ring_theory.laurent_series
⟷
Mathlib.RingTheory.LaurentSeries
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,7 +3,7 @@ Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
-import RingTheory.HahnSeries
+import RingTheory.HahnSeries.Basic
import RingTheory.Localization.FractionRing
#align_import ring_theory.laurent_series from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
@@ -112,8 +112,7 @@ theorem single_order_mul_powerSeriesPart (x : LaurentSeries R) :
by_cases h : x.order ≤ n
·
rw [Int.eq_natAbs_of_zero_le (sub_nonneg_of_le h), coeff_coe_power_series,
- power_series_part_coeff, ← Int.eq_natAbs_of_zero_le (sub_nonneg_of_le h),
- add_sub_cancel'_right]
+ power_series_part_coeff, ← Int.eq_natAbs_of_zero_le (sub_nonneg_of_le h), add_sub_cancel]
· rw [coe_power_series, of_power_series_apply, emb_domain_notin_range]
· contrapose! h
exact order_le_of_coeff_ne_zero h.symm
@@ -254,12 +253,12 @@ theorem coeff_coe (i : ℤ) :
by
cases i
·
- rw [Int.natAbs_ofNat_core, Int.ofNat_eq_coe, coeff_coe_power_series,
- if_neg (Int.coe_nat_nonneg _).not_lt]
+ rw [Int.natAbs_ofNat', Int.ofNat_eq_coe, coeff_coe_power_series,
+ if_neg (Int.natCast_nonneg _).not_lt]
· rw [coe_power_series, of_power_series_apply, emb_domain_notin_image_support,
if_pos (Int.negSucc_lt_zero _)]
simp only [not_exists, RelEmbedding.coe_mk, Set.mem_image, not_and, Function.Embedding.coeFn_mk,
- Ne.def, to_power_series_symm_apply_coeff, mem_support, Int.coe_nat_eq, imp_true_iff,
+ Ne.def, to_power_series_symm_apply_coeff, mem_support, Int.natCast_eq_ofNat, imp_true_iff,
not_false_iff]
#align power_series.coeff_coe PowerSeries.coeff_coe
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -118,7 +118,7 @@ theorem single_order_mul_powerSeriesPart (x : LaurentSeries R) :
· contrapose! h
exact order_le_of_coeff_ne_zero h.symm
· contrapose! h
- simp only [Set.mem_range, RelEmbedding.coe_mk, Function.Embedding.coeFn_mk] at h
+ simp only [Set.mem_range, RelEmbedding.coe_mk, Function.Embedding.coeFn_mk] at h
obtain ⟨m, hm⟩ := h
rw [← sub_nonneg, ← hm]
exact Int.zero_le_ofNat _
@@ -182,13 +182,13 @@ instance of_powerSeries_localization [CommRing R] :
· rintro rfl
exact ⟨1, rfl⟩
· rintro ⟨⟨_, n, rfl⟩, hc⟩
- rw [← sub_eq_zero, ← mul_sub, PowerSeries.ext_iff] at hc
+ rw [← sub_eq_zero, ← mul_sub, PowerSeries.ext_iff] at hc
rw [← sub_eq_zero, PowerSeries.ext_iff]
intro m
have h := hc (m + n)
rwa [LinearMap.map_zero, Subtype.coe_mk, PowerSeries.X_pow_eq, PowerSeries.monomial,
add_comm m, PowerSeries.coeff, Finsupp.single_add, MvPowerSeries.coeff_add_monomial_mul,
- one_mul] at h
+ one_mul] at h
#align laurent_series.of_power_series_localization LaurentSeries.of_powerSeries_localization
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010
@@ -94,7 +94,7 @@ theorem powerSeriesPart_eq_zero (x : LaurentSeries R) : x.powerSeriesPart = 0
constructor
· contrapose!
