, h]
     else by
       classical
-      have : ((0 : σ →₀ ℕ), n) ∈ n.antidiagonal := by rw [Finsupp.mem_antidiagonal, zero_add]
+      have : ((0 : σ →₀ ℕ), n) ∈ antidiagonal n := by rw [mem_antidiagonal, zero_add]
       rw [coeff_one, if_neg H, coeff_mul, ← Finset.insert_erase this,
         Finset.sum_insert (Finset.not_mem_erase _ _), coeff_zero_eq_constantCoeff_apply, h,
         coeff_invOfUnit, if_neg H, neg_mul, mul_neg, Units.mul_inv_cancel_left, ←
@@ -900,7 +904,7 @@ theorem mul_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) (h : constantCoeff σ
         Finset.insert_erase this, if_neg (not_lt_of_ge <| le_rfl), zero_add, add_comm, ←
         sub_eq_add_neg, sub_eq_zero, Finset.sum_congr rfl]
       rintro ⟨i, j⟩ hij
-      rw [Finset.mem_erase, Finsupp.mem_antidiagonal] at hij
+      rw [Finset.mem_erase, mem_antidiagonal] at hij
       cases' hij with h₁ h₂
       subst n
       rw [if_pos]
@@ -971,7 +975,7 @@ theorem coeff_inv [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ k)
       if n = 0 then (constantCoeff σ k φ)⁻¹
       else
         -(constantCoeff σ k φ)⁻¹ *
-          ∑ x in n.antidiagonal, if x.2 < n then coeff k x.1 φ * coeff k x.2 φ⁻¹ else 0 :=
+          ∑ x in antidiagonal n, if x.2 < n then coeff k x.1 φ * coeff k x.2 φ⁻¹ else 0 :=
   coeff_inv_aux n _ φ
 #align mv_power_series.coeff_inv MvPowerSeries.coeff_inv
 
@@ -1517,7 +1521,7 @@ theorem coeff_zero_one : coeff R 0 (1 : R⟦X⟧) = 1 :=
 #align power_series.coeff_zero_one PowerSeries.coeff_zero_one
 
 theorem coeff_mul (n : ℕ) (φ ψ : R⟦X⟧) :
-    coeff R n (φ * ψ) = ∑ p in Finset.Nat.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ := by
+    coeff R n (φ * ψ) = ∑ p in antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ := by
   -- `rw` can't see that `PowerSeries = MvPowerSeries Unit`, so use `.trans`
   refine (MvPowerSeries.coeff_mul _ φ ψ).trans ?_
   rw [Finsupp.antidiagonal_single, Finset.sum_map]
@@ -1620,10 +1624,10 @@ theorem coeff_mul_X_pow (p : R⟦X⟧) (n d : ℕ) :
     rw [coeff_X_pow, if_neg, mul_zero]
     rintro rfl
     apply h2
-    rw [Finset.Nat.mem_antidiagonal, add_right_cancel_iff] at h1
+    rw [mem_antidiagonal, add_right_cancel_iff] at h1
     subst h1
     rfl
-  · exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
+  · exact fun h1 => (h1 (mem_antidiagonal.2 rfl)).elim
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_X_pow
 
@@ -1635,11 +1639,11 @@ theorem coeff_X_pow_mul (p : R⟦X⟧) (n d : ℕ) :
     rw [coeff_X_pow, if_neg, zero_mul]
     rintro rfl
     apply h2
-    rw [Finset.Nat.mem_antidiagonal, add_comm, add_right_cancel_iff] at h1
+    rw [mem_antidiagonal, add_comm, add_right_cancel_iff] at h1
     subst h1
     rfl
   · rw [add_comm]
-    exact fun h1 => (h1 (Finset.Nat.mem_antidiagonal.2 rfl)).elim
+    exact fun h1 => (h1 (mem_antidiagonal.2 rfl)).elim
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_X_pow_mul PowerSeries.coeff_X_pow_mul
 
@@ -1649,7 +1653,7 @@ theorem coeff_mul_X_pow' (p : R⟦X⟧) (n d : ℕ) :
   · rw [← tsub_add_cancel_of_le h, coeff_mul_X_pow, add_tsub_cancel_right]
   · refine' (coeff_mul _ _ _).trans (Finset.sum_eq_zero fun x hx => _)
     rw [coeff_X_pow, if_neg, mul_zero]
-    exact ((le_of_add_le_right (Finset.Nat.mem_antidiagonal.mp hx).le).trans_lt <| not_le.mp h).ne
+    exact ((le_of_add_le_right (mem_antidiagonal.mp hx).le).trans_lt <| not_le.mp h).ne
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_mul_X_pow' PowerSeries.coeff_mul_X_pow'
 
@@ -1660,7 +1664,7 @@ theorem coeff_X_pow_mul' (p : R⟦X⟧) (n d : ℕ) :
     simp
   · refine' (coeff_mul _ _ _).trans (Finset.sum_eq_zero fun x hx => _)
     rw [coeff_X_pow, if_neg, zero_mul]
-    have := Finset.Nat.mem_antidiagonal.mp hx
+    have := mem_antidiagonal.mp hx
     rw [add_comm] at this
     exact ((le_of_add_le_right this.le).trans_lt <| not_le.mp h).ne
 set_option linter.uppercaseLean3 false in
@@ -1785,7 +1789,7 @@ noncomputable def rescale (a : R) : R⟦X⟧ →+* R⟦X⟧ where
     ext
     rw [PowerSeries.coeff_mul, PowerSeries.coeff_mk, PowerSeries.coeff_mul, Finset.mul_sum]
     apply sum_congr rfl
-    simp only [coeff_mk, Prod.forall, Nat.mem_antidiagonal]
+    simp only [coeff_mk, Prod.forall, mem_antidiagonal]
     intro b c H
     rw [← H, pow_add, mul_mul_mul_comm]
 #align power_series.rescale PowerSeries.rescale
@@ -1956,7 +1960,7 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : R⟦X⟧) :
       if n = 0 then a
       else
         -a *
-          ∑ x in Finset.Nat.antidiagonal n,
+          ∑ x in antidiagonal n,
             if x.2 < n then coeff R x.1 φ * coeff R x.2 (inv.aux a φ) else 0 := by
   -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
   erw [coeff, inv.aux, MvPowerSeries.coeff_inv_aux]
@@ -1966,8 +1970,8 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : R⟦X⟧) :
   symm
   apply Finset.sum_bij fun (p : ℕ × ℕ) _h => (single () p.1, single () p.2)
   · rintro ⟨i, j⟩ hij
-    rw [Finset.Nat.mem_antidiagonal] at hij
-    rw [Finsupp.mem_antidiagonal, ← Finsupp.single_add, hij]
+    rw [mem_antidiagonal] at hij
+    rw [mem_antidiagonal, ← Finsupp.single_add, hij]
   · rintro ⟨i, j⟩ _hij
     by_cases H : j < n
     · rw [if_pos H, if_pos]
@@ -1988,8 +1992,8 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : R⟦X⟧) :
     simpa only [Prod.mk.inj_iff, Finsupp.unique_single_eq_iff] using id
   · rintro ⟨f, g⟩ hfg
     refine' ⟨(f (), g ()), _, _⟩
-    · rw [Finsupp.mem_antidiagonal] at hfg
-      rw [Finset.Nat.mem_antidiagonal, ← Finsupp.add_apply, hfg, Finsupp.single_eq_same]
+    · rw [mem_antidiagonal] at hfg
+      rw [mem_antidiagonal, ← Finsupp.add_apply, hfg, Finsupp.single_eq_same]
     · rw [Prod.mk.inj_iff]
       dsimp
       exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
@@ -2005,7 +2009,7 @@ theorem coeff_invOfUnit (n : ℕ) (φ : R⟦X⟧) (u : Rˣ) :
       if n = 0 then ↑u⁻¹
       else
         -↑u⁻¹ *
-          ∑ x in Finset.Nat.antidiagonal n,
+          ∑ x in antidiagonal n,
             if x.2 < n then coeff R x.1 φ * coeff R x.2 (invOfUnit φ u) else 0 :=
   coeff_inv_aux n (↑u⁻¹ : R) φ
 #align power_series.coeff_inv_of_unit PowerSeries.coeff_invOfUnit
@@ -2096,7 +2100,7 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : R⟦X⟧)
     · specialize hm₂ _ hi
       push_neg at hm₂
       rw [hm₂, zero_mul]
-    rw [Finset.Nat.mem_antidiagonal] at hij
+    rw [mem_antidiagonal] at hij
     push_neg at hi hj
     suffices m < i by
       have : m + n < i + j := add_lt_add_of_lt_of_le this hj
@@ -2107,7 +2111,7 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : R⟦X⟧)
     simpa [Ne.def, Prod.mk.inj_iff] using (add_right_inj m).mp hij
   · contrapose!
     intro
-    rw [Finset.Nat.mem_antidiagonal]
+    rw [mem_antidiagonal]
 #align power_series.eq_zero_or_eq_zero_of_mul_eq_zero PowerSeries.eq_zero_or_eq_zero_of_mul_eq_zero
 
 instance [NoZeroDivisors R] : NoZeroDivisors R⟦X⟧ where
@@ -2211,7 +2215,7 @@ theorem coeff_inv (n) (φ : PowerSeries k) :
       if n = 0 then (constantCoeff k φ)⁻¹
       else
         -(constantCoeff k φ)⁻¹ *
-          ∑ x in Finset.Nat.antidiagonal n,
+          ∑ x in antidiagonal n,
             if x.2 < n then coeff k x.1 φ * coeff k x.2 φ⁻¹ else 0 :=
   by rw [inv_eq_inv_aux, coeff_inv_aux n (constantCoeff k φ)⁻¹ φ]
 #align power_series.coeff_inv PowerSeries.coeff_inv
@@ -2473,7 +2477,7 @@ theorem order_mul_ge (φ ψ : R⟦X⟧) : order φ + order ψ ≤ order (φ * ψ
   · rw [coeff_of_lt_order i hi, zero_mul]
   by_cases hj : ↑j < order ψ
   · rw [coeff_of_lt_order j hj, mul_zero]
-  rw [not_lt] at hi hj; rw [Finset.Nat.mem_antidiagonal] at hij
+  rw [not_lt] at hi hj; rw [mem_antidiagonal] at hij
   exfalso
   apply ne_of_lt (lt_of_lt_of_le hn <| add_le_add hi hj)
   rw [← Nat.cast_add, hij]
@@ -2503,13 +2507,13 @@ theorem order_monomial_of_ne_zero (n : ℕ) (a : R) (h : a ≠ 0) : order (monom
 with any other power series is `0`. -/
 theorem coeff_mul_of_lt_order {φ ψ : R⟦X⟧} {n : ℕ} (h : ↑n < ψ.order) :
     coeff R n (φ * ψ) = 0 := by
-  suffices : coeff R n (φ * ψ) = ∑ p in Finset.Nat.antidiagonal n, 0
+  suffices : coeff R n (φ * ψ) = ∑ p in antidiagonal n, 0
   rw [this, Finset.sum_const_zero]
   rw [coeff_mul]
   apply Finset.sum_congr rfl
   intro x hx
   refine' mul_eq_zero_of_right (coeff R x.fst φ) (coeff_of_lt_order x.snd (lt_of_le_of_lt _ h))
-  rw [Finset.Nat.mem_antidiagonal] at hx
+  rw [mem_antidiagonal] at hx
   norm_cast
   linarith
 #align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_order
@@ -2536,7 +2540,8 @@ theorem X_pow_order_dvd (h : (order φ).Dom) : X ^ (order φ).get h ∣ φ := by
   refine' ⟨PowerSeries.mk fun n => coeff R (n + (order φ).get h) φ, _⟩
   ext n
   simp only [coeff_mul, coeff_X_pow, coeff_mk, boole_mul, Finset.sum_ite,
-    Finset.Nat.filter_fst_eq_antidiagonal, Finset.sum_const_zero, add_zero]
+    Finset.sum_const_zero, add_zero]
+  rw [Finset.filter_fst_eq_antidiagonal n (Part.get (order φ) h)]
   split_ifs with hn
   · simp [tsub_add_cancel_of_le hn]
   · simp only [Finset.sum_empty]

@@ -769,6 +769,7 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
     rintro ⟨i, j⟩ hij
     rw [coeff_X_pow, if_neg, zero_mul]
     contrapose! h
+    dsimp at h
     subst i
     rw [Finsupp.mem_antidiagonal] at hij
     rw [← hij, Finsupp.add_apply, Finsupp.single_eq_same]

This reverts commit f3695eb2.

@@ -150,9 +150,11 @@ theorem monomial_def [DecidableEq σ] (n : σ →₀ ℕ) :
 
 theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
     coeff R m (monomial R n a) = if m = n then a else 0 := by
-  rw [coeff, monomial_def, LinearMap.proj_apply]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [coeff, monomial_def, LinearMap.proj_apply (i := m)]
   dsimp only
-  rw [LinearMap.stdBasis_apply, Function.update_apply, Pi.zero_apply]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [LinearMap.stdBasis_apply, Function.update_apply, Pi.zero_apply]
 #align mv_power_series.coeff_monomial MvPowerSeries.coeff_monomial
 
 @[simp]
@@ -1440,7 +1442,8 @@ theorem coeff_zero_eq_constantCoeff_apply (φ : R⟦X⟧) : coeff R 0 φ = const
 
 @[simp]
 theorem monomial_zero_eq_C : ⇑(monomial R 0) = C R := by
-  rw [monomial, Finsupp.single_zero, MvPowerSeries.monomial_zero_eq_C, C]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [monomial, Finsupp.single_zero, MvPowerSeries.monomial_zero_eq_C]
 set_option linter.uppercaseLean3 false in
 #align power_series.monomial_zero_eq_C PowerSeries.monomial_zero_eq_C
 
@@ -1471,7 +1474,8 @@ set_option linter.uppercaseLean3 false in
 
 @[simp]
 theorem coeff_zero_X : coeff R 0 (X : R⟦X⟧) = 0 := by
-  rw [coeff, Finsupp.single_zero, X, MvPowerSeries.coeff_zero_X]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [coeff, Finsupp.single_zero, X, MvPowerSeries.coeff_zero_X]
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_zero_X PowerSeries.coeff_zero_X
 
@@ -1547,7 +1551,7 @@ set_option linter.uppercaseLean3 false in
 theorem coeff_succ_mul_X (n : ℕ) (φ : R⟦X⟧) : coeff R (n + 1) (φ * X) = coeff R n φ := by
   simp only [coeff, Finsupp.single_add]
   convert φ.coeff_add_mul_monomial (single () n) (single () 1) _
-  rw [mul_one]
+  rw [mul_one]; rfl
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_succ_mul_X PowerSeries.coeff_succ_mul_X
 
@@ -1555,7 +1559,7 @@ set_option linter.uppercaseLean3 false in
 theorem coeff_succ_X_mul (n : ℕ) (φ : R⟦X⟧) : coeff R (n + 1) (X * φ) = coeff R n φ := by
   simp only [coeff, Finsupp.single_add, add_comm n 1]
   convert φ.coeff_add_monomial_mul (single () 1) (single () n) _
-  rw [one_mul]
+  rw [one_mul]; rfl
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_succ_X_mul PowerSeries.coeff_succ_X_mul
 
@@ -1953,7 +1957,8 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : R⟦X⟧) :
         -a *
           ∑ x in Finset.Nat.antidiagonal n,
             if x.2 < n then coeff R x.1 φ * coeff R x.2 (inv.aux a φ) else 0 := by
-  rw [coeff, inv.aux, MvPowerSeries.coeff_inv_aux]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [coeff, inv.aux, MvPowerSeries.coeff_inv_aux]
   simp only [Finsupp.single_eq_zero]
   split_ifs; · rfl
   congr 1

This reverts commit 26eb2b0a.