intro h
- rw [PowerSeries.ext_iff, not_forall]
+ rw [PowerSeries.ext_iff, Classical.not_forall]
refine' ⟨0, _⟩
simp [coeff_order_ne_zero h]
· rintro rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
-import Mathbin.RingTheory.HahnSeries
-import Mathbin.RingTheory.Localization.FractionRing
+import RingTheory.HahnSeries
+import RingTheory.Localization.FractionRing
#align_import ring_theory.laurent_series from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -243,7 +243,7 @@ theorem coe_neg : ((-f' : PowerSeries R') : LaurentSeries R') = -f' :=
#print PowerSeries.coe_mul /-
@[simp, norm_cast]
theorem coe_mul : ((f * g : PowerSeries R) : LaurentSeries R) = f * g :=
- (ofPowerSeries ℤ R).map_mul _ _
+ (ofPowerSeries ℤ R).map_hMul _ _
#align power_series.coe_mul PowerSeries.coe_mul
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module ring_theory.laurent_series
-! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.RingTheory.HahnSeries
import Mathbin.RingTheory.Localization.FractionRing
+#align_import ring_theory.laurent_series from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
+
/-!
# Laurent Series
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -59,29 +59,38 @@ theorem coe_powerSeries (x : PowerSeries R) :
rfl
#align laurent_series.coe_power_series LaurentSeries.coe_powerSeries
+#print LaurentSeries.coeff_coe_powerSeries /-
@[simp]
theorem coeff_coe_powerSeries (x : PowerSeries R) (n : ℕ) :
HahnSeries.coeff (x : LaurentSeries R) n = PowerSeries.coeff R n x := by
rw [coe_power_series, of_power_series_apply_coeff]
#align laurent_series.coeff_coe_power_series LaurentSeries.coeff_coe_powerSeries
+-/
+#print LaurentSeries.powerSeriesPart /-
/-- This is a power series that can be multiplied by an integer power of `X` to give our
Laurent series. If the Laurent series is nonzero, `power_series_part` has a nonzero
constant term. -/
def powerSeriesPart (x : LaurentSeries R) : PowerSeries R :=
PowerSeries.mk fun n => x.coeff (x.order + n)
#align laurent_series.power_series_part LaurentSeries.powerSeriesPart
+-/
+#print LaurentSeries.powerSeriesPart_coeff /-
@[simp]
theorem powerSeriesPart_coeff (x : LaurentSeries R) (n : ℕ) :
PowerSeries.coeff R n x.powerSeriesPart = x.coeff (x.order + n) :=
PowerSeries.coeff_mk _ _
#align laurent_series.power_series_part_coeff LaurentSeries.powerSeriesPart_coeff
+-/
+#print LaurentSeries.powerSeriesPart_zero /-
@[simp]
theorem powerSeriesPart_zero : powerSeriesPart (0 : LaurentSeries R) = 0 := by ext; simp
#align laurent_series.power_series_part_zero LaurentSeries.powerSeriesPart_zero
+-/
+#print LaurentSeries.powerSeriesPart_eq_zero /-
@[simp]
theorem powerSeriesPart_eq_zero (x : LaurentSeries R) : x.powerSeriesPart = 0 ↔ x = 0 :=
by
@@ -94,7 +103,9 @@ theorem powerSeriesPart_eq_zero (x : LaurentSeries R) : x.powerSeriesPart = 0
· rintro rfl
simp
#align laurent_series.power_series_part_eq_zero LaurentSeries.powerSeriesPart_eq_zero
+-/
+#print LaurentSeries.single_order_mul_powerSeriesPart /-
@[simp]
theorem single_order_mul_powerSeriesPart (x : LaurentSeries R) :
(single x.order 1 : LaurentSeries R) * x.powerSeriesPart = x :=
@@ -115,7 +126,9 @@ theorem single_order_mul_powerSeriesPart (x : LaurentSeries R) :
rw [← sub_nonneg, ← hm]
exact Int.zero_le_ofNat _
#align laurent_series.single_order_mul_power_series_part LaurentSeries.single_order_mul_powerSeriesPart
+-/
+#print LaurentSeries.ofPowerSeries_powerSeriesPart /-
theorem ofPowerSeries_powerSeriesPart (x : LaurentSeries R) :
ofPowerSeries ℤ R x.powerSeriesPart = single (-x.order) 1 * x :=
by
@@ -123,18 +136,22 @@ theorem ofPowerSeries_powerSeriesPart (x : LaurentSeries R) :
rw [← mul_assoc, single_mul_single, neg_add_self, mul_one, ← C_apply, C_one, one_mul,
coe_power_series]
#align laurent_series.of_power_series_power_series_part LaurentSeries.ofPowerSeries_powerSeriesPart
+-/
end Semiring
instance [CommSemiring R] : Algebra (PowerSeries R) (LaurentSeries R) :=
(HahnSeries.ofPowerSeries ℤ R).toAlgebra
+#print LaurentSeries.coe_algebraMap /-
@[simp]
theorem coe_algebraMap [CommSemiring R] :
⇑(algebraMap (PowerSeries R) (LaurentSeries R)) = HahnSeries.ofPowerSeries ℤ R :=
rfl
#align laurent_series.coe_algebra_map LaurentSeries.coe_algebraMap
+-/
+#print LaurentSeries.of_powerSeries_localization /-
/-- The localization map from power series to Laurent series. -/
@[simps]
instance of_powerSeries_localization [CommRing R] :
@@ -176,6 +193,7 @@ instance of_powerSeries_localization [CommRing R] :
add_comm m, PowerSeries.coeff, Finsupp.single_add, MvPowerSeries.coeff_add_monomial_mul,
one_mul] at h
#align laurent_series.of_power_series_localization LaurentSeries.of_powerSeries_localization
+-/
instance {K : Type u} [Field K] : IsFractionRing (PowerSeries K) (LaurentSeries K) :=
IsLocalization.of_le (Submonoid.powers (PowerSeries.X : PowerSeries K)) _
@@ -190,36 +208,49 @@ open LaurentSeries
variable {R' : Type _} [Semiring R] [Ring R'] (f g : PowerSeries R) (f' g' : PowerSeries R')
+#print PowerSeries.coe_zero /-
@[simp, norm_cast]
theorem coe_zero : ((0 : PowerSeries R) : LaurentSeries R) = 0 :=
(ofPowerSeries ℤ R).map_zero
#align power_series.coe_zero PowerSeries.coe_zero
+-/
+#print PowerSeries.coe_one /-
@[simp, norm_cast]
theorem coe_one : ((1 : PowerSeries R) : LaurentSeries R) = 1 :=
(ofPowerSeries ℤ R).map_one
#align power_series.coe_one PowerSeries.coe_one
+-/
+#print PowerSeries.coe_add /-
@[simp, norm_cast]
theorem coe_add : ((f + g : PowerSeries R) : LaurentSeries R) = f + g :=
(ofPowerSeries ℤ R).map_add _ _
#align power_series.coe_add PowerSeries.coe_add
+-/
+#print PowerSeries.coe_sub /-
@[simp, norm_cast]
theorem coe_sub : ((f' - g' : PowerSeries R') : LaurentSeries R') = f' - g' :=
(ofPowerSeries ℤ R').map_sub _ _
#align power_series.coe_sub PowerSeries.coe_sub
+-/
+#print PowerSeries.coe_neg /-
@[simp, norm_cast]
theorem coe_neg : ((-f' : PowerSeries R') : LaurentSeries R') = -f' :=
(ofPowerSeries ℤ R').map_neg _
#align power_series.coe_neg PowerSeries.coe_neg
+-/
+#print PowerSeries.coe_mul /-
@[simp, norm_cast]
theorem coe_mul : ((f * g : PowerSeries R) : LaurentSeries R) = f * g :=
(ofPowerSeries ℤ R).map_mul _ _
#align power_series.coe_mul PowerSeries.coe_mul
+-/
+#print PowerSeries.coeff_coe /-
theorem coeff_coe (i : ℤ) :
((f : PowerSeries R) : LaurentSeries R).coeff i =
if i < 0 then 0 else PowerSeries.coeff R i.natAbs f :=
@@ -234,22 +265,29 @@ theorem coeff_coe (i : ℤ) :
Ne.def, to_power_series_symm_apply_coeff, mem_support, Int.coe_nat_eq, imp_true_iff,
not_false_iff]
#align power_series.coeff_coe PowerSeries.coeff_coe
+-/
+#print PowerSeries.coe_C /-
@[simp, norm_cast]
theorem coe_C (r : R) : ((C R r : PowerSeries R) : LaurentSeries R) = HahnSeries.C r :=
ofPowerSeries_C _
#align power_series.coe_C PowerSeries.coe_C
+-/
+#print PowerSeries.coe_X /-
@[simp]
theorem coe_X : ((X : PowerSeries R) : LaurentSeries R) = single 1 1 :=
ofPowerSeries_X