@@ -150,11 +150,9 @@ theorem monomial_def [DecidableEq σ] (n : σ →₀ ℕ) :
 
 theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
     coeff R m (monomial R n a) = if m = n then a else 0 := by
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [coeff, monomial_def, LinearMap.proj_apply (i := m)]
+  rw [coeff, monomial_def, LinearMap.proj_apply]
   dsimp only
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [LinearMap.stdBasis_apply, Function.update_apply, Pi.zero_apply]
+  rw [LinearMap.stdBasis_apply, Function.update_apply, Pi.zero_apply]
 #align mv_power_series.coeff_monomial MvPowerSeries.coeff_monomial
 
 @[simp]
@@ -1442,8 +1440,7 @@ theorem coeff_zero_eq_constantCoeff_apply (φ : R⟦X⟧) : coeff R 0 φ = const
 
 @[simp]
 theorem monomial_zero_eq_C : ⇑(monomial R 0) = C R := by
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [monomial, Finsupp.single_zero, MvPowerSeries.monomial_zero_eq_C]
+  rw [monomial, Finsupp.single_zero, MvPowerSeries.monomial_zero_eq_C, C]
 set_option linter.uppercaseLean3 false in
 #align power_series.monomial_zero_eq_C PowerSeries.monomial_zero_eq_C
 
@@ -1474,8 +1471,7 @@ set_option linter.uppercaseLean3 false in
 
 @[simp]
 theorem coeff_zero_X : coeff R 0 (X : R⟦X⟧) = 0 := by
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [coeff, Finsupp.single_zero, X, MvPowerSeries.coeff_zero_X]
+  rw [coeff, Finsupp.single_zero, X, MvPowerSeries.coeff_zero_X]
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_zero_X PowerSeries.coeff_zero_X
 
@@ -1551,7 +1547,7 @@ set_option linter.uppercaseLean3 false in
 theorem coeff_succ_mul_X (n : ℕ) (φ : R⟦X⟧) : coeff R (n + 1) (φ * X) = coeff R n φ := by
   simp only [coeff, Finsupp.single_add]
   convert φ.coeff_add_mul_monomial (single () n) (single () 1) _
-  rw [mul_one]; rfl
+  rw [mul_one]
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_succ_mul_X PowerSeries.coeff_succ_mul_X
 
@@ -1559,7 +1555,7 @@ set_option linter.uppercaseLean3 false in
 theorem coeff_succ_X_mul (n : ℕ) (φ : R⟦X⟧) : coeff R (n + 1) (X * φ) = coeff R n φ := by
   simp only [coeff, Finsupp.single_add, add_comm n 1]
   convert φ.coeff_add_monomial_mul (single () 1) (single () n) _
-  rw [one_mul]; rfl
+  rw [one_mul]
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_succ_X_mul PowerSeries.coeff_succ_X_mul
 
@@ -1957,8 +1953,7 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : R⟦X⟧) :
         -a *
           ∑ x in Finset.Nat.antidiagonal n,
             if x.2 < n then coeff R x.1 φ * coeff R x.2 (inv.aux a φ) else 0 := by
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [coeff, inv.aux, MvPowerSeries.coeff_inv_aux]
+  rw [coeff, inv.aux, MvPowerSeries.coeff_inv_aux]
   simp only [Finsupp.single_eq_zero]
   split_ifs; · rfl
   congr 1

Only two lemma statements have changed:

• coeff_truncFun now contains the missing [DecidableEq σ] needed to make the statement make sense
• order_eq_multiplicity_X now contains a missing DecidableRel argument needed to make the RHS fully general.

Everywhere else, classical has just been inserted into the proof.

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@u-paris.fr>

@@ -70,7 +70,7 @@ Occasionally this leads to proofs that are uglier than expected.
 
 noncomputable section
 
-open Classical BigOperators Polynomial
+open BigOperators Polynomial
 
 /-- Multivariate formal power series, where `σ` is the index set of the variables
 and `R` is the coefficient ring.-/
@@ -118,6 +118,7 @@ variable (R) [Semiring R]
 
 /-- The `n`th monomial with coefficient `a` as multivariate formal power series.-/
 def monomial (n : σ →₀ ℕ) : R →ₗ[R] MvPowerSeries σ R :=
+  letI := Classical.decEq σ
   LinearMap.stdBasis R (fun _ ↦ R) n
 #align mv_power_series.monomial MvPowerSeries.monomial
 
@@ -158,11 +159,13 @@ theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
 
 @[simp]
 theorem coeff_monomial_same (n : σ →₀ ℕ) (a : R) : coeff R n (monomial R n a) = a := by
+  classical
   rw [monomial_def]
   exact LinearMap.stdBasis_same R (fun _ ↦ R) n a
 #align mv_power_series.coeff_monomial_same MvPowerSeries.coeff_monomial_same
 
 theorem coeff_monomial_ne {m n : σ →₀ ℕ} (h : m ≠ n) (a : R) : coeff R m (monomial R n a) = 0 := by
+  classical
   rw [monomial_def]
   exact LinearMap.stdBasis_ne R (fun _ ↦ R) _ _ h a
 #align mv_power_series.coeff_monomial_ne MvPowerSeries.coeff_monomial_ne
@@ -208,24 +211,26 @@ instance : AddMonoidWithOne (MvPowerSeries σ R) :=
     one := 1 }
 
 instance : Mul (MvPowerSeries σ R) :=
+  letI := Classical.decEq σ
   ⟨fun φ ψ n => ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ⟩
 
 theorem coeff_mul [DecidableEq σ] :
     coeff R n (φ * ψ) = ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ := by
   refine Finset.sum_congr ?_ fun _ _ => rfl
-  rw [Subsingleton.elim (fun a b => propDecidable (a = b)) ‹DecidableEq σ›]
+  rw [Subsingleton.elim (Classical.decEq σ) ‹DecidableEq σ›]
 #align mv_power_series.coeff_mul MvPowerSeries.coeff_mul
 
 protected theorem zero_mul : (0 : MvPowerSeries σ R) * φ = 0 :=
-  ext fun n => by simp [coeff_mul]
+  ext fun n => by classical simp [coeff_mul]
 #align mv_power_series.zero_mul MvPowerSeries.zero_mul
 
 protected theorem mul_zero : φ * 0 = 0 :=
-  ext fun n => by simp [coeff_mul]
+  ext fun n => by classical simp [coeff_mul]
 #align mv_power_series.mul_zero MvPowerSeries.mul_zero
 
 theorem coeff_monomial_mul (a : R) :
     coeff R m (monomial R n a * φ) = if n ≤ m then a * coeff R (m - n) φ else 0 := by
+  classical
   have :
     ∀ p ∈ antidiagonal m,
       coeff R (p : (σ →₀ ℕ) × (σ →₀ ℕ)).1 (monomial R n a) * coeff R p.2 φ ≠ 0 → p.1 = n :=
@@ -236,6 +241,7 @@ theorem coeff_monomial_mul (a : R) :
 
 theorem coeff_mul_monomial (a : R) :
     coeff R m (φ * monomial R n a) = if n ≤ m then coeff R (m - n) φ * a else 0 := by
+  classical
   have :
     ∀ p ∈ antidiagonal m,
       coeff R (p : (σ →₀ ℕ) × (σ →₀ ℕ)).1 φ * coeff R p.2 (monomial R n a) ≠ 0 → p.2 = n :=
@@ -275,15 +281,18 @@ protected theorem mul_one : φ * 1 = φ :=
 #align mv_power_series.mul_one MvPowerSeries.mul_one
 
 protected theorem mul_add (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : φ₁ * (φ₂ + φ₃) = φ₁ * φ₂ + φ₁ * φ₃ :=
-  ext fun n => by simp only [coeff_mul, mul_add, Finset.sum_add_distrib, LinearMap.map_add]
+  ext fun n => by
+    classical simp only [coeff_mul, mul_add, Finset.sum_add_distrib, LinearMap.map_add]
 #align mv_power_series.mul_add MvPowerSeries.mul_add
 
 protected theorem add_mul (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : (φ₁ + φ₂) * φ₃ = φ₁ * φ₃ + φ₂ * φ₃ :=
-  ext fun n => by simp only [coeff_mul, add_mul, Finset.sum_add_distrib, LinearMap.map_add]
+  ext fun n => by
+    classical simp only [coeff_mul, add_mul, Finset.sum_add_distrib, LinearMap.map_add]
 #align mv_power_series.add_mul MvPowerSeries.add_mul
 
 protected theorem mul_assoc (φ₁ φ₂ φ₃ : MvPowerSeries σ R) : φ₁ * φ₂ * φ₃ = φ₁ * (φ₂ * φ₃) := by
   ext1 n
+  classical
   simp only [coeff_mul, Finset.sum_mul, Finset.mul_sum, Finset.sum_sigma']
   refine' Finset.sum_bij (fun p _ => ⟨(p.2.1, p.2.2 + p.1.2), (p.2.2, p.1.2)⟩) _ _ _ _ <;>
     simp only [mem_antidiagonal, Finset.mem_sigma, heq_iff_eq, Prod.mk.inj_iff, and_imp,
@@ -326,6 +335,7 @@ instance [CommSemiring R] : CommSemiring (MvPowerSeries σ R) :=
   { show Semiring (MvPowerSeries σ R) by infer_instance with
     mul_comm := fun φ ψ =>
       ext fun n => by
+        classical
         simpa only [coeff_mul, mul_comm] using
           sum_antidiagonal_swap n fun a b => coeff R a φ * coeff R b ψ }
 
@@ -343,6 +353,7 @@ variable [Semiring R]
 
 theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
     monomial R m a * monomial R n b = monomial R (m + n) (a * b) := by
+  classical
   ext k
   simp only [coeff_mul_monomial, coeff_monomial]
   split_ifs with h₁ h₂ h₃ h₃ h₂ <;> try rfl
@@ -415,6 +426,7 @@ set_option linter.uppercaseLean3 false in
 #align mv_power_series.coeff_index_single_self_X MvPowerSeries.coeff_index_single_self_X
 
 theorem coeff_zero_X (s : σ) : coeff R (0 : σ →₀ ℕ) (X s : MvPowerSeries σ R) = 0 := by
+  classical
   rw [coeff_X, if_neg]
   intro h
   exact one_ne_zero (single_eq_zero.mp h.symm)
@@ -474,7 +486,7 @@ def constantCoeff : MvPowerSeries σ R →+* R :=
   { coeff R (0 : σ →₀ ℕ) with
     toFun := coeff R (0 : σ →₀ ℕ)
     map_one' := coeff_zero_one
-    map_mul' := fun φ ψ => by simp [coeff_mul, support_single_ne_zero]
+    map_mul' := fun φ ψ => by classical simp [coeff_mul, support_single_ne_zero]
     map_zero' := LinearMap.map_zero _ }
 #align mv_power_series.constant_coeff MvPowerSeries.constantCoeff
 
@@ -541,6 +553,7 @@ set_option linter.uppercaseLean3 false in
 
 theorem X_inj [Nontrivial R] {s t : σ} : (X s : MvPowerSeries σ R) = X t ↔ s = t :=
   ⟨by
+    classical
     intro h
     replace h := congr_arg (coeff R (single s 1)) h
     rw [coeff_X, if_pos rfl, coeff_X] at h
@@ -572,6 +585,7 @@ def map : MvPowerSeries σ R →+* MvPowerSeries σ S where
   map_one' :=
     ext fun n =>
       show f ((coeff R n) 1) = (coeff S n) 1 by
+        classical
         rw [coeff_one, coeff_one]
         split_ifs with h
         · simp only [RingHom.map_ite_one_zero, ite_true, map_one, h]
@@ -581,6 +595,7 @@ def map : MvPowerSeries σ R →+* MvPowerSeries σ S where
   map_mul' φ ψ :=
     ext fun n =>
       show f _ = _ by
+        classical
         rw [coeff_mul, map_sum, coeff_mul]
         apply Finset.sum_congr rfl
         rintro ⟨i, j⟩ _; rw [f.map_mul]; rfl
@@ -610,6 +625,7 @@ theorem constantCoeff_map (φ : MvPowerSeries σ R) :
 
 @[simp]
 theorem map_monomial (n : σ →₀ ℕ) (a : R) : map σ f (monomial R n a) = monomial S n (f a) := by
+  classical
   ext m
   simp [coeff_monomial, apply_ite f]
 #align mv_power_series.map_monomial MvPowerSeries.map_monomial
@@ -655,6 +671,7 @@ theorem algebraMap_apply {r : R} :
 
 instance [Nonempty σ] [Nontrivial R] : Nontrivial (Subalgebra R (MvPowerSeries σ R)) :=
   ⟨⟨⊥, ⊤, by
+      classical
       rw [Ne.def, SetLike.ext_iff, not_forall]
       inhabit σ
       refine' ⟨X default, _⟩
@@ -675,8 +692,9 @@ def truncFun (φ : MvPowerSeries σ R) : MvPolynomial σ R :=
   ∑ m in Finset.Iio n, MvPolynomial.monomial m (coeff R m φ)
 #align mv_power_series.trunc_fun MvPowerSeries.truncFun
 
-theorem coeff_truncFun (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
+theorem coeff_truncFun [DecidableEq σ] (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
     (truncFun n φ).coeff m = if m < n then coeff R m φ else 0 := by
+  classical
   simp [truncFun, MvPolynomial.coeff_sum]
 #align mv_power_series.coeff_trunc_fun MvPowerSeries.coeff_truncFun
 
@@ -686,9 +704,11 @@ variable (R)
 def trunc : MvPowerSeries σ R →+ MvPolynomial σ R where
   toFun := truncFun n
   map_zero' := by
+    classical
     ext
     simp [coeff_truncFun]
   map_add' := by
+    classical
     intros x y
     ext m
     simp only [coeff_truncFun, MvPolynomial.coeff_add]
@@ -701,12 +721,14 @@ def trunc : MvPowerSeries σ R →+ MvPolynomial σ R where
 variable {R}
 
 theorem coeff_trunc (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
-    (trunc R n φ).coeff m = if m < n then coeff R m φ else 0 := by simp [trunc, coeff_truncFun]
+    (trunc R n φ).coeff m = if m < n then coeff R m φ else 0 := by
+  classical simp [trunc, coeff_truncFun]
 #align mv_power_series.coeff_trunc MvPowerSeries.coeff_trunc
 
 @[simp]
 theorem trunc_one (n : σ →₀ ℕ) (hnn : n ≠ 0) : trunc R n 1 = 1 :=
   MvPolynomial.ext _ _ fun m => by
+    classical
     rw [coeff_trunc, coeff_one]
     split_ifs with H H'
     · subst m
@@ -725,6 +747,7 @@ theorem trunc_one (n : σ →₀ ℕ) (hnn : n ≠ 0) : trunc R n 1 = 1 :=
 @[simp]
 theorem trunc_c (n : σ →₀ ℕ) (hnn : n ≠ 0) (a : R) : trunc R n (C σ R a) = MvPolynomial.C a :=
   MvPolynomial.ext _ _ fun m => by
+    classical
     rw [coeff_trunc, coeff_C, MvPolynomial.coeff_C]
     split_ifs with H <;> first |rfl|try simp_all
     exfalso; apply H; subst m; exact Ne.bot_lt hnn
@@ -739,6 +762,7 @@ variable [Semiring R]
 
 theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
     (X s : MvPowerSeries σ R) ^ n ∣ φ ↔ ∀ m : σ →₀ ℕ, m s < n → coeff R m φ = 0 := by
+  classical
   constructor
   · rintro ⟨φ, rfl⟩ m h
     rw [coeff_mul, Finset.sum_eq_zero]
@@ -816,6 +840,7 @@ well-founded recursion on the coefficients of the inverse.
  an inverse of the constant coefficient `invOfUnit`.-/
 protected noncomputable def inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerSeries σ R
   | n =>
+    letI := Classical.decEq σ
     if n = 0 then a
     else
       -a *
@@ -853,16 +878,19 @@ theorem coeff_invOfUnit [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries
 @[simp]
 theorem constantCoeff_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) :
     constantCoeff σ R (invOfUnit φ u) = ↑u⁻¹ := by
+  classical
   rw [← coeff_zero_eq_constantCoeff_apply, coeff_invOfUnit, if_pos rfl]
 #align mv_power_series.constant_coeff_inv_of_unit MvPowerSeries.constantCoeff_invOfUnit
 
 theorem mul_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) (h : constantCoeff σ R φ = u) :
     φ * invOfUnit φ u = 1 :=
   ext fun n =>
+    letI := Classical.decEq (σ →₀ ℕ)
     if H : n = 0 then by
       rw [H]
       simp [coeff_mul, support_single_ne_zero, h]
     else by
+      classical
       have : ((0 : σ →₀ ℕ), n) ∈ n.antidiagonal := by rw [Finsupp.mem_antidiagonal, zero_add]
       rw [coeff_one, if_neg H, coeff_mul, ← Finset.insert_erase this,
         Finset.sum_insert (Finset.not_mem_erase _ _), coeff_zero_eq_constantCoeff_apply, h,
@@ -949,12 +977,14 @@ theorem coeff_inv [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries σ k)
 @[simp]
 theorem constantCoeff_inv (φ : MvPowerSeries σ k) :
     constantCoeff σ k φ⁻¹ = (constantCoeff σ k φ)⁻¹ := by
+  classical
   rw [← coeff_zero_eq_constantCoeff_apply, coeff_inv, if_pos rfl]
 #align mv_power_series.constant_coeff_inv MvPowerSeries.constantCoeff_inv
 
 theorem inv_eq_zero {φ : MvPowerSeries σ k} : φ⁻¹ = 0 ↔ constantCoeff σ k φ = 0 :=
   ⟨fun h => by simpa using congr_arg (constantCoeff σ k) h, fun h =>
     ext fun n => by
+      classical
       rw [coeff_inv]
       split_ifs <;>
         simp only [h, map_zero, zero_mul, inv_zero, neg_zero]⟩
@@ -1080,6 +1110,7 @@ theorem coeff_coe (n : σ →₀ ℕ) : MvPowerSeries.coeff R n ↑φ = coeff n
 theorem coe_monomial (n : σ →₀ ℕ) (a : R) :
     (monomial n a : MvPowerSeries σ R) = MvPowerSeries.monomial R n a :=
   MvPowerSeries.ext fun m => by
+    classical
     rw [coeff_coe, coeff_monomial, MvPowerSeries.coeff_monomial]
     split_ifs with h₁ h₂ <;> first |rfl|subst m; contradiction
 #align mv_polynomial.coe_monomial MvPolynomial.coe_monomial
@@ -1101,7 +1132,9 @@ theorem coe_add : ((φ + ψ : MvPolynomial σ R) : MvPowerSeries σ R) = φ + ψ
 
 @[simp, norm_cast]
 theorem coe_mul : ((φ * ψ : MvPolynomial σ R) : MvPowerSeries σ R) = φ * ψ :=
-  MvPowerSeries.ext fun n => by simp only [coeff_coe, MvPowerSeries.coeff_mul, coeff_mul]
+  MvPowerSeries.ext fun n => by
+    classical
+    simp only [coeff_coe, MvPowerSeries.coeff_mul, coeff_mul]
 #align mv_polynomial.coe_mul MvPolynomial.coe_mul
 
 @[simp, norm_cast]
@@ -2038,6 +2071,7 @@ variable [Ring R]
 
 theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : R⟦X⟧) (h : φ * ψ = 0) :
     φ = 0 ∨ ψ = 0 := by
+  classical
   rw [or_iff_not_imp_left]
   intro H
   have ex : ∃ m, coeff R m φ ≠ 0 := by
@@ -2266,8 +2300,6 @@ namespace PowerSeries
 
 variable {R : Type*}
 
-attribute [local instance 1] Classical.propDecidable
-
 section OrderBasic
 
 open multiplicity
@@ -2283,6 +2315,8 @@ theorem exists_coeff_ne_zero_iff_ne_zero : (∃ n : ℕ, coeff R n φ ≠ 0) ↔
 /-- The order of a formal power series `φ` is the greatest `n : PartENat`
 such that `X^n` divides `φ`. The order is `⊤` if and only if `φ = 0`. -/
 def order (φ : R⟦X⟧) : PartENat :=
+  letI := Classical.decEq R
+  letI := Classical.decEq R⟦X⟧
   if h : φ = 0 then ⊤ else Nat.find (exists_coeff_ne_zero_iff_ne_zero.mpr h)
 #align power_series.order PowerSeries.order
 
@@ -2307,6 +2341,7 @@ theorem order_finite_iff_ne_zero : (order φ).Dom ↔ φ ≠ 0 := by
 /-- If the order of a formal power series is finite,
 then the coefficient indexed by the order is nonzero.-/
 theorem coeff_order (h : (order φ).Dom) : coeff R (φ.order.get h) φ ≠ 0 := by
+  classical
   simp only [order, order_finite_iff_ne_zero.mp h, not_false_iff, dif_neg, PartENat.get_natCast']
   generalize_proofs h
   exact Nat.find_spec h
@@ -2315,6 +2350,7 @@ theorem coeff_order (h : (order φ).Dom) : coeff R (φ.order.get h) φ ≠ 0 :=
 /-- If the `n`th coefficient of a formal power series is nonzero,
 then the order of the power series is less than or equal to `n`.-/
 theorem order_le (n : ℕ) (h : coeff R n φ ≠ 0) : order φ ≤ n := by
+  classical
   have _ :  ∃ n, coeff R n φ ≠ 0 := Exists.intro n h
   rw [order, dif_neg]
   · simp only [PartENat.coe_le_coe, Nat.find_le_iff]
@@ -2367,6 +2403,7 @@ theorem le_order (φ : R⟦X⟧) (n : PartENat) (h : ∀ i : ℕ, ↑i < n → c
 and the `i`th coefficient is `0` for all `i < n`.-/
 theorem order_eq_nat {φ : R⟦X⟧} {n : ℕ} :
     order φ = n ↔ coeff R n φ ≠ 0 ∧ ∀ i, i < n → coeff R i φ = 0 := by
+  classical
   rcases eq_or_ne φ 0 with (rfl | hφ)
   · simpa using (PartENat.natCast_ne_top _).symm
   simp [order, dif_neg hφ, Nat.find_eq_iff]
@@ -2457,6 +2494,7 @@ theorem order_monomial (n : ℕ) (a : R) [Decidable (a = 0)] :
 
 /-- The order of the monomial `a*X^n` is `n` if `a ≠ 0`.-/
 theorem order_monomial_of_ne_zero (n : ℕ) (a : R) (h : a ≠ 0) : order (monomial R n a) = n := by
+  classical
   rw [order_monomial, if_neg h]
 #align power_series.order_monomial_of_ne_zero PowerSeries.order_monomial_of_ne_zero
 
@@ -2483,6 +2521,7 @@ theorem coeff_mul_one_sub_of_lt_order {R : Type*} [CommRing R] {φ ψ : R⟦X⟧
 theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type*} [CommRing R] (k : ℕ) (s : Finset ι)
     (φ : R⟦X⟧) (f : ι → R⟦X⟧) :
     (∀ i ∈ s, ↑k < (f i).order) → coeff R k (φ * ∏ i in s, (1 - f i)) = coeff R k φ := by
+  classical
   induction' s using Finset.induction_on with a s ha ih t
   · simp
   · intro t
@@ -2505,8 +2544,9 @@ theorem X_pow_order_dvd (h : (order φ).Dom) : X ^ (order φ).get h ∣ φ := by
 set_option linter.uppercaseLean3 false in
 #align power_series.X_pow_order_dvd PowerSeries.X_pow_order_dvd
 
-theorem order_eq_multiplicity_X {R : Type*} [Semiring R] (φ : R⟦X⟧) :
+theorem order_eq_multiplicity_X {R : Type*} [Semiring R] [@DecidableRel R⟦X⟧ (· ∣ ·)] (φ : R⟦X⟧) :
     order φ = multiplicity X φ := by
+  classical
   rcases eq_or_ne φ 0 with (rfl | hφ)
   · simp
   induction' ho : order φ using PartENat.casesOn with n
@@ -2565,6 +2605,7 @@ variable [CommRing R] [IsDomain R]
 /-- The order of the product of two formal power series over an integral domain
  is the sum of their orders.-/
 theorem order_mul (φ ψ : R⟦X⟧) : order (φ * ψ) = order φ + order ψ := by
+  classical
   simp_rw [order_eq_multiplicity_X]
   exact multiplicity.mul X_prime
 #align power_series.order_mul PowerSeries.order_mul

This includes all the changes from #7606.

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

@@ -149,9 +149,11 @@ theorem monomial_def [DecidableEq σ] (n : σ →₀ ℕ) :
 
 theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
     coeff R m (monomial R n a) = if m = n then a else 0 := by
-  rw [coeff, monomial_def, LinearMap.proj_apply]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [coeff, monomial_def, LinearMap.proj_apply (i := m)]
   dsimp only
-  rw [LinearMap.stdBasis_apply, Function.update_apply, Pi.zero_apply]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [LinearMap.stdBasis_apply, Function.update_apply, Pi.zero_apply]
 #align mv_power_series.coeff_monomial MvPowerSeries.coeff_monomial
 
 @[simp]
@@ -1407,7 +1409,8 @@ theorem coeff_zero_eq_constantCoeff_apply (φ : R⟦X⟧) : coeff R 0 φ = const
 
 @[simp]
 theorem monomial_zero_eq_C : ⇑(monomial R 0) = C R := by
-  rw [monomial, Finsupp.single_zero, MvPowerSeries.monomial_zero_eq_C, C]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [monomial, Finsupp.single_zero, MvPowerSeries.monomial_zero_eq_C]
 set_option linter.uppercaseLean3 false in
 #align power_series.monomial_zero_eq_C PowerSeries.monomial_zero_eq_C
 
@@ -1438,7 +1441,8 @@ set_option linter.uppercaseLean3 false in
 
 @[simp]
 theorem coeff_zero_X : coeff R 0 (X : R⟦X⟧) = 0 := by
-  rw [coeff, Finsupp.single_zero, X, MvPowerSeries.coeff_zero_X]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [coeff, Finsupp.single_zero, X, MvPowerSeries.coeff_zero_X]
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_zero_X PowerSeries.coeff_zero_X
 
@@ -1514,7 +1518,7 @@ set_option linter.uppercaseLean3 false in
 theorem coeff_succ_mul_X (n : ℕ) (φ : R⟦X⟧) : coeff R (n + 1) (φ * X) = coeff R n φ := by
   simp only [coeff, Finsupp.single_add]
   convert φ.coeff_add_mul_monomial (single () n) (single () 1) _
-  rw [mul_one]
+  rw [mul_one]; rfl
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_succ_mul_X PowerSeries.coeff_succ_mul_X
 
@@ -1522,7 +1526,7 @@ set_option linter.uppercaseLean3 false in
 theorem coeff_succ_X_mul (n : ℕ) (φ : R⟦X⟧) : coeff R (n + 1) (X * φ) = coeff R n φ := by
   simp only [coeff, Finsupp.single_add, add_comm n 1]
   convert φ.coeff_add_monomial_mul (single () 1) (single () n) _
-  rw [one_mul]
+  rw [one_mul]; rfl
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_succ_X_mul PowerSeries.coeff_succ_X_mul
 
@@ -1920,7 +1924,8 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : R⟦X⟧) :
         -a *
           ∑ x in Finset.Nat.antidiagonal n,
             if x.2 < n then coeff R x.1 φ * coeff R x.2 (inv.aux a φ) else 0 := by
-  rw [coeff, inv.aux, MvPowerSeries.coeff_inv_aux]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [coeff, inv.aux, MvPowerSeries.coeff_inv_aux]
   simp only [Finsupp.single_eq_zero]
   split_ifs; · rfl
   congr 1

Add lemmas on truncation of pormal power series

Co-authored-by: Richard M. Hill <86743862+rmhi@users.noreply.github.com>

@@ -1240,59 +1240,66 @@ section
 -- Porting note: not available in Lean 4
 -- local reducible PowerSeries
 
-instance [Inhabited R] : Inhabited (PowerSeries R) := by
+
+/--
+`R⟦X⟧` is notation for `PowerSeries R`,
+the semiring of formal power series in one variable over a semiring `R`.
+-/
+scoped notation:9000 R "⟦X⟧" => PowerSeries R
+
+instance [Inhabited R] : Inhabited R⟦X⟧ := by
   dsimp only [PowerSeries]
   infer_instance
 
-instance [Zero R] : Zero (PowerSeries R) := by
+instance [Zero R] : Zero R⟦X⟧ := by
   dsimp only [PowerSeries]
   infer_instance
 
-instance [AddMonoid R] : AddMonoid (PowerSeries R) := by
+instance [AddMonoid R] : AddMonoid R⟦X⟧ := by
   dsimp only [PowerSeries]
   infer_instance
 
-instance [AddGroup R] : AddGroup (PowerSeries R) := by
+instance [AddGroup R] : AddGroup R⟦X⟧ := by
   dsimp only [PowerSeries]
   infer_instance
 
-instance [AddCommMonoid R] : AddCommMonoid (PowerSeries R) := by
+instance [AddCommMonoid R] : AddCommMonoid R⟦X⟧ := by
   dsimp only [PowerSeries]
   infer_instance
 
-instance [AddCommGroup R] : AddCommGroup (PowerSeries R) := by
+instance [AddCommGroup R] : AddCommGroup R⟦X⟧ := by
   dsimp only [PowerSeries]
   infer_instance
 
-instance [Semiring R] : Semiring (PowerSeries R) := by
+instance [Semiring R] : Semiring R⟦X⟧ := by
   dsimp only [PowerSeries]
   infer_instance
 
-instance [CommSemiring R] : CommSemiring (PowerSeries R) := by
+instance [CommSemiring R] : CommSemiring R⟦X⟧ := by
   dsimp only [PowerSeries]
   infer_instance
 
-instance [Ring R] : Ring (PowerSeries R) := by
+instance [Ring R] : Ring R⟦X⟧ := by
   dsimp only [PowerSeries]
   infer_instance
 
-instance [CommRing R] : CommRing (PowerSeries R) := by
+instance [CommRing R] : CommRing R⟦X⟧ := by
   dsimp only [PowerSeries]
   infer_instance
 
-instance [Nontrivial R] : Nontrivial (PowerSeries R) := by
+instance [Nontrivial R] : Nontrivial R⟦X⟧ := by
   dsimp only [PowerSeries]
   infer_instance
 
-instance {A} [Semiring R] [AddCommMonoid A] [Module R A] : Module R (PowerSeries A) := by
+instance {A} [Semiring R] [AddCommMonoid A] [Module R A] : Module R A⟦X⟧ := by
   dsimp only [PowerSeries]
   infer_instance
 
 instance {A S} [Semiring R] [Semiring S] [AddCommMonoid A] [Module R A] [Module S A] [SMul R S]
-    [IsScalarTower R S A] : IsScalarTower R S (PowerSeries A) :=
+    [IsScalarTower R S A] : IsScalarTower R S A⟦X⟧ :=
   Pi.isScalarTower
 
-instance {A} [Semiring A] [CommSemiring R] [Algebra R A] : Algebra R (PowerSeries A) := by
+instance {A} [Semiring A] [CommSemiring R] [Algebra R A] : Algebra R A⟦X⟧ := by
   dsimp only [PowerSeries]
   infer_instance
 
@@ -1303,12 +1310,12 @@ section Semiring
 variable (R) [Semiring R]
 
 /-- The `n`th coefficient of a formal power series.-/
-def coeff (n : ℕ) : PowerSeries R →ₗ[R] R :=
+def coeff (n : ℕ) : R⟦X⟧ →ₗ[R] R :=
   MvPowerSeries.coeff R (single () n)
 #align power_series.coeff PowerSeries.coeff
 
 /-- The `n`th monomial with coefficient `a` as formal power series.-/
-def monomial (n : ℕ) : R →ₗ[R] PowerSeries R :=
+def monomial (n : ℕ) : R →ₗ[R] R⟦X⟧ :=
   MvPowerSeries.monomial R (single () n)
 #align power_series.monomial PowerSeries.monomial
 
@@ -1320,7 +1327,7 @@ theorem coeff_def {s : Unit →₀ ℕ} {n : ℕ} (h : s () = n) : coeff R n = M
 