#align power_series.coe_X PowerSeries.coe_X
+-/
+#print PowerSeries.coe_smul /-
@[simp, norm_cast]
theorem coe_smul {S : Type _} [Semiring S] [Module R S] (r : R) (x : PowerSeries S) :
((r • x : PowerSeries S) : LaurentSeries S) = r • x := by ext;
simp [coeff_coe, coeff_smul, smul_ite]
#align power_series.coe_smul PowerSeries.coe_smul
+-/
@[simp, norm_cast]
theorem coe_bit0 : ((bit0 f : PowerSeries R) : LaurentSeries R) = bit0 f :=
@@ -261,10 +299,12 @@ theorem coe_bit1 : ((bit1 f : PowerSeries R) : LaurentSeries R) = bit1 f :=
(ofPowerSeries ℤ R).map_bit1 _
#align power_series.coe_bit1 PowerSeries.coe_bit1
+#print PowerSeries.coe_pow /-
@[simp, norm_cast]
theorem coe_pow (n : ℕ) : ((f ^ n : PowerSeries R) : LaurentSeries R) = f ^ n :=
(ofPowerSeries ℤ R).map_pow _ _
#align power_series.coe_pow PowerSeries.coe_pow
+-/
end PowerSeries
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -110,7 +110,7 @@ theorem single_order_mul_powerSeriesPart (x : LaurentSeries R) :
· contrapose! h
exact order_le_of_coeff_ne_zero h.symm
· contrapose! h
- simp only [Set.mem_range, RelEmbedding.coe_mk, Function.Embedding.coeFn_mk] at h
+ simp only [Set.mem_range, RelEmbedding.coe_mk, Function.Embedding.coeFn_mk] at h
obtain ⟨m, hm⟩ := h
rw [← sub_nonneg, ← hm]
exact Int.zero_le_ofNat _
@@ -168,13 +168,13 @@ instance of_powerSeries_localization [CommRing R] :
· rintro rfl
exact ⟨1, rfl⟩
· rintro ⟨⟨_, n, rfl⟩, hc⟩
- rw [← sub_eq_zero, ← mul_sub, PowerSeries.ext_iff] at hc
+ rw [← sub_eq_zero, ← mul_sub, PowerSeries.ext_iff] at hc
rw [← sub_eq_zero, PowerSeries.ext_iff]
intro m
have h := hc (m + n)
rwa [LinearMap.map_zero, Subtype.coe_mk, PowerSeries.X_pow_eq, PowerSeries.monomial,
add_comm m, PowerSeries.coeff, Finsupp.single_add, MvPowerSeries.coeff_add_monomial_mul,
- one_mul] at h
+ one_mul] at h
#align laurent_series.of_power_series_localization LaurentSeries.of_powerSeries_localization
instance {K : Type u} [Field K] : IsFractionRing (PowerSeries K) (LaurentSeries K) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -54,11 +54,10 @@ variable [Semiring R]
instance : Coe (PowerSeries R) (LaurentSeries R) :=
⟨HahnSeries.ofPowerSeries ℤ R⟩
-/- warning: laurent_series.coe_power_series clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align laurent_series.coe_power_series [anonymous]ₓ'. -/
-theorem [anonymous] (x : PowerSeries R) : (x : LaurentSeries R) = HahnSeries.ofPowerSeries ℤ R x :=
+theorem coe_powerSeries (x : PowerSeries R) :
+ (x : LaurentSeries R) = HahnSeries.ofPowerSeries ℤ R x :=
rfl
-#align laurent_series.coe_power_series [anonymous]
+#align laurent_series.coe_power_series LaurentSeries.coe_powerSeries
@[simp]
theorem coeff_coe_powerSeries (x : PowerSeries R) (n : ℕ) :
@@ -252,19 +251,15 @@ theorem coe_smul {S : Type _} [Semiring S] [Module R S] (r : R) (x : PowerSeries
simp [coeff_coe, coeff_smul, smul_ite]
#align power_series.coe_smul PowerSeries.coe_smul
-/- warning: power_series.coe_bit0 clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align power_series.coe_bit0 [anonymous]ₓ'. -/
@[simp, norm_cast]
-theorem [anonymous] : ((bit0 f : PowerSeries R) : LaurentSeries R) = bit0 f :=
+theorem coe_bit0 : ((bit0 f : PowerSeries R) : LaurentSeries R) = bit0 f :=
(ofPowerSeries ℤ R).map_bit0 _
-#align power_series.coe_bit0 [anonymous]
+#align power_series.coe_bit0 PowerSeries.coe_bit0
-/- warning: power_series.coe_bit1 clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align power_series.coe_bit1 [anonymous]ₓ'. -/
@[simp, norm_cast]
-theorem [anonymous] : ((bit1 f : PowerSeries R) : LaurentSeries R) = bit1 f :=
+theorem coe_bit1 : ((bit1 f : PowerSeries R) : LaurentSeries R) = bit1 f :=
(ofPowerSeries ℤ R).map_bit1 _
-#align power_series.coe_bit1 [anonymous]
+#align power_series.coe_bit1 PowerSeries.coe_bit1
@[simp, norm_cast]
theorem coe_pow (n : ℕ) : ((f ^ n : PowerSeries R) : LaurentSeries R) = f ^ n :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -30,7 +30,7 @@ import Mathbin.RingTheory.Localization.FractionRing
open HahnSeries
-open BigOperators Classical Polynomial
+open scoped BigOperators Classical Polynomial
noncomputable section
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -55,31 +55,17 @@ instance : Coe (PowerSeries R) (LaurentSeries R) :=
⟨HahnSeries.ofPowerSeries ℤ R⟩
/- warning: laurent_series.coe_power_series clashes with [anonymous] -> [anonymous]
-warning: laurent_series.coe_power_series -> [anonymous] is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u}} [_inst_1 : Semiring.{u} R] (x : PowerSeries.{u} R), Eq.{max 1 (succ u)} (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) ((fun (a : Sort.{max 1 (succ u)}) (b : Sort.{max 1 (succ u)}) [self : HasLiftT.{max 1 (succ u), max 1 (succ u)} a b] => self.0) (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (HasLiftT.mk.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (CoeTCₓ.coe.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (coeBase.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (LaurentSeries.hasCoe.{u} R _inst_1)))) x) (coeFn.{succ u, succ u} (RingHom.{u, u} (PowerSeries.{u} R) (HahnSeries.{0, u} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (Semiring.toNonAssocSemiring.{u} (PowerSeries.{u} R) (PowerSeries.semiring.{u} R _inst_1)) (HahnSeries.nonAssocSemiring.{0, u} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u} R _inst_1))) (fun (_x : RingHom.{u, u} (PowerSeries.{u} R) (HahnSeries.{0, u} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (Semiring.toNonAssocSemiring.{u} (PowerSeries.{u} R) (PowerSeries.semiring.{u} R _inst_1)) (HahnSeries.nonAssocSemiring.{0, u} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u} R _inst_1))) => (PowerSeries.{u} R) -> (HahnSeries.{0, u} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1)))))) (RingHom.hasCoeToFun.{u, u} (PowerSeries.{u} R) (HahnSeries.{0, u} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (Semiring.toNonAssocSemiring.{u} (PowerSeries.{u} R) (PowerSeries.semiring.{u} R _inst_1)) (HahnSeries.nonAssocSemiring.{0, u} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u} R _inst_1))) (HahnSeries.ofPowerSeries.{0, u} Int R _inst_1 (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) x)
-but is expected to have type
- forall {R : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> R -> _inst_1) -> Nat -> (List.{u} R) -> (List.{v} _inst_1)
Case conversion may be inaccurate. Consider using '#align laurent_series.coe_power_series [anonymous]ₓ'. -/
theorem [anonymous] (x : PowerSeries R) : (x : LaurentSeries R) = HahnSeries.ofPowerSeries ℤ R x :=
rfl
#align laurent_series.coe_power_series [anonymous]
-/- warning: laurent_series.coeff_coe_power_series -> LaurentSeries.coeff_coe_powerSeries is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align laurent_series.coeff_coe_power_series LaurentSeries.coeff_coe_powerSeriesₓ'. -/
@[simp]
theorem coeff_coe_powerSeries (x : PowerSeries R) (n : ℕ) :