 /-- Two formal power series are equal if all their coefficients are equal.-/
 @[ext]
-theorem ext {φ ψ : PowerSeries R} (h : ∀ n, coeff R n φ = coeff R n ψ) : φ = ψ :=
+theorem ext {φ ψ : R⟦X⟧} (h : ∀ n, coeff R n φ = coeff R n ψ) : φ = ψ :=
   MvPowerSeries.ext fun n => by
     rw [← coeff_def]
     · apply h
@@ -1328,12 +1335,12 @@ theorem ext {φ ψ : PowerSeries R} (h : ∀ n, coeff R n φ = coeff R n ψ) : 
 #align power_series.ext PowerSeries.ext
 
 /-- Two formal power series are equal if all their coefficients are equal.-/
-theorem ext_iff {φ ψ : PowerSeries R} : φ = ψ ↔ ∀ n, coeff R n φ = coeff R n ψ :=
+theorem ext_iff {φ ψ : R⟦X⟧} : φ = ψ ↔ ∀ n, coeff R n φ = coeff R n ψ :=
   ⟨fun h n => congr_arg (coeff R n) h, ext⟩
 #align power_series.ext_iff PowerSeries.ext_iff
 
 /-- Constructor for formal power series.-/
-def mk {R} (f : ℕ → R) : PowerSeries R := fun s => f (s ())
+def mk {R} (f : ℕ → R) : R⟦X⟧ := fun s => f (s ())
 #align power_series.mk PowerSeries.mk
 
 @[simp]
@@ -1365,12 +1372,12 @@ theorem coeff_comp_monomial (n : ℕ) : (coeff R n).comp (monomial R n) = Linear
 variable (R)
 
 /-- The constant coefficient of a formal power series. -/
-def constantCoeff : PowerSeries R →+* R :=
+def constantCoeff : R⟦X⟧ →+* R :=
   MvPowerSeries.constantCoeff Unit R
 #align power_series.constant_coeff PowerSeries.constantCoeff
 
 /-- The constant formal power series.-/
-def C : R →+* PowerSeries R :=
+def C : R →+* R⟦X⟧ :=
   MvPowerSeries.C Unit R
 set_option linter.uppercaseLean3 false in
 #align power_series.C PowerSeries.C
@@ -1378,12 +1385,12 @@ set_option linter.uppercaseLean3 false in
 variable {R}
 
 /-- The variable of the formal power series ring.-/
-def X : PowerSeries R :=
+def X : R⟦X⟧ :=
   MvPowerSeries.X ()
 set_option linter.uppercaseLean3 false in
 #align power_series.X PowerSeries.X
 
-theorem commute_X (φ : PowerSeries R) : Commute φ X :=
+theorem commute_X (φ : R⟦X⟧) : Commute φ X :=
   MvPowerSeries.commute_X _ _
 set_option linter.uppercaseLean3 false in
 #align power_series.commute_X PowerSeries.commute_X
@@ -1394,7 +1401,7 @@ theorem coeff_zero_eq_constantCoeff : ⇑(coeff R 0) = constantCoeff R := by
   rfl
 #align power_series.coeff_zero_eq_constant_coeff PowerSeries.coeff_zero_eq_constantCoeff
 
-theorem coeff_zero_eq_constantCoeff_apply (φ : PowerSeries R) : coeff R 0 φ = constantCoeff R φ :=
+theorem coeff_zero_eq_constantCoeff_apply (φ : R⟦X⟧) : coeff R 0 φ = constantCoeff R φ :=
   by rw [coeff_zero_eq_constantCoeff]
 #align power_series.coeff_zero_eq_constant_coeff_apply PowerSeries.coeff_zero_eq_constantCoeff_apply
 
@@ -1408,7 +1415,7 @@ theorem monomial_zero_eq_C_apply (a : R) : monomial R 0 a = C R a := by simp
 set_option linter.uppercaseLean3 false in
 #align power_series.monomial_zero_eq_C_apply PowerSeries.monomial_zero_eq_C_apply
 
-theorem coeff_C (n : ℕ) (a : R) : coeff R n (C R a : PowerSeries R) = if n = 0 then a else 0 := by
+theorem coeff_C (n : ℕ) (a : R) : coeff R n (C R a : R⟦X⟧) = if n = 0 then a else 0 := by
   rw [← monomial_zero_eq_C_apply, coeff_monomial]
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_C PowerSeries.coeff_C
@@ -1419,59 +1426,59 @@ theorem coeff_zero_C (a : R) : coeff R 0 (C R a) = a := by
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_zero_C PowerSeries.coeff_zero_C
 
-theorem X_eq : (X : PowerSeries R) = monomial R 1 1 :=
+theorem X_eq : (X : R⟦X⟧) = monomial R 1 1 :=
   rfl
 set_option linter.uppercaseLean3 false in
 #align power_series.X_eq PowerSeries.X_eq
 
-theorem coeff_X (n : ℕ) : coeff R n (X : PowerSeries R) = if n = 1 then 1 else 0 := by
+theorem coeff_X (n : ℕ) : coeff R n (X : R⟦X⟧) = if n = 1 then 1 else 0 := by
   rw [X_eq, coeff_monomial]
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_X PowerSeries.coeff_X
 
 @[simp]
-theorem coeff_zero_X : coeff R 0 (X : PowerSeries R) = 0 := by
+theorem coeff_zero_X : coeff R 0 (X : R⟦X⟧) = 0 := by
   rw [coeff, Finsupp.single_zero, X, MvPowerSeries.coeff_zero_X]
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_zero_X PowerSeries.coeff_zero_X
 
 @[simp]
-theorem coeff_one_X : coeff R 1 (X : PowerSeries R) = 1 := by rw [coeff_X, if_pos rfl]
+theorem coeff_one_X : coeff R 1 (X : R⟦X⟧) = 1 := by rw [coeff_X, if_pos rfl]
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_one_X PowerSeries.coeff_one_X
 
 @[simp]
-theorem X_ne_zero [Nontrivial R] : (X : PowerSeries R) ≠ 0 := fun H => by
+theorem X_ne_zero [Nontrivial R] : (X : R⟦X⟧) ≠ 0 := fun H => by
   simpa only [coeff_one_X, one_ne_zero, map_zero] using congr_arg (coeff R 1) H
 set_option linter.uppercaseLean3 false in
 #align power_series.X_ne_zero PowerSeries.X_ne_zero
 
-theorem X_pow_eq (n : ℕ) : (X : PowerSeries R) ^ n = monomial R n 1 :=
+theorem X_pow_eq (n : ℕ) : (X : R⟦X⟧) ^ n = monomial R n 1 :=
   MvPowerSeries.X_pow_eq _ n
 set_option linter.uppercaseLean3 false in
 #align power_series.X_pow_eq PowerSeries.X_pow_eq
 
-theorem coeff_X_pow (m n : ℕ) : coeff R m ((X : PowerSeries R) ^ n) = if m = n then 1 else 0 := by
+theorem coeff_X_pow (m n : ℕ) : coeff R m ((X : R⟦X⟧) ^ n) = if m = n then 1 else 0 := by
   rw [X_pow_eq, coeff_monomial]
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_X_pow PowerSeries.coeff_X_pow
 
 @[simp]
-theorem coeff_X_pow_self (n : ℕ) : coeff R n ((X : PowerSeries R) ^ n) = 1 := by
+theorem coeff_X_pow_self (n : ℕ) : coeff R n ((X : R⟦X⟧) ^ n) = 1 := by
   rw [coeff_X_pow, if_pos rfl]
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_X_pow_self PowerSeries.coeff_X_pow_self
 
 @[simp]
-theorem coeff_one (n : ℕ) : coeff R n (1 : PowerSeries R) = if n = 0 then 1 else 0 :=
+theorem coeff_one (n : ℕ) : coeff R n (1 : R⟦X⟧) = if n = 0 then 1 else 0 :=
   coeff_C n 1
 #align power_series.coeff_one PowerSeries.coeff_one
 
-theorem coeff_zero_one : coeff R 0 (1 : PowerSeries R) = 1 :=
+theorem coeff_zero_one : coeff R 0 (1 : R⟦X⟧) = 1 :=
   coeff_zero_C 1
 #align power_series.coeff_zero_one PowerSeries.coeff_zero_one
 
-theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
+theorem coeff_mul (n : ℕ) (φ ψ : R⟦X⟧) :
     coeff R n (φ * ψ) = ∑ p in Finset.Nat.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ := by
   -- `rw` can't see that `PowerSeries = MvPowerSeries Unit`, so use `.trans`
   refine (MvPowerSeries.coeff_mul _ φ ψ).trans ?_
@@ -1480,13 +1487,13 @@ theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
 #align power_series.coeff_mul PowerSeries.coeff_mul
 
 @[simp]
-theorem coeff_mul_C (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (φ * C R a) = coeff R n φ * a :=
+theorem coeff_mul_C (n : ℕ) (φ : R⟦X⟧) (a : R) : coeff R n (φ * C R a) = coeff R n φ * a :=
   MvPowerSeries.coeff_mul_C _ φ a
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_mul_C PowerSeries.coeff_mul_C
 
 @[simp]
-theorem coeff_C_mul (n : ℕ) (φ : PowerSeries R) (a : R) : coeff R n (C R a * φ) = a * coeff R n φ :=
+theorem coeff_C_mul (n : ℕ) (φ : R⟦X⟧) (a : R) : coeff R n (C R a * φ) = a * coeff R n φ :=
   MvPowerSeries.coeff_C_mul _ φ a
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_C_mul PowerSeries.coeff_C_mul
@@ -1497,14 +1504,14 @@ theorem coeff_smul {S : Type*} [Semiring S] [Module R S] (n : ℕ) (φ : PowerSe
   rfl
 #align power_series.coeff_smul PowerSeries.coeff_smul
 
-theorem smul_eq_C_mul (f : PowerSeries R) (a : R) : a • f = C R a * f := by
+theorem smul_eq_C_mul (f : R⟦X⟧) (a : R) : a • f = C R a * f := by
   ext
   simp
 set_option linter.uppercaseLean3 false in
 #align power_series.smul_eq_C_mul PowerSeries.smul_eq_C_mul
 
 @[simp]
-theorem coeff_succ_mul_X (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (φ * X) = coeff R n φ := by
+theorem coeff_succ_mul_X (n : ℕ) (φ : R⟦X⟧) : coeff R (n + 1) (φ * X) = coeff R n φ := by
   simp only [coeff, Finsupp.single_add]
   convert φ.coeff_add_mul_monomial (single () n) (single () 1) _
   rw [mul_one]
@@ -1512,7 +1519,7 @@ set_option linter.uppercaseLean3 false in
 #align power_series.coeff_succ_mul_X PowerSeries.coeff_succ_mul_X
 
 @[simp]
-theorem coeff_succ_X_mul (n : ℕ) (φ : PowerSeries R) : coeff R (n + 1) (X * φ) = coeff R n φ := by
+theorem coeff_succ_X_mul (n : ℕ) (φ : R⟦X⟧) : coeff R (n + 1) (X * φ) = coeff R n φ := by
   simp only [coeff, Finsupp.single_add, add_comm n 1]
   convert φ.coeff_add_monomial_mul (single () 1) (single () n) _
   rw [one_mul]
@@ -1549,11 +1556,11 @@ theorem constantCoeff_X : constantCoeff R X = 0 :=
 set_option linter.uppercaseLean3 false in
 #align power_series.constant_coeff_X PowerSeries.constantCoeff_X
 
-theorem coeff_zero_mul_X (φ : PowerSeries R) : coeff R 0 (φ * X) = 0 := by simp
+theorem coeff_zero_mul_X (φ : R⟦X⟧) : coeff R 0 (φ * X) = 0 := by simp
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_zero_mul_X PowerSeries.coeff_zero_mul_X
 
-theorem coeff_zero_X_mul (φ : PowerSeries R) : coeff R 0 (X * φ) = 0 := by simp
+theorem coeff_zero_X_mul (φ : R⟦X⟧) : coeff R 0 (X * φ) = 0 := by simp
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_zero_X_mul PowerSeries.coeff_zero_X_mul
 
@@ -1562,13 +1569,13 @@ set_option linter.uppercaseLean3 false in
 section
 
 theorem coeff_C_mul_X_pow (x : R) (k n : ℕ) :
-    coeff R n (C R x * X ^ k : PowerSeries R) = if n = k then x else 0 := by
+    coeff R n (C R x * X ^ k : R⟦X⟧) = if n = k then x else 0 := by
   simp [X_pow_eq, coeff_monomial]
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_C_mul_X_pow PowerSeries.coeff_C_mul_X_pow
 
 @[simp]
-theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) :
+theorem coeff_mul_X_pow (p : R⟦X⟧) (n d : ℕ) :
     coeff R (d + n) (p * X ^ n) = coeff R d p := by
   rw [coeff_mul, Finset.sum_eq_single (d, n), coeff_X_pow, if_pos rfl, mul_one]
   · rintro ⟨i, j⟩ h1 h2
@@ -1583,7 +1590,7 @@ set_option linter.uppercaseLean3 false in
 #align power_series.coeff_mul_X_pow PowerSeries.coeff_mul_X_pow
 
 @[simp]
-theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) :
+theorem coeff_X_pow_mul (p : R⟦X⟧) (n d : ℕ) :
     coeff R (d + n) (X ^ n * p) = coeff R d p := by
   rw [coeff_mul, Finset.sum_eq_single (n, d), coeff_X_pow, if_pos rfl, one_mul]
   · rintro ⟨i, j⟩ h1 h2
@@ -1598,7 +1605,7 @@ theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) :
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_X_pow_mul PowerSeries.coeff_X_pow_mul
 
-theorem coeff_mul_X_pow' (p : PowerSeries R) (n d : ℕ) :
+theorem coeff_mul_X_pow' (p : R⟦X⟧) (n d : ℕ) :
     coeff R d (p * X ^ n) = ite (n ≤ d) (coeff R (d - n) p) 0 := by
   split_ifs with h
   · rw [← tsub_add_cancel_of_le h, coeff_mul_X_pow, add_tsub_cancel_right]
@@ -1608,7 +1615,7 @@ theorem coeff_mul_X_pow' (p : PowerSeries R) (n d : ℕ) :
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_mul_X_pow' PowerSeries.coeff_mul_X_pow'
 
-theorem coeff_X_pow_mul' (p : PowerSeries R) (n d : ℕ) :
+theorem coeff_X_pow_mul' (p : R⟦X⟧) (n d : ℕ) :
     coeff R d (X ^ n * p) = ite (n ≤ d) (coeff R (d - n) p) 0 := by
   split_ifs with h
   · rw [← tsub_add_cancel_of_le h, coeff_X_pow_mul]
@@ -1624,12 +1631,12 @@ set_option linter.uppercaseLean3 false in
 end
 
 /-- If a formal power series is invertible, then so is its constant coefficient.-/
-theorem isUnit_constantCoeff (φ : PowerSeries R) (h : IsUnit φ) : IsUnit (constantCoeff R φ) :=
+theorem isUnit_constantCoeff (φ : R⟦X⟧) (h : IsUnit φ) : IsUnit (constantCoeff R φ) :=
   MvPowerSeries.isUnit_constantCoeff φ h
 #align power_series.is_unit_constant_coeff PowerSeries.isUnit_constantCoeff
 
 /-- Split off the constant coefficient. -/
-theorem eq_shift_mul_X_add_const (φ : PowerSeries R) :
+theorem eq_shift_mul_X_add_const (φ : R⟦X⟧) :
     φ = (mk fun p => coeff R (p + 1) φ) * X + C R (constantCoeff R φ) := by
   ext (_ | n)
   · simp only [Nat.zero_eq, coeff_zero_eq_constantCoeff, map_add, map_mul, constantCoeff_X,
@@ -1640,7 +1647,7 @@ set_option linter.uppercaseLean3 false in
 #align power_series.eq_shift_mul_X_add_const PowerSeries.eq_shift_mul_X_add_const
 
 /-- Split off the constant coefficient. -/
-theorem eq_X_mul_shift_add_const (φ : PowerSeries R) :
+theorem eq_X_mul_shift_add_const (φ : R⟦X⟧) :
     φ = (X * mk fun p => coeff R (p + 1) φ) + C R (constantCoeff R φ) := by
   ext (_ | n)
   · simp only [Nat.zero_eq, coeff_zero_eq_constantCoeff, map_add, map_mul, constantCoeff_X,
@@ -1657,12 +1664,12 @@ variable {S : Type*} {T : Type*} [Semiring S] [Semiring T]
 variable (f : R →+* S) (g : S →+* T)
 