HahnSeries.coeff (x : LaurentSeries R) n = PowerSeries.coeff R n x := by
rw [coe_power_series, of_power_series_apply_coeff]
#align laurent_series.coeff_coe_power_series LaurentSeries.coeff_coe_powerSeries
-/- warning: laurent_series.power_series_part -> LaurentSeries.powerSeriesPart is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> (PowerSeries.{u1} R)
-but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) -> (PowerSeries.{u1} R)
-Case conversion may be inaccurate. Consider using '#align laurent_series.power_series_part LaurentSeries.powerSeriesPartₓ'. -/
/-- This is a power series that can be multiplied by an integer power of `X` to give our
Laurent series. If the Laurent series is nonzero, `power_series_part` has a nonzero
constant term. -/
@@ -87,34 +73,16 @@ def powerSeriesPart (x : LaurentSeries R) : PowerSeries R :=
PowerSeries.mk fun n => x.coeff (x.order + n)
#align laurent_series.power_series_part LaurentSeries.powerSeriesPart
-/- warning: laurent_series.power_series_part_coeff -> LaurentSeries.powerSeriesPart_coeff is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align laurent_series.power_series_part_coeff LaurentSeries.powerSeriesPart_coeffₓ'. -/
@[simp]
theorem powerSeriesPart_coeff (x : LaurentSeries R) (n : ℕ) :
PowerSeries.coeff R n x.powerSeriesPart = x.coeff (x.order + n) :=
PowerSeries.coeff_mk _ _
#align laurent_series.power_series_part_coeff LaurentSeries.powerSeriesPart_coeff
-/- warning: laurent_series.power_series_part_zero -> LaurentSeries.powerSeriesPart_zero 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], Eq.{succ u1} (PowerSeries.{u1} R) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 (OfNat.ofNat.{u1} (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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 laurent_series.power_series_part_zero LaurentSeries.powerSeriesPart_zeroₓ'. -/
@[simp]
theorem powerSeriesPart_zero : powerSeriesPart (0 : LaurentSeries R) = 0 := by ext; simp
#align laurent_series.power_series_part_zero LaurentSeries.powerSeriesPart_zero
-/- warning: laurent_series.power_series_part_eq_zero -> LaurentSeries.powerSeriesPart_eq_zero is a dubious translation:
-lean 3 declaration is
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- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))), Iff (Eq.{succ u1} (PowerSeries.{u1} R) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x) (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)))))) (Eq.{succ u1} (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) x (OfNat.ofNat.{u1} (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align laurent_series.power_series_part_eq_zero LaurentSeries.powerSeriesPart_eq_zeroₓ'. -/
@[simp]
theorem powerSeriesPart_eq_zero (x : LaurentSeries R) : x.powerSeriesPart = 0 ↔ x = 0 :=
by
@@ -128,9 +96,6 @@ theorem powerSeriesPart_eq_zero (x : LaurentSeries R) : x.powerSeriesPart = 0
simp
#align laurent_series.power_series_part_eq_zero LaurentSeries.powerSeriesPart_eq_zero
-/- warning: laurent_series.single_order_mul_power_series_part -> LaurentSeries.single_order_mul_powerSeriesPart is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align laurent_series.single_order_mul_power_series_part LaurentSeries.single_order_mul_powerSeriesPartₓ'. -/
@[simp]
theorem single_order_mul_powerSeriesPart (x : LaurentSeries R) :
(single x.order 1 : LaurentSeries R) * x.powerSeriesPart = x :=