 /-- The map between formal power series induced by a map on the coefficients.-/
-def map : PowerSeries R →+* PowerSeries S :=
+def map : R⟦X⟧ →+* S⟦X⟧ :=
   MvPowerSeries.map _ f
 #align power_series.map PowerSeries.map
 
 @[simp]
-theorem map_id : (map (RingHom.id R) : PowerSeries R → PowerSeries R) = id :=
+theorem map_id : (map (RingHom.id R) : R⟦X⟧ → R⟦X⟧) = id :=
   rfl
 #align power_series.map_id PowerSeries.map_id
 
@@ -1671,7 +1678,7 @@ theorem map_comp : map (g.comp f) = (map g).comp (map f) :=
 #align power_series.map_comp PowerSeries.map_comp
 
 @[simp]
-theorem coeff_map (n : ℕ) (φ : PowerSeries R) : coeff S n (map f φ) = f (coeff R n φ) :=
+theorem coeff_map (n : ℕ) (φ : R⟦X⟧) : coeff S n (map f φ) = f (coeff R n φ) :=
   rfl
 #align power_series.coeff_map PowerSeries.coeff_map
 
@@ -1691,8 +1698,8 @@ set_option linter.uppercaseLean3 false in
 
 end Map
 
-theorem X_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
-    (X : PowerSeries R) ^ n ∣ φ ↔ ∀ m, m < n → coeff R m φ = 0 := by
+theorem X_pow_dvd_iff {n : ℕ} {φ : R⟦X⟧} :
+    (X : R⟦X⟧) ^ n ∣ φ ↔ ∀ m, m < n → coeff R m φ = 0 := by
   convert@MvPowerSeries.X_pow_dvd_iff Unit R _ () n φ
   constructor <;> intro h m hm
   · rw [Finsupp.unique_single m]
@@ -1702,8 +1709,8 @@ theorem X_pow_dvd_iff {n : ℕ} {φ : PowerSeries R} :
 set_option linter.uppercaseLean3 false in
 #align power_series.X_pow_dvd_iff PowerSeries.X_pow_dvd_iff
 
-theorem X_dvd_iff {φ : PowerSeries R} : (X : PowerSeries R) ∣ φ ↔ constantCoeff R φ = 0 := by
-  rw [← pow_one (X : PowerSeries R), X_pow_dvd_iff, ← coeff_zero_eq_constantCoeff_apply]
+theorem X_dvd_iff {φ : R⟦X⟧} : (X : R⟦X⟧) ∣ φ ↔ constantCoeff R φ = 0 := by
+  rw [← pow_one (X : R⟦X⟧), X_pow_dvd_iff, ← coeff_zero_eq_constantCoeff_apply]
   constructor <;> intro h
   · exact h 0 zero_lt_one
   · intro m hm
@@ -1720,7 +1727,7 @@ variable [CommSemiring R]
 open Finset Nat
 
 /-- The ring homomorphism taking a power series `f(X)` to `f(aX)`. -/
-noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R where
+noncomputable def rescale (a : R) : R⟦X⟧ →+* R⟦X⟧ where
   toFun f := PowerSeries.mk fun n => a ^ n * PowerSeries.coeff R n f
   map_zero' := by
     ext
@@ -1746,7 +1753,7 @@ noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R where
 #align power_series.rescale PowerSeries.rescale
 
 @[simp]
-theorem coeff_rescale (f : PowerSeries R) (a : R) (n : ℕ) :
+theorem coeff_rescale (f : R⟦X⟧) (a : R) (n : ℕ) :
     coeff R n (rescale a f) = a ^ n * coeff R n f :=
   coeff_mk n (fun n ↦ a ^ n * (coeff R n) f)
 #align power_series.coeff_rescale PowerSeries.coeff_rescale
@@ -1763,7 +1770,7 @@ theorem rescale_zero_apply : rescale 0 X = C R (constantCoeff R X) := by simp
 #align power_series.rescale_zero_apply PowerSeries.rescale_zero_apply
 
 @[simp]
-theorem rescale_one : rescale 1 = RingHom.id (PowerSeries R) := by
+theorem rescale_one : rescale 1 = RingHom.id R⟦X⟧ := by
   ext
   simp only [coeff_rescale, one_pow, one_mul, RingHom.id_apply]
 #align power_series.rescale_one PowerSeries.rescale_one
@@ -1773,7 +1780,7 @@ theorem rescale_mk (f : ℕ → R) (a : R) : rescale a (mk f) = mk fun n : ℕ =
   rw [coeff_rescale, coeff_mk, coeff_mk]
 #align power_series.rescale_mk PowerSeries.rescale_mk
 
-theorem rescale_rescale (f : PowerSeries R) (a b : R) :
+theorem rescale_rescale (f : R⟦X⟧) (a b : R) :
     rescale b (rescale a f) = rescale (a * b) f := by
   ext n
   simp_rw [coeff_rescale]
@@ -1785,27 +1792,31 @@ theorem rescale_mul (a b : R) : rescale (a * b) = (rescale b).comp (rescale a) :
   simp [← rescale_rescale]
 #align power_series.rescale_mul PowerSeries.rescale_mul
 
+end CommSemiring
+
 section Trunc
+variable [Semiring R]
+open Finset Nat
 
 /-- The `n`th truncation of a formal power series to a polynomial -/
-def trunc (n : ℕ) (φ : PowerSeries R) : R[X] :=
+def trunc (n : ℕ) (φ : R⟦X⟧) : R[X] :=
   ∑ m in Ico 0 n, Polynomial.monomial m (coeff R m φ)
 #align power_series.trunc PowerSeries.trunc
 
-theorem coeff_trunc (m) (n) (φ : PowerSeries R) :
+theorem coeff_trunc (m) (n) (φ : R⟦X⟧) :
     (trunc n φ).coeff m = if m < n then coeff R m φ else 0 := by
   simp [trunc, Polynomial.coeff_sum, Polynomial.coeff_monomial, Nat.lt_succ_iff]
 #align power_series.coeff_trunc PowerSeries.coeff_trunc
 
 @[simp]
-theorem trunc_zero (n) : trunc n (0 : PowerSeries R) = 0 :=
+theorem trunc_zero (n) : trunc n (0 : R⟦X⟧) = 0 :=
   Polynomial.ext fun m => by
     rw [coeff_trunc, LinearMap.map_zero, Polynomial.coeff_zero]
     split_ifs <;> rfl
 #align power_series.trunc_zero PowerSeries.trunc_zero
 
 @[simp]
-theorem trunc_one (n) : trunc (n + 1) (1 : PowerSeries R) = 1 :=
+theorem trunc_one (n) : trunc (n + 1) (1 : R⟦X⟧) = 1 :=
   Polynomial.ext fun m => by
     rw [coeff_trunc, coeff_one, Polynomial.coeff_one]
     split_ifs with h _ h'
@@ -1824,7 +1835,7 @@ set_option linter.uppercaseLean3 false in
 #align power_series.trunc_C PowerSeries.trunc_C
 
 @[simp]
-theorem trunc_add (n) (φ ψ : PowerSeries R) : trunc n (φ + ψ) = trunc n φ + trunc n ψ :=
+theorem trunc_add (n) (φ ψ : R⟦X⟧) : trunc n (φ + ψ) = trunc n φ + trunc n ψ :=
   Polynomial.ext fun m => by
     simp only [coeff_trunc, AddMonoidHom.map_add, Polynomial.coeff_add]
     split_ifs with H
@@ -1832,20 +1843,77 @@ theorem trunc_add (n) (φ ψ : PowerSeries R) : trunc n (φ + ψ) = trunc n φ +
     · rw [zero_add]
 #align power_series.trunc_add PowerSeries.trunc_add
 
+theorem trunc_succ (f : R⟦X⟧) (n : ℕ) :
+    trunc n.succ f = trunc n f + Polynomial.monomial n (coeff R n f) := by
+  rw [trunc, Ico_zero_eq_range, sum_range_succ, trunc, Ico_zero_eq_range]
+
+theorem natDegree_trunc_lt (f : R⟦X⟧) (n) : (trunc (n + 1) f).natDegree < n + 1 := by
+  rw [lt_succ_iff, natDegree_le_iff_coeff_eq_zero]
+  intros
+  rw [coeff_trunc]
+  split_ifs with h
+  · rw [lt_succ, ←not_lt] at h
+    contradiction
+  · rfl
+
+@[simp] lemma trunc_zero' {f : R⟦X⟧} : trunc 0 f = 0 := rfl
+
+theorem degree_trunc_lt (f : R⟦X⟧) (n) : (trunc n f).degree < n := by
+  rw [degree_lt_iff_coeff_zero]
+  intros
+  rw [coeff_trunc]
+  split_ifs with h
+  · rw [←not_le] at h
+    contradiction
+  · rfl
+
+theorem eval₂_trunc_eq_sum_range {S : Type*} [Semiring S] (s : S) (G : R →+* S) (n) (f : R⟦X⟧) :
+    (trunc n f).eval₂ G s = ∑ i in range n, G (coeff R i f) * s ^ i := by
+  cases n with
+  | zero =>
+    rw [trunc_zero', range_zero, sum_empty, eval₂_zero]
+  | succ n =>
+    have := natDegree_trunc_lt f n
+    rw [eval₂_eq_sum_range' (hn := this)]
+    apply sum_congr rfl
+    intro _ h
+    rw [mem_range] at h
+    congr
+    rw [coeff_trunc, if_pos h]
+
+@[simp] theorem trunc_X (n) : trunc (n + 2) X = (Polynomial.X : R[X]) := by
+  ext d
+  rw [coeff_trunc, coeff_X]
+  split_ifs with h₁ h₂
+  · rw [h₂, coeff_X_one]
+  · rw [coeff_X_of_ne_one h₂]
+  · rw [coeff_X_of_ne_one]
+    intro hd
+    apply h₁
+    rw [hd]
+    exact n.one_lt_succ_succ
+
+lemma trunc_X_of {n : ℕ} (hn : 2 ≤ n) : trunc n X = (Polynomial.X : R[X]) := by
+  cases n with
+  | zero => contradiction
+  | succ n =>
+    cases n with
+    | zero => contradiction
+    | succ n => exact trunc_X n
+
 end Trunc
 
-end CommSemiring
 
 section Ring
 
 variable [Ring R]
 
 /-- Auxiliary function used for computing inverse of a power series -/
-protected def inv.aux : R → PowerSeries R → PowerSeries R :=
+protected def inv.aux : R → R⟦X⟧ → R⟦X⟧ :=
   MvPowerSeries.inv.aux
 #align power_series.inv.aux PowerSeries.inv.aux
 
-theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
+theorem coeff_inv_aux (n : ℕ) (a : R) (φ : R⟦X⟧) :
     coeff R n (inv.aux a φ) =
       if n = 0 then a
       else
@@ -1889,11 +1957,11 @@ theorem coeff_inv_aux (n : ℕ) (a : R) (φ : PowerSeries R) :
 #align power_series.coeff_inv_aux PowerSeries.coeff_inv_aux
 
 /-- A formal power series is invertible if the constant coefficient is invertible.-/
-def invOfUnit (φ : PowerSeries R) (u : Rˣ) : PowerSeries R :=
+def invOfUnit (φ : R⟦X⟧) (u : Rˣ) : R⟦X⟧ :=
   MvPowerSeries.invOfUnit φ u
 #align power_series.inv_of_unit PowerSeries.invOfUnit
 
-theorem coeff_invOfUnit (n : ℕ) (φ : PowerSeries R) (u : Rˣ) :
+theorem coeff_invOfUnit (n : ℕ) (φ : R⟦X⟧) (u : Rˣ) :
     coeff R n (invOfUnit φ u) =
       if n = 0 then ↑u⁻¹
       else
@@ -1904,24 +1972,24 @@ theorem coeff_invOfUnit (n : ℕ) (φ : PowerSeries R) (u : Rˣ) :
 #align power_series.coeff_inv_of_unit PowerSeries.coeff_invOfUnit
 
 @[simp]
-theorem constantCoeff_invOfUnit (φ : PowerSeries R) (u : Rˣ) :
+theorem constantCoeff_invOfUnit (φ : R⟦X⟧) (u : Rˣ) :
     constantCoeff R (invOfUnit φ u) = ↑u⁻¹ := by
   rw [← coeff_zero_eq_constantCoeff_apply, coeff_invOfUnit, if_pos rfl]
 #align power_series.constant_coeff_inv_of_unit PowerSeries.constantCoeff_invOfUnit
 
-theorem mul_invOfUnit (φ : PowerSeries R) (u : Rˣ) (h : constantCoeff R φ = u) :
+theorem mul_invOfUnit (φ : R⟦X⟧) (u : Rˣ) (h : constantCoeff R φ = u) :
     φ * invOfUnit φ u = 1 :=
   MvPowerSeries.mul_invOfUnit φ u <| h
 #align power_series.mul_inv_of_unit PowerSeries.mul_invOfUnit
 
 /-- Two ways of removing the constant coefficient of a power series are the same. -/
-theorem sub_const_eq_shift_mul_X (φ : PowerSeries R) :
+theorem sub_const_eq_shift_mul_X (φ : R⟦X⟧) :
     φ - C R (constantCoeff R φ) = (PowerSeries.mk fun p => coeff R (p + 1) φ) * X :=
   sub_eq_iff_eq_add.mpr (eq_shift_mul_X_add_const φ)
 set_option linter.uppercaseLean3 false in
 #align power_series.sub_const_eq_shift_mul_X PowerSeries.sub_const_eq_shift_mul_X
 
-theorem sub_const_eq_X_mul_shift (φ : PowerSeries R) :
+theorem sub_const_eq_X_mul_shift (φ : R⟦X⟧) :
     φ - C R (constantCoeff R φ) = X * PowerSeries.mk fun p => coeff R (p + 1) φ :=
   sub_eq_iff_eq_add.mpr (eq_X_mul_shift_add_const φ)
 set_option linter.uppercaseLean3 false in
@@ -1947,12 +2015,12 @@ set_option linter.uppercaseLean3 false in
 #align power_series.rescale_neg_one_X PowerSeries.rescale_neg_one_X
 
 /-- The ring homomorphism taking a power series `f(X)` to `f(-X)`. -/
-noncomputable def evalNegHom : PowerSeries A →+* PowerSeries A :=
+noncomputable def evalNegHom : A⟦X⟧ →+* A⟦X⟧ :=
   rescale (-1 : A)
 #align power_series.eval_neg_hom PowerSeries.evalNegHom
 
 @[simp]
-theorem evalNegHom_X : evalNegHom (X : PowerSeries A) = -X :=
+theorem evalNegHom_X : evalNegHom (X : A⟦X⟧) = -X :=
   rescale_neg_one_X
 set_option linter.uppercaseLean3 false in
 #align power_series.eval_neg_hom_X PowerSeries.evalNegHom_X
@@ -1963,7 +2031,7 @@ section Domain
 
 variable [Ring R]
 
-theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSeries R) (h : φ * ψ = 0) :
+theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : R⟦X⟧) (h : φ * ψ = 0) :
     φ = 0 ∨ ψ = 0 := by
   rw [or_iff_not_imp_left]
   intro H
@@ -2002,10 +2070,10 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSerie
     rw [Finset.Nat.mem_antidiagonal]
 #align power_series.eq_zero_or_eq_zero_of_mul_eq_zero PowerSeries.eq_zero_or_eq_zero_of_mul_eq_zero
 
-instance [NoZeroDivisors R] : NoZeroDivisors (PowerSeries R) where
+instance [NoZeroDivisors R] : NoZeroDivisors R⟦X⟧ where
   eq_zero_or_eq_zero_of_mul_eq_zero := eq_zero_or_eq_zero_of_mul_eq_zero _ _
 