@@ -152,9 +117,6 @@ theorem single_order_mul_powerSeriesPart (x : LaurentSeries R) :
exact Int.zero_le_ofNat _
#align laurent_series.single_order_mul_power_series_part LaurentSeries.single_order_mul_powerSeriesPart
-/- warning: laurent_series.of_power_series_power_series_part -> LaurentSeries.ofPowerSeries_powerSeriesPart is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align laurent_series.of_power_series_power_series_part LaurentSeries.ofPowerSeries_powerSeriesPartₓ'. -/
theorem ofPowerSeries_powerSeriesPart (x : LaurentSeries R) :
ofPowerSeries ℤ R x.powerSeriesPart = single (-x.order) 1 * x :=
by
@@ -168,21 +130,12 @@ end Semiring
instance [CommSemiring R] : Algebra (PowerSeries R) (LaurentSeries R) :=
(HahnSeries.ofPowerSeries ℤ R).toAlgebra
-/- warning: laurent_series.coe_algebra_map -> LaurentSeries.coe_algebraMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align laurent_series.coe_algebra_map LaurentSeries.coe_algebraMapₓ'. -/
@[simp]
theorem coe_algebraMap [CommSemiring R] :
⇑(algebraMap (PowerSeries R) (LaurentSeries R)) = HahnSeries.ofPowerSeries ℤ R :=
rfl
#align laurent_series.coe_algebra_map LaurentSeries.coe_algebraMap
-/- warning: laurent_series.of_power_series_localization -> LaurentSeries.of_powerSeries_localization is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], IsLocalization.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submonoid.powers.{u1} (PowerSeries.{u1} R) (Ring.toMonoid.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PowerSeries.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LaurentSeries.{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))))))) (HahnSeries.commSemiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (CommRing.toCommSemiring.{u1} R _inst_1)) (LaurentSeries.algebra.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))
-but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], IsLocalization.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submonoid.powers.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HahnSeries.instCommSemiringHahnSeriesToPartialOrderToZeroToCommMonoidWithZero.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (CommRing.toCommSemiring.{u1} R _inst_1)) (LaurentSeries.instAlgebraPowerSeriesLaurentSeriesToZeroToCommMonoidWithZeroInstCommSemiringPowerSeriesInstSemiringHahnSeriesToPartialOrderToZeroToMonoidWithZeroIntToOrderedCancelAddCommMonoidToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringLinearOrderedCommRingToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))
-Case conversion may be inaccurate. Consider using '#align laurent_series.of_power_series_localization LaurentSeries.of_powerSeries_localizationₓ'. -/
/-- The localization map from power series to Laurent series. -/
@[simps]
instance of_powerSeries_localization [CommRing R] :
@@ -238,57 +191,36 @@ open LaurentSeries
variable {R' : Type _} [Semiring R] [Ring R'] (f g : PowerSeries R) (f' g' : PowerSeries R')
-/- warning: power_series.coe_zero -> PowerSeries.coe_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coe_zero PowerSeries.coe_zeroₓ'. -/
@[simp, norm_cast]
theorem coe_zero : ((0 : PowerSeries R) : LaurentSeries R) = 0 :=
(ofPowerSeries ℤ R).map_zero
#align power_series.coe_zero PowerSeries.coe_zero
-/- warning: power_series.coe_one -> PowerSeries.coe_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coe_one PowerSeries.coe_oneₓ'. -/
@[simp, norm_cast]
theorem coe_one : ((1 : PowerSeries R) : LaurentSeries R) = 1 :=