-instance [IsDomain R] : IsDomain (PowerSeries R) :=
+instance [IsDomain R] : IsDomain R⟦X⟧ :=
   NoZeroDivisors.to_isDomain _
 
 end Domain
@@ -2016,8 +2084,8 @@ variable [CommRing R] [IsDomain R]
 
 /-- The ideal spanned by the variable in the power series ring
  over an integral domain is a prime ideal.-/
-theorem span_X_isPrime : (Ideal.span ({X} : Set (PowerSeries R))).IsPrime := by
-  suffices Ideal.span ({X} : Set (PowerSeries R)) = RingHom.ker (constantCoeff R) by
+theorem span_X_isPrime : (Ideal.span ({X} : Set R⟦X⟧)).IsPrime := by
+  suffices Ideal.span ({X} : Set R⟦X⟧) = RingHom.ker (constantCoeff R) by
     rw [this]
     exact RingHom.ker_isPrime _
   apply Ideal.ext
@@ -2027,7 +2095,7 @@ set_option linter.uppercaseLean3 false in
 #align power_series.span_X_is_prime PowerSeries.span_X_isPrime
 
 /-- The variable of the power series ring over an integral domain is prime.-/
-theorem X_prime : Prime (X : PowerSeries R) := by
+theorem X_prime : Prime (X : R⟦X⟧) := by
   rw [← Ideal.span_singleton_prime]
   · exact span_X_isPrime
   · intro h
@@ -2058,7 +2126,7 @@ instance map.isLocalRingHom : IsLocalRingHom (map f) :=
 
 variable [LocalRing R] [LocalRing S]
 
-instance : LocalRing (PowerSeries R) :=
+instance : LocalRing R⟦X⟧ :=
   { inferInstanceAs <| LocalRing <| MvPowerSeries Unit R with }
 
 
@@ -2068,16 +2136,16 @@ section Algebra
 
 variable {A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
 
-theorem C_eq_algebraMap {r : R} : C R r = (algebraMap R (PowerSeries R)) r :=
+theorem C_eq_algebraMap {r : R} : C R r = (algebraMap R R⟦X⟧) r :=
   rfl
 set_option linter.uppercaseLean3 false in
 #align power_series.C_eq_algebra_map PowerSeries.C_eq_algebraMap
 
-theorem algebraMap_apply {r : R} : algebraMap R (PowerSeries A) r = C A (algebraMap R A r) :=
+theorem algebraMap_apply {r : R} : algebraMap R A⟦X⟧ r = C A (algebraMap R A r) :=
   MvPowerSeries.algebraMap_apply
 #align power_series.algebra_map_apply PowerSeries.algebraMap_apply
 
-instance [Nontrivial R] : Nontrivial (Subalgebra R (PowerSeries R)) :=
+instance [Nontrivial R] : Nontrivial (Subalgebra R R⟦X⟧) :=
   { inferInstanceAs <| Nontrivial <| Subalgebra R <| MvPowerSeries Unit R with }
 
 end Algebra
@@ -2199,7 +2267,7 @@ section OrderBasic
 
 open multiplicity
 
-variable [Semiring R] {φ : PowerSeries R}
+variable [Semiring R] {φ : R⟦X⟧}
 
 theorem exists_coeff_ne_zero_iff_ne_zero : (∃ n : ℕ, coeff R n φ ≠ 0) ↔ φ ≠ 0 := by
   refine' not_iff_not.mp _
@@ -2209,13 +2277,13 @@ theorem exists_coeff_ne_zero_iff_ne_zero : (∃ n : ℕ, coeff R n φ ≠ 0) ↔
 
 /-- The order of a formal power series `φ` is the greatest `n : PartENat`
 such that `X^n` divides `φ`. The order is `⊤` if and only if `φ = 0`. -/
-def order (φ : PowerSeries R) : PartENat :=
+def order (φ : R⟦X⟧) : PartENat :=
   if h : φ = 0 then ⊤ else Nat.find (exists_coeff_ne_zero_iff_ne_zero.mpr h)
 #align power_series.order PowerSeries.order
 
 /-- The order of the `0` power series is infinite.-/
 @[simp]
-theorem order_zero : order (0 : PowerSeries R) = ⊤ :=
+theorem order_zero : order (0 : R⟦X⟧) = ⊤ :=
   dif_pos rfl
 #align power_series.order_zero PowerSeries.order_zero
 
@@ -2258,7 +2326,7 @@ theorem coeff_of_lt_order (n : ℕ) (h : ↑n < order φ) : coeff R n φ = 0 :=
 
 /-- The `0` power series is the unique power series with infinite order.-/
 @[simp]
-theorem order_eq_top {φ : PowerSeries R} : φ.order = ⊤ ↔ φ = 0 := by
+theorem order_eq_top {φ : R⟦X⟧} : φ.order = ⊤ ↔ φ = 0 := by
   constructor
   · intro h
     ext n
@@ -2270,7 +2338,7 @@ theorem order_eq_top {φ : PowerSeries R} : φ.order = ⊤ ↔ φ = 0 := by
 
 /-- The order of a formal power series is at least `n` if
 the `i`th coefficient is `0` for all `i < n`.-/
-theorem nat_le_order (φ : PowerSeries R) (n : ℕ) (h : ∀ i < n, coeff R i φ = 0) : ↑n ≤ order φ := by
+theorem nat_le_order (φ : R⟦X⟧) (n : ℕ) (h : ∀ i < n, coeff R i φ = 0) : ↑n ≤ order φ := by
   by_contra H; rw [not_le] at H
   have : (order φ).Dom := PartENat.dom_of_le_natCast H.le
   rw [← PartENat.natCast_get this, PartENat.coe_lt_coe] at H
@@ -2279,7 +2347,7 @@ theorem nat_le_order (φ : PowerSeries R) (n : ℕ) (h : ∀ i < n, coeff R i φ
 
 /-- The order of a formal power series is at least `n` if
 the `i`th coefficient is `0` for all `i < n`.-/
-theorem le_order (φ : PowerSeries R) (n : PartENat) (h : ∀ i : ℕ, ↑i < n → coeff R i φ = 0) :
+theorem le_order (φ : R⟦X⟧) (n : PartENat) (h : ∀ i : ℕ, ↑i < n → coeff R i φ = 0) :
     n ≤ order φ := by
   induction n using PartENat.casesOn
   · show _ ≤ _
@@ -2292,7 +2360,7 @@ theorem le_order (φ : PowerSeries R) (n : PartENat) (h : ∀ i : ℕ, ↑i < n
 
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
 and the `i`th coefficient is `0` for all `i < n`.-/
-theorem order_eq_nat {φ : PowerSeries R} {n : ℕ} :
+theorem order_eq_nat {φ : R⟦X⟧} {n : ℕ} :
     order φ = n ↔ coeff R n φ ≠ 0 ∧ ∀ i, i < n → coeff R i φ = 0 := by
   rcases eq_or_ne φ 0 with (rfl | hφ)
   · simpa using (PartENat.natCast_ne_top _).symm
@@ -2301,7 +2369,7 @@ theorem order_eq_nat {φ : PowerSeries R} {n : ℕ} :
 
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
 and the `i`th coefficient is `0` for all `i < n`.-/
-theorem order_eq {φ : PowerSeries R} {n : PartENat} :
+theorem order_eq {φ : R⟦X⟧} {n : PartENat} :
     order φ = n ↔ (∀ i : ℕ, ↑i = n → coeff R i φ ≠ 0) ∧ ∀ i : ℕ, ↑i < n → coeff R i φ = 0 := by
   induction n using PartENat.casesOn
   · rw [order_eq_top]
@@ -2319,12 +2387,12 @@ theorem order_eq {φ : PowerSeries R} {n : PartENat} :
 
 /-- The order of the sum of two formal power series
  is at least the minimum of their orders.-/
-theorem le_order_add (φ ψ : PowerSeries R) : min (order φ) (order ψ) ≤ order (φ + ψ) := by
+theorem le_order_add (φ ψ : R⟦X⟧) : min (order φ) (order ψ) ≤ order (φ + ψ) := by
   refine' le_order _ _ _
   simp (config := { contextual := true }) [coeff_of_lt_order]
 #align power_series.le_order_add PowerSeries.le_order_add
 
-private theorem order_add_of_order_eq.aux (φ ψ : PowerSeries R) (_h : order φ ≠ order ψ)
+private theorem order_add_of_order_eq.aux (φ ψ : R⟦X⟧) (_h : order φ ≠ order ψ)
     (H : order φ < order ψ) : order (φ + ψ) ≤ order φ ⊓ order ψ := by
   suffices order (φ + ψ) = order φ by
     rw [le_inf_iff, this]
@@ -2342,7 +2410,7 @@ private theorem order_add_of_order_eq.aux (φ ψ : PowerSeries R) (_h : order φ
 
 /-- The order of the sum of two formal power series
  is the minimum of their orders if their orders differ.-/
-theorem order_add_of_order_eq (φ ψ : PowerSeries R) (h : order φ ≠ order ψ) :
+theorem order_add_of_order_eq (φ ψ : R⟦X⟧) (h : order φ ≠ order ψ) :
     order (φ + ψ) = order φ ⊓ order ψ := by
   refine' le_antisymm _ (le_order_add _ _)
   by_cases H₁ : order φ < order ψ
@@ -2354,7 +2422,7 @@ theorem order_add_of_order_eq (φ ψ : PowerSeries R) (h : order φ ≠ order ψ
 
 /-- The order of the product of two formal power series
  is at least the sum of their orders.-/
-theorem order_mul_ge (φ ψ : PowerSeries R) : order φ + order ψ ≤ order (φ * ψ) := by
+theorem order_mul_ge (φ ψ : R⟦X⟧) : order φ + order ψ ≤ order (φ * ψ) := by
   apply le_order
   intro n hn; rw [coeff_mul, Finset.sum_eq_zero]
   rintro ⟨i, j⟩ hij
@@ -2389,7 +2457,7 @@ theorem order_monomial_of_ne_zero (n : ℕ) (a : R) (h : a ≠ 0) : order (monom
 
 /-- If `n` is strictly smaller than the order of `ψ`, then the `n`th coefficient of its product
 with any other power series is `0`. -/
-theorem coeff_mul_of_lt_order {φ ψ : PowerSeries R} {n : ℕ} (h : ↑n < ψ.order) :
+theorem coeff_mul_of_lt_order {φ ψ : R⟦X⟧} {n : ℕ} (h : ↑n < ψ.order) :
     coeff R n (φ * ψ) = 0 := by
   suffices : coeff R n (φ * ψ) = ∑ p in Finset.Nat.antidiagonal n, 0
   rw [this, Finset.sum_const_zero]
@@ -2402,13 +2470,13 @@ theorem coeff_mul_of_lt_order {φ ψ : PowerSeries R} {n : ℕ} (h : ↑n < ψ.o
   linarith
 #align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_order
 
-theorem coeff_mul_one_sub_of_lt_order {R : Type*} [CommRing R] {φ ψ : PowerSeries R} (n : ℕ)
+theorem coeff_mul_one_sub_of_lt_order {R : Type*} [CommRing R] {φ ψ : R⟦X⟧} (n : ℕ)
     (h : ↑n < ψ.order) : coeff R n (φ * (1 - ψ)) = coeff R n φ := by
   simp [coeff_mul_of_lt_order h, mul_sub]
 #align power_series.coeff_mul_one_sub_of_lt_order PowerSeries.coeff_mul_one_sub_of_lt_order
 
 theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type*} [CommRing R] (k : ℕ) (s : Finset ι)
-    (φ : PowerSeries R) (f : ι → PowerSeries R) :
+    (φ : R⟦X⟧) (f : ι → R⟦X⟧) :
     (∀ i ∈ s, ↑k < (f i).order) → coeff R k (φ * ∏ i in s, (1 - f i)) = coeff R k φ := by
   induction' s using Finset.induction_on with a s ha ih t
   · simp
@@ -2432,7 +2500,7 @@ theorem X_pow_order_dvd (h : (order φ).Dom) : X ^ (order φ).get h ∣ φ := by
 set_option linter.uppercaseLean3 false in
 #align power_series.X_pow_order_dvd PowerSeries.X_pow_order_dvd
 
-theorem order_eq_multiplicity_X {R : Type*} [Semiring R] (φ : PowerSeries R) :
+theorem order_eq_multiplicity_X {R : Type*} [Semiring R] (φ : R⟦X⟧) :
     order φ = multiplicity X φ := by
   rcases eq_or_ne φ 0 with (rfl | hφ)
   · simp
@@ -2463,20 +2531,20 @@ variable [Semiring R] [Nontrivial R]
 
 /-- The order of the formal power series `1` is `0`.-/
 @[simp]
-theorem order_one : order (1 : PowerSeries R) = 0 := by
+theorem order_one : order (1 : R⟦X⟧) = 0 := by
   simpa using order_monomial_of_ne_zero 0 (1 : R) one_ne_zero
 #align power_series.order_one PowerSeries.order_one
 
 /-- The order of the formal power series `X` is `1`.-/
 @[simp]
-theorem order_X : order (X : PowerSeries R) = 1 := by
+theorem order_X : order (X : R⟦X⟧) = 1 := by
   simpa only [Nat.cast_one] using order_monomial_of_ne_zero 1 (1 : R) one_ne_zero
 set_option linter.uppercaseLean3 false in
 #align power_series.order_X PowerSeries.order_X
 
 /-- The order of the formal power series `X^n` is `n`.-/
 @[simp]
-theorem order_X_pow (n : ℕ) : order ((X : PowerSeries R) ^ n) = n := by
+theorem order_X_pow (n : ℕ) : order ((X : R⟦X⟧) ^ n) = n := by
   rw [X_pow_eq, order_monomial_of_ne_zero]
   exact one_ne_zero
 set_option linter.uppercaseLean3 false in
@@ -2491,7 +2559,7 @@ variable [CommRing R] [IsDomain R]
 
 /-- The order of the product of two formal power series over an integral domain
  is the sum of their orders.-/
-theorem order_mul (φ ψ : PowerSeries R) : order (φ * ψ) = order φ + order ψ := by
+theorem order_mul (φ ψ : R⟦X⟧) : order (φ * ψ) = order φ + order ψ := by
   simp_rw [order_eq_multiplicity_X]
   exact multiplicity.mul X_prime
 #align power_series.order_mul PowerSeries.order_mul
@@ -2632,6 +2700,14 @@ theorem coe_pow (n : ℕ) : ((φ ^ n : R[X]) : PowerSeries R) = (φ : PowerSerie
   coeToPowerSeries.ringHom.map_pow _ _
 #align polynomial.coe_pow Polynomial.coe_pow
 
+theorem eval₂_C_X_eq_coe : φ.eval₂ (PowerSeries.C R) PowerSeries.X = ↑φ := by
+  nth_rw 2 [←eval₂_C_X (p := φ)]
+  rw [←coeToPowerSeries.ringHom_apply, eval₂_eq_sum_range, eval₂_eq_sum_range, map_sum]
+  apply Finset.sum_congr rfl
+  intros
+  rw [map_mul, map_pow, coeToPowerSeries.ringHom_apply,
+    coeToPowerSeries.ringHom_apply, coe_C, coe_X]
+
 variable (A : Type*) [Semiring A] [Algebra R A]
 
 /-- The coercion from polynomials to power series
@@ -2652,31 +2728,113 @@ end Polynomial
 
 namespace PowerSeries
 
-variable {R A : Type*} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : PowerSeries R)
+section Algebra
+
+variable {R A : Type*} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : R⟦X⟧)
 
-instance algebraPolynomial : Algebra R[X] (PowerSeries A) :=
+instance algebraPolynomial : Algebra R[X] A⟦X⟧ :=
   RingHom.toAlgebra (Polynomial.coeToPowerSeries.algHom A).toRingHom
 #align power_series.algebra_polynomial PowerSeries.algebraPolynomial
 
-instance algebraPowerSeries : Algebra (PowerSeries R) (PowerSeries A) :=
+instance algebraPowerSeries : Algebra R⟦X⟧ A⟦X⟧ :=
   (map (algebraMap R A)).toAlgebra
 #align power_series.algebra_power_series PowerSeries.algebraPowerSeries
 
 -- see Note [lower instance priority]
 instance (priority := 100) algebraPolynomial' {A : Type*} [CommSemiring A] [Algebra R A[X]] :
-    Algebra R (PowerSeries A) :=
+    Algebra R A⟦X⟧ :=
   RingHom.toAlgebra <| Polynomial.coeToPowerSeries.ringHom.comp (algebraMap R A[X])
 #align power_series.algebra_polynomial' PowerSeries.algebraPolynomial'
 
 variable (A)
 
-theorem algebraMap_apply' (p : R[X]) : algebraMap R[X] (PowerSeries A) p = map (algebraMap R A) p :=
+theorem algebraMap_apply' (p : R[X]) : algebraMap R[X] A⟦X⟧ p = map (algebraMap R A) p :=
   rfl
 #align power_series.algebra_map_apply' PowerSeries.algebraMap_apply'
 
 theorem algebraMap_apply'' :
-    algebraMap (PowerSeries R) (PowerSeries A) f = map (algebraMap R A) f :=
+    algebraMap R⟦X⟧ A⟦X⟧ f = map (algebraMap R A) f :=
   rfl
 #align power_series.algebra_map_apply'' PowerSeries.algebraMap_apply''
 
+end Algebra
+
+section Trunc
+/-
+Lemmas in this section involve the coercion `R[X] → R⟦X⟧`, so they may only be stated in the case
+`R` is commutative. This is because the coercion is an `R`-algebra map.
+-/
+variable {R : Type*} [CommSemiring R]
+
+open Nat hiding pow_succ pow_zero
+open Polynomial BigOperators Finset Finset.Nat
+
+theorem trunc_trunc_of_le {n m} (f : R⟦X⟧) (hnm : n ≤ m := by rfl) :
+    trunc n ↑(trunc m f) = trunc n f := by
+  ext d
+  rw [coeff_trunc, coeff_trunc, coeff_coe]
+  split_ifs with h
+  · rw [coeff_trunc, if_pos <| lt_of_lt_of_le h hnm]
+  · rfl
+
+@[simp] theorem trunc_trunc {n} (f : R⟦X⟧) : trunc n ↑(trunc n f) = trunc n f :=
+  trunc_trunc_of_le f
+
+@[simp] theorem trunc_trunc_mul {n} (f g : R ⟦X⟧) :
+    trunc n ((trunc n f) * g : R⟦X⟧) = trunc n (f * g) := by
+  ext m
+  rw [coeff_trunc, coeff_trunc]
+  split_ifs with h
+  · rw [coeff_mul, coeff_mul, sum_congr rfl]
+    intro _ hab
+    have ha := lt_of_le_of_lt (antidiagonal.fst_le hab) h
+    rw [coeff_coe, coeff_trunc, if_pos ha]
+  · rfl
+
+@[simp] theorem trunc_mul_trunc {n} (f g : R ⟦X⟧) :
+    trunc n (f * (trunc n g) : R⟦X⟧) = trunc n (f * g) := by
+  rw [mul_comm, trunc_trunc_mul, mul_comm]
+
+theorem trunc_trunc_mul_trunc {n} (f g : R⟦X⟧) :
+    trunc n (trunc n f * trunc n g : R⟦X⟧) = trunc n (f * g) := by
+  rw [trunc_trunc_mul, trunc_mul_trunc]
+
+@[simp] theorem trunc_trunc_pow (f : R⟦X⟧) (n a : ℕ) :
+    trunc n ((trunc n f : R⟦X⟧) ^ a) = trunc n (f ^ a) := by
+  induction a with
+  | zero =>
+    rw [pow_zero, pow_zero]
+  | succ a ih =>
+    rw [pow_succ, pow_succ, trunc_trunc_mul, ←trunc_trunc_mul_trunc, ih, trunc_trunc_mul_trunc]
+
+theorem trunc_coe_eq_self {n} {f : R[X]} (hn : natDegree f < n) : trunc n (f : R⟦X⟧) = f := by
+  rw [←Polynomial.coe_inj]
+  ext m
+  rw [coeff_coe, coeff_trunc]
+  split
+  case inl h => rfl
+  case inr h =>
+    rw [not_lt] at h
+    rw [coeff_coe]; symm
+    exact coeff_eq_zero_of_natDegree_lt <| lt_of_lt_of_le hn h
+
+/-- The function `coeff n : R⟦X⟧ → R` is continuous. I.e. `coeff n f` depends only on a sufficiently
+long truncation of the power series `f`.-/
+theorem coeff_coe_trunc_of_lt {n m} {f : R⟦X⟧} (h : n < m) :
+    coeff R n (trunc m f) = coeff R n f := by
+  rwa [coeff_coe, coeff_trunc, if_pos]
+
+/-- The `n`-th coefficient of `f*g` may be calculated
+from the truncations of `f` and `g`.-/
+theorem coeff_mul_eq_coeff_trunc_mul_trunc₂ {n a b} (f g) (ha : n < a) (hb : n < b) :
+    coeff R n (f * g) = coeff R n (trunc a f * trunc b g) := by
+  symm
+  rw [←coeff_coe_trunc_of_lt n.lt_succ_self, ←trunc_trunc_mul_trunc, trunc_trunc_of_le f ha,
+    trunc_trunc_of_le g hb, trunc_trunc_mul_trunc, coeff_coe_trunc_of_lt n.lt_succ_self]
+
+theorem coeff_mul_eq_coeff_trunc_mul_trunc {d n} (f g) (h : d < n) :
+    coeff R d (f * g) = coeff R d (trunc n f * trunc n g) :=
+  coeff_mul_eq_coeff_trunc_mul_trunc₂ f g h h
+
+end Trunc
 end PowerSeries

@@ -2002,8 +2002,8 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSerie
     rw [Finset.Nat.mem_antidiagonal]
 #align power_series.eq_zero_or_eq_zero_of_mul_eq_zero PowerSeries.eq_zero_or_eq_zero_of_mul_eq_zero
 
-instance [NoZeroDivisors R] : NoZeroDivisors (PowerSeries R)
-    where eq_zero_or_eq_zero_of_mul_eq_zero := eq_zero_or_eq_zero_of_mul_eq_zero _ _
+instance [NoZeroDivisors R] : NoZeroDivisors (PowerSeries R) where
+  eq_zero_or_eq_zero_of_mul_eq_zero := eq_zero_or_eq_zero_of_mul_eq_zero _ _
 
 instance [IsDomain R] : IsDomain (PowerSeries R) :=
   NoZeroDivisors.to_isDomain _

Also some related results

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

@@ -1807,17 +1807,12 @@ theorem trunc_zero (n) : trunc n (0 : PowerSeries R) = 0 :=
 @[simp]
 theorem trunc_one (n) : trunc (n + 1) (1 : PowerSeries R) = 1 :=
   Polynomial.ext fun m => by
-    rw [coeff_trunc, coeff_one]
-    split_ifs with H H' <;> rw [Polynomial.coeff_one]
-    · subst m
-      rw [if_pos rfl]
-    · symm
-      exact if_neg (Ne.elim (Ne.symm H'))
-    · symm
-      refine' if_neg _
-      rintro rfl
-      apply H
-      exact Nat.zero_lt_succ _
+    rw [coeff_trunc, coeff_one, Polynomial.coeff_one]
+    split_ifs with h _ h'
+    · rfl
+    · rfl
+    · subst h'; simp at h
+    · rfl
 #align power_series.trunc_one PowerSeries.trunc_one
 
 @[simp]

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).

@@ -348,7 +348,7 @@ theorem monomial_mul_monomial (m n : σ →₀ ℕ) (a b : R) :
     exact (h₃ rfl).elim
   · rw [h₃, add_tsub_cancel_right] at h₂
     exact (h₂ rfl).elim
-  · exact MulZeroClass.zero_mul b
+  · exact zero_mul b
   · rw [h₂] at h₁
     exact (h₁ <| le_add_left le_rfl).elim
 #align mv_power_series.monomial_mul_monomial MvPowerSeries.monomial_mul_monomial
@@ -741,7 +741,7 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
   · rintro ⟨φ, rfl⟩ m h
     rw [coeff_mul, Finset.sum_eq_zero]
     rintro ⟨i, j⟩ hij
-    rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
+    rw [coeff_X_pow, if_neg, zero_mul]
     contrapose! h
     subst i
     rw [Finsupp.mem_antidiagonal] at hij
@@ -764,7 +764,7 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
           refine' ⟨rfl, _⟩
           ext t
           simp only [add_tsub_cancel_left, Finsupp.add_apply, Finsupp.tsub_apply]
-        · exact MulZeroClass.zero_mul _
+        · exact zero_mul _
       · intro hni
         exfalso
         apply hni
@@ -779,7 +779,7 @@ theorem X_pow_dvd_iff {s : σ} {n : ℕ} {φ : MvPowerSeries σ R} :
           rw [← hij, hi]
           ext
           rw [coe_add, coe_add, Pi.add_apply, Pi.add_apply, add_tsub_cancel_left, add_comm]
-        · exact MulZeroClass.zero_mul _
+        · exact zero_mul _
       · contrapose! H
         ext t
         by_cases hst : s = t
@@ -1572,7 +1572,7 @@ theorem coeff_mul_X_pow (p : PowerSeries R) (n d : ℕ) :
     coeff R (d + n) (p * X ^ n) = coeff R d p := by
   rw [coeff_mul, Finset.sum_eq_single (d, n), coeff_X_pow, if_pos rfl, mul_one]
   · rintro ⟨i, j⟩ h1 h2
-    rw [coeff_X_pow, if_neg, MulZeroClass.mul_zero]
+    rw [coeff_X_pow, if_neg, mul_zero]
     rintro rfl
     apply h2
     rw [Finset.Nat.mem_antidiagonal, add_right_cancel_iff] at h1
@@ -1587,7 +1587,7 @@ theorem coeff_X_pow_mul (p : PowerSeries R) (n d : ℕ) :
     coeff R (d + n) (X ^ n * p) = coeff R d p := by
   rw [coeff_mul, Finset.sum_eq_single (n, d), coeff_X_pow, if_pos rfl, one_mul]
   · rintro ⟨i, j⟩ h1 h2
-    rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
+    rw [coeff_X_pow, if_neg, zero_mul]
     rintro rfl
     apply h2
     rw [Finset.Nat.mem_antidiagonal, add_comm, add_right_cancel_iff] at h1
@@ -1603,7 +1603,7 @@ theorem coeff_mul_X_pow' (p : PowerSeries R) (n d : ℕ) :
   split_ifs with h
   · rw [← tsub_add_cancel_of_le h, coeff_mul_X_pow, add_tsub_cancel_right]
   · refine' (coeff_mul _ _ _).trans (Finset.sum_eq_zero fun x hx => _)
-    rw [coeff_X_pow, if_neg, MulZeroClass.mul_zero]
+    rw [coeff_X_pow, if_neg, mul_zero]
     exact ((le_of_add_le_right (Finset.Nat.mem_antidiagonal.mp hx).le).trans_lt <| not_le.mp h).ne
 set_option linter.uppercaseLean3 false in
 #align power_series.coeff_mul_X_pow' PowerSeries.coeff_mul_X_pow'
@@ -1614,7 +1614,7 @@ theorem coeff_X_pow_mul' (p : PowerSeries R) (n d : ℕ) :
   · rw [← tsub_add_cancel_of_le h, coeff_X_pow_mul]
     simp
   · refine' (coeff_mul _ _ _).trans (Finset.sum_eq_zero fun x hx => _)
-    rw [coeff_X_pow, if_neg, MulZeroClass.zero_mul]
+    rw [coeff_X_pow, if_neg, zero_mul]
     have := Finset.Nat.mem_antidiagonal.mp hx
     rw [add_comm] at this
     exact ((le_of_add_le_right this.le).trans_lt <| not_le.mp h).ne
@@ -1724,7 +1724,7 @@ noncomputable def rescale (a : R) : PowerSeries R →+* PowerSeries R where
   toFun f := PowerSeries.mk fun n => a ^ n * PowerSeries.coeff R n f
   map_zero' := by
     ext
-    simp only [LinearMap.map_zero, PowerSeries.coeff_mk, MulZeroClass.mul_zero]
+    simp only [LinearMap.map_zero, PowerSeries.coeff_mk, mul_zero]
   map_one' := by
     ext1
     simp only [mul_boole, PowerSeries.coeff_mk, PowerSeries.coeff_one]
@@ -1988,11 +1988,11 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSerie
     exact h hm₁
   · rintro ⟨i, j⟩ hij hne
     by_cases hj : j < n
-    · rw [ih j hj, MulZeroClass.mul_zero]
+    · rw [ih j hj, mul_zero]
     by_cases hi : i < m
     · specialize hm₂ _ hi
       push_neg at hm₂
-      rw [hm₂, MulZeroClass.zero_mul]
+      rw [hm₂, zero_mul]
     rw [Finset.Nat.mem_antidiagonal] at hij
     push_neg at hi hj
     suffices m < i by
@@ -2364,9 +2364,9 @@ theorem order_mul_ge (φ ψ : PowerSeries R) : order φ + order ψ ≤ order (φ
   intro n hn; rw [coeff_mul, Finset.sum_eq_zero]
   rintro ⟨i, j⟩ hij
   by_cases hi : ↑i < order φ
-  · rw [coeff_of_lt_order i hi, MulZeroClass.zero_mul]
+  · rw [coeff_of_lt_order i hi, zero_mul]
   by_cases hj : ↑j < order ψ
-  · rw [coeff_of_lt_order j hj, MulZeroClass.mul_zero]
+  · rw [coeff_of_lt_order j hj, mul_zero]
   rw [not_lt] at hi hj; rw [Finset.Nat.mem_antidiagonal] at hij
   exfalso
   apply ne_of_lt (lt_of_lt_of_le hn <| add_le_add hi hj)

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

This has nice performance benefits.

@@ -74,7 +74,7 @@ open Classical BigOperators Polynomial
 
 /-- Multivariate formal power series, where `σ` is the index set of the variables
 and `R` is the coefficient ring.-/
-def MvPowerSeries (σ : Type _) (R : Type _) :=
+def MvPowerSeries (σ : Type*) (R : Type*) :=
   (σ →₀ ℕ) → R
 #align mv_power_series MvPowerSeries
 
@@ -82,7 +82,7 @@ namespace MvPowerSeries
 
 open Finsupp
 
-variable {σ R : Type _}
+variable {σ R : Type*}
 
 instance [Inhabited R] : Inhabited (MvPowerSeries σ R) :=
   ⟨fun _ => default⟩
@@ -557,7 +557,7 @@ end Semiring
 
 section Map
 
-variable {S T : Type _} [Semiring R] [Semiring S] [Semiring T]
+variable {S T : Type*} [Semiring R] [Semiring S] [Semiring T]
 
 variable (f : R →+* S) (g : S →+* T)
 
@@ -627,7 +627,7 @@ end Map
 
 section Algebra
 
-variable {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
+variable {A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
 
 instance : Algebra R (MvPowerSeries σ A) :=
   {
@@ -905,7 +905,7 @@ end CommRing
 
 section LocalRing
 
-variable {S : Type _} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalRingHom f]
+variable {S : Type*} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalRingHom f]
 
 -- Thanks to the linter for informing us that this instance does
 -- not actually need R and S to be local rings!
@@ -925,7 +925,7 @@ end LocalRing
 
 section Field
 
-variable {k : Type _} [Field k]
+variable {k : Type*} [Field k]
 
 /-- The inverse `1/f` of a multivariable power series `f` over a field -/
 protected def inv (φ : MvPowerSeries σ k) : MvPowerSeries σ k :=
@@ -1052,7 +1052,7 @@ namespace MvPolynomial
 
 open Finsupp
 
-variable {σ : Type _} {R : Type _} [CommSemiring R] (φ ψ : MvPolynomial σ R)
+variable {σ : Type*} {R : Type*} [CommSemiring R] (φ ψ : MvPolynomial σ R)
 
 -- Porting note: added so we can add the `@[coe]` attribute
 /-- The natural inclusion from multivariate polynomials into multivariate formal power series.-/
@@ -1178,7 +1178,7 @@ theorem coeToMvPowerSeries.ringHom_apply : coeToMvPowerSeries.ringHom φ = φ :=
 
 section Algebra
 
-variable (A : Type _) [CommSemiring A] [Algebra R A]
+variable (A : Type*) [CommSemiring A] [Algebra R A]
 
 /-- The coercion from multivariable polynomials to multivariable power series
 as an algebra homomorphism.
@@ -1200,7 +1200,7 @@ end MvPolynomial
 
 namespace MvPowerSeries
 
-variable {σ R A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : MvPowerSeries σ R)
+variable {σ R A : Type*} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : MvPowerSeries σ R)
 
 instance algebraMvPolynomial : Algebra (MvPolynomial σ R) (MvPowerSeries σ A) :=
   RingHom.toAlgebra (MvPolynomial.coeToMvPowerSeries.algHom A).toRingHom
@@ -1225,7 +1225,7 @@ theorem algebraMap_apply'' :
 end MvPowerSeries
 
 /-- Formal power series over the coefficient ring `R`.-/
-def PowerSeries (R : Type _) :=
+def PowerSeries (R : Type*) :=
   MvPowerSeries Unit R
 #align power_series PowerSeries
 
@@ -1233,7 +1233,7 @@ namespace PowerSeries
 
 open Finsupp (single)
 
-variable {R : Type _}
+variable {R : Type*}
 
 section
 
@@ -1492,7 +1492,7 @@ set_option linter.uppercaseLean3 false in
 #align power_series.coeff_C_mul PowerSeries.coeff_C_mul
 
 @[simp]
-theorem coeff_smul {S : Type _} [Semiring S] [Module R S] (n : ℕ) (φ : PowerSeries S) (a : R) :
+theorem coeff_smul {S : Type*} [Semiring S] [Module R S] (n : ℕ) (φ : PowerSeries S) (a : R) :
     coeff S n (a • φ) = a • coeff S n φ :=
   rfl
 #align power_series.coeff_smul PowerSeries.coeff_smul
@@ -1652,7 +1652,7 @@ set_option linter.uppercaseLean3 false in
 
 section Map
 
-variable {S : Type _} {T : Type _} [Semiring S] [Semiring T]
+variable {S : Type*} {T : Type*} [Semiring S] [Semiring T]
 
 variable (f : R →+* S) (g : S →+* T)
 
@@ -1936,7 +1936,7 @@ end Ring
 
 section CommRing
 
-variable {A : Type _} [CommRing A]
+variable {A : Type*} [CommRing A]
 
 @[simp]
 theorem rescale_X (a : A) : rescale a X = C A a * X := by
@@ -2055,7 +2055,7 @@ end IsDomain
 
 section LocalRing
 
-variable {S : Type _} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalRingHom f]
+variable {S : Type*} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalRingHom f]
 
 instance map.isLocalRingHom : IsLocalRingHom (map f) :=
   MvPowerSeries.map.isLocalRingHom f
@@ -2071,7 +2071,7 @@ end LocalRing
 
 section Algebra
 
-variable {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
+variable {A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
 
 theorem C_eq_algebraMap {r : R} : C R r = (algebraMap R (PowerSeries R)) r :=
   rfl
@@ -2089,7 +2089,7 @@ end Algebra
 
 section Field
 
-variable {k : Type _} [Field k]
+variable {k : Type*} [Field k]
 
 /-- The inverse 1/f of a power series f defined over a field -/
 protected def inv : PowerSeries k → PowerSeries k :=
@@ -2196,7 +2196,7 @@ end PowerSeries
 
 namespace PowerSeries
 
-variable {R : Type _}
+variable {R : Type*}
 
 attribute [local instance 1] Classical.propDecidable
 
@@ -2407,12 +2407,12 @@ theorem coeff_mul_of_lt_order {φ ψ : PowerSeries R} {n : ℕ} (h : ↑n < ψ.o
   linarith
 #align power_series.coeff_mul_of_lt_order PowerSeries.coeff_mul_of_lt_order
 
-theorem coeff_mul_one_sub_of_lt_order {R : Type _} [CommRing R] {φ ψ : PowerSeries R} (n : ℕ)
+theorem coeff_mul_one_sub_of_lt_order {R : Type*} [CommRing R] {φ ψ : PowerSeries R} (n : ℕ)
     (h : ↑n < ψ.order) : coeff R n (φ * (1 - ψ)) = coeff R n φ := by
   simp [coeff_mul_of_lt_order h, mul_sub]
 #align power_series.coeff_mul_one_sub_of_lt_order PowerSeries.coeff_mul_one_sub_of_lt_order
 
-theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type _} [CommRing R] (k : ℕ) (s : Finset ι)
+theorem coeff_mul_prod_one_sub_of_lt_order {R ι : Type*} [CommRing R] (k : ℕ) (s : Finset ι)
     (φ : PowerSeries R) (f : ι → PowerSeries R) :
     (∀ i ∈ s, ↑k < (f i).order) → coeff R k (φ * ∏ i in s, (1 - f i)) = coeff R k φ := by
   induction' s using Finset.induction_on with a s ha ih t
@@ -2437,7 +2437,7 @@ theorem X_pow_order_dvd (h : (order φ).Dom) : X ^ (order φ).get h ∣ φ := by
 set_option linter.uppercaseLean3 false in
 #align power_series.X_pow_order_dvd PowerSeries.X_pow_order_dvd
 
-theorem order_eq_multiplicity_X {R : Type _} [Semiring R] (φ : PowerSeries R) :
+theorem order_eq_multiplicity_X {R : Type*} [Semiring R] (φ : PowerSeries R) :
     order φ = multiplicity X φ := by
   rcases eq_or_ne φ 0 with (rfl | hφ)
   · simp
@@ -2509,7 +2509,7 @@ namespace Polynomial
 
 open Finsupp
 
-variable {σ : Type _} {R : Type _} [CommSemiring R] (φ ψ : R[X])
+variable {σ : Type*} {R : Type*} [CommSemiring R] (φ ψ : R[X])
 
 -- Porting note: added so we can add the `@[coe]` attribute
 /-- The natural inclusion from polynomials into formal power series.-/
@@ -2637,7 +2637,7 @@ theorem coe_pow (n : ℕ) : ((φ ^ n : R[X]) : PowerSeries R) = (φ : PowerSerie
   coeToPowerSeries.ringHom.map_pow _ _
 #align polynomial.coe_pow Polynomial.coe_pow
 
-variable (A : Type _) [Semiring A] [Algebra R A]
+variable (A : Type*) [Semiring A] [Algebra R A]
 
 /-- The coercion from polynomials to power series
 as an algebra homomorphism.
@@ -2657,7 +2657,7 @@ end Polynomial
 
 namespace PowerSeries
 
-variable {R A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : PowerSeries R)
+variable {R A : Type*} [CommSemiring R] [CommSemiring A] [Algebra R A] (f : PowerSeries R)
 
 instance algebraPolynomial : Algebra R[X] (PowerSeries A) :=
   RingHom.toAlgebra (Polynomial.coeToPowerSeries.algHom A).toRingHom
@@ -2668,7 +2668,7 @@ instance algebraPowerSeries : Algebra (PowerSeries R) (PowerSeries A) :=
 #align power_series.algebra_power_series PowerSeries.algebraPowerSeries
 
 -- see Note [lower instance priority]
-instance (priority := 100) algebraPolynomial' {A : Type _} [CommSemiring A] [Algebra R A[X]] :
+instance (priority := 100) algebraPolynomial' {A : Type*} [CommSemiring A] [Algebra R A[X]] :
     Algebra R (PowerSeries A) :=
   RingHom.toAlgebra <| Polynomial.coeToPowerSeries.ringHom.comp (algebraMap R A[X])
 #align power_series.algebra_polynomial' PowerSeries.algebraPolynomial'

@@ -1475,22 +1475,8 @@ theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
     coeff R n (φ * ψ) = ∑ p in Finset.Nat.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ := by
   -- `rw` can't see that `PowerSeries = MvPowerSeries Unit`, so use `.trans`
   refine (MvPowerSeries.coeff_mul _ φ ψ).trans ?_
-  symm
-  apply Finset.sum_bij fun (p : ℕ × ℕ) _h => (single () p.1, single () p.2)
-  · rintro ⟨i, j⟩ hij
-    rw [Finset.Nat.mem_antidiagonal] at hij
-    rw [Finsupp.mem_antidiagonal, ← Finsupp.single_add, hij]
-  · rintro ⟨i, j⟩ _hij
-    rfl
-  · rintro ⟨i, j⟩ ⟨k, l⟩ _hij _hkl
-    simpa only [Prod.mk.inj_iff, Finsupp.unique_single_eq_iff] using id
-  · rintro ⟨f, g⟩ hfg
-    refine' ⟨(f (), g ()), _, _⟩
-    · rw [Finsupp.mem_antidiagonal] at hfg
-      rw [Finset.Nat.mem_antidiagonal, ← Finsupp.add_apply, hfg, Finsupp.single_eq_same]
-    · rw [Prod.mk.inj_iff]
-      dsimp
-      exact ⟨Finsupp.unique_single f, Finsupp.unique_single g⟩
+  rw [Finsupp.antidiagonal_single, Finset.sum_map]
+  rfl
 #align power_series.coeff_mul PowerSeries.coeff_mul
 
 @[simp]

In Lean 3, the computability of Finsupp.toMultiset was poisoned by the AddMonoid (α →₀ ℕ) instance, even though this was not used in computation. This is no longer the case in Lean 4, so we can make this computable by adding a DecidableEq α argument.

We loosely follow the pattern used with DFinsupp, where we split the declaration in two, as only one direction needs DecidableEq α. As a result, Finsupp.toMultiset is now only an AddMonoidHom, though Multiset.toFinset remains an equiv.

We're missing some of the formatting infrastructure for this to be pretty, but this now works:

#eval ((Finsupp.mk Finset.univ ![1, 2, 3] sorry).antidiagonal).image
  fun x : _ × _ => (x.1.toFun, x.2.toFun)

@@ -208,9 +208,10 @@ instance : AddMonoidWithOne (MvPowerSeries σ R) :=
 instance : Mul (MvPowerSeries σ R) :=
   ⟨fun φ ψ n => ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ⟩
 
-theorem coeff_mul :
-    coeff R n (φ * ψ) = ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ :=
-  rfl
+theorem coeff_mul [DecidableEq σ] :
+    coeff R n (φ * ψ) = ∑ p in Finsupp.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ := by
+  refine Finset.sum_congr ?_ fun _ _ => rfl
+  rw [Subsingleton.elim (fun a b => propDecidable (a = b)) ‹DecidableEq σ›]
 #align mv_power_series.coeff_mul MvPowerSeries.coeff_mul
 
 protected theorem zero_mul : (0 : MvPowerSeries σ R) * φ = 0 :=
@@ -1472,6 +1473,8 @@ theorem coeff_zero_one : coeff R 0 (1 : PowerSeries R) = 1 :=
 
 theorem coeff_mul (n : ℕ) (φ ψ : PowerSeries R) :
     coeff R n (φ * ψ) = ∑ p in Finset.Nat.antidiagonal n, coeff R p.1 φ * coeff R p.2 ψ := by
+  -- `rw` can't see that `PowerSeries = MvPowerSeries Unit`, so use `.trans`
+  refine (MvPowerSeries.coeff_mul _ φ ψ).trans ?_
   symm
   apply Finset.sum_bij fun (p : ℕ × ℕ) _h => (single () p.1, single () p.2)
   · rintro ⟨i, j⟩ hij

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
-
-! This file was ported from Lean 3 source module ring_theory.power_series.basic
-! leanprover-community/mathlib commit 2d5739b61641ee4e7e53eca5688a08f66f2e6a60
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Finsupp.Interval
 import Mathlib.Data.MvPolynomial.Basic
@@ -17,6 +12,8 @@ import Mathlib.RingTheory.Ideal.LocalRing
 import Mathlib.RingTheory.Multiplicity
 import Mathlib.Tactic.Linarith
 
+#align_import ring_theory.power_series.basic from "leanprover-community/mathlib"@"2d5739b61641ee4e7e53eca5688a08f66f2e6a60"
+
 /-!
 # Formal power series
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -909,7 +909,7 @@ section LocalRing
 
 variable {S : Type _} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalRingHom f]
 
--- Thanks to the linter for informing us that  this instance does
+-- Thanks to the linter for informing us that this instance does
 -- not actually need R and S to be local rings!
 /-- The map `A[[X]] → B[[X]]` induced by a local ring hom `A → B` is local -/
 instance map.isLocalRingHom : IsLocalRingHom (map σ f) :=

This adds a couple of WellFoundedRelation instances, like for example WellFoundedRelation (WithBot Nat). Longer-term, we should probably add a WellFoundedOrder class for types with a well-founded less-than relation and a [WellFoundOrder α] : WellFoundedRelation α instance (or maybe just [LT α] [IsWellFounded fun a b : α => a < b] : WellFoundedRelation α).

@@ -820,7 +820,7 @@ protected noncomputable def inv.aux (a : R) (φ : MvPowerSeries σ R) : MvPowerS
     else
       -a *
         ∑ x in n.antidiagonal, if _ : x.2 < n then coeff R x.1 φ * inv.aux a φ x.2 else 0
-  termination_by' ⟨_, Finsupp.lt_wf σ⟩
+termination_by _ n => n
 #align mv_power_series.inv.aux MvPowerSeries.inv.aux
 
 theorem coeff_inv_aux [DecidableEq σ] (n : σ →₀ ℕ) (a : R) (φ : MvPowerSeries σ R) :

Changes are of the form

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

@@ -544,7 +544,7 @@ theorem X_inj [Nontrivial R] {s t : σ} : (X s : MvPowerSeries σ R) = X t ↔ s
     intro h
     replace h := congr_arg (coeff R (single s 1)) h
     rw [coeff_X, if_pos rfl, coeff_X] at h
-    split_ifs  at h with H
+    split_ifs at h with H
     · rw [Finsupp.single_eq_single_iff] at H
       cases' H with H H
       · exact H.1
@@ -2005,10 +2005,10 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero [NoZeroDivisors R] (φ ψ : PowerSerie
     · rw [ih j hj, MulZeroClass.mul_zero]
     by_cases hi : i < m
     · specialize hm₂ _ hi
-      push_neg  at hm₂
+      push_neg at hm₂
       rw [hm₂, MulZeroClass.zero_mul]
     rw [Finset.Nat.mem_antidiagonal] at hij
-    push_neg  at hi hj
+    push_neg at hi hj
     suffices m < i by
       have : m + n < i + j := add_lt_add_of_lt_of_le this hj
       exfalso

Run codespell Mathlib and keep some suggestions.

@@ -808,7 +808,7 @@ variable [Ring R]
 
 /-
 The inverse of a multivariate formal power series is defined by
-well-founded recursion on the coeffients of the inverse.
+well-founded recursion on the coefficients of the inverse.
 -/
 /-- Auxiliary definition that unifies
  the totalised inverse formal power series `(_)⁻¹` and

The main breaking change is that tac <;> [t1, t2] is now written tac <;> [t1; t2], to avoid clashing with tactics like cases and use that take comma-separated lists.

@@ -263,7 +263,7 @@ theorem commute_monomial {a : R} {n} :
   · have := h (m + n)
     rwa [coeff_add_mul_monomial, add_comm, coeff_add_monomial_mul] at this
   · rw [coeff_mul_monomial, coeff_monomial_mul]
-    split_ifs <;> [apply h, rfl]
+    split_ifs <;> [apply h; rfl]
 #align mv_power_series.commute_monomial MvPowerSeries.commute_monomial
 
 protected theorem one_mul : (1 : MvPowerSeries σ R) * φ = φ :=
@@ -898,7 +898,7 @@ instance [LocalRing R] : LocalRing (MvPowerSeries σ R) :=
   LocalRing.of_isUnit_or_isUnit_one_sub_self <| by
     intro φ
     rcases LocalRing.isUnit_or_isUnit_one_sub_self (constantCoeff σ R φ) with (⟨u, h⟩ | ⟨u, h⟩) <;>
-        [left, right] <;>
+        [left; right] <;>
       · refine' isUnit_of_mul_eq_one _ _ (mul_invOfUnit _ u _)
         simpa using h.symm