(ofPowerSeries ℤ R).map_one
#align power_series.coe_one PowerSeries.coe_one
-/- warning: power_series.coe_add -> PowerSeries.coe_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coe_add PowerSeries.coe_addₓ'. -/
@[simp, norm_cast]
theorem coe_add : ((f + g : PowerSeries R) : LaurentSeries R) = f + g :=
(ofPowerSeries ℤ R).map_add _ _
#align power_series.coe_add PowerSeries.coe_add
-/- warning: power_series.coe_sub -> PowerSeries.coe_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coe_sub PowerSeries.coe_subₓ'. -/
@[simp, norm_cast]
theorem coe_sub : ((f' - g' : PowerSeries R') : LaurentSeries R') = f' - g' :=
(ofPowerSeries ℤ R').map_sub _ _
#align power_series.coe_sub PowerSeries.coe_sub
-/- warning: power_series.coe_neg -> PowerSeries.coe_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coe_neg PowerSeries.coe_negₓ'. -/
@[simp, norm_cast]
theorem coe_neg : ((-f' : PowerSeries R') : LaurentSeries R') = -f' :=
(ofPowerSeries ℤ R').map_neg _
#align power_series.coe_neg PowerSeries.coe_neg
-/- warning: power_series.coe_mul -> PowerSeries.coe_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coe_mul PowerSeries.coe_mulₓ'. -/
@[simp, norm_cast]
theorem coe_mul : ((f * g : PowerSeries R) : LaurentSeries R) = f * g :=
(ofPowerSeries ℤ R).map_mul _ _
#align power_series.coe_mul PowerSeries.coe_mul
-/- warning: power_series.coeff_coe -> PowerSeries.coeff_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coeff_coe PowerSeries.coeff_coeₓ'. -/
theorem coeff_coe (i : ℤ) :
((f : PowerSeries R) : LaurentSeries R).coeff i =
if i < 0 then 0 else PowerSeries.coeff R i.natAbs f :=
@@ -304,25 +236,16 @@ theorem coeff_coe (i : ℤ) :
not_false_iff]
#align power_series.coeff_coe PowerSeries.coeff_coe
-/- warning: power_series.coe_C -> PowerSeries.coe_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coe_C PowerSeries.coe_Cₓ'. -/
@[simp, norm_cast]
theorem coe_C (r : R) : ((C R r : PowerSeries R) : LaurentSeries R) = HahnSeries.C r :=
ofPowerSeries_C _
#align power_series.coe_C PowerSeries.coe_C
-/- warning: power_series.coe_X -> PowerSeries.coe_X is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coe_X PowerSeries.coe_Xₓ'. -/
@[simp]
theorem coe_X : ((X : PowerSeries R) : LaurentSeries R) = single 1 1 :=
ofPowerSeries_X
#align power_series.coe_X PowerSeries.coe_X
-/- warning: power_series.coe_smul -> PowerSeries.coe_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coe_smul PowerSeries.coe_smulₓ'. -/
@[simp, norm_cast]
theorem coe_smul {S : Type _} [Semiring S] [Module R S] (r : R) (x : PowerSeries S) :
((r • x : PowerSeries S) : LaurentSeries S) = r • x := by ext;
@@ -330,11 +253,6 @@ theorem coe_smul {S : Type _} [Semiring S] [Module R S] (r : R) (x : PowerSeries
#align power_series.coe_smul PowerSeries.coe_smul
/- warning: power_series.coe_bit0 clashes with [anonymous] -> [anonymous]
-warning: power_series.coe_bit0 -> [anonymous] is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
- forall {R : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> R -> _inst_1) -> Nat -> (List.{u} R) -> (List.{v} _inst_1)
Case conversion may be inaccurate. Consider using '#align power_series.coe_bit0 [anonymous]ₓ'. -/
@[simp, norm_cast]
theorem [anonymous] : ((bit0 f : PowerSeries R) : LaurentSeries R) = bit0 f :=
@@ -342,20 +260,12 @@ theorem [anonymous] : ((bit0 f : PowerSeries R) : LaurentSeries R) = bit0 f :=
#align power_series.coe_bit0 [anonymous]
/- warning: power_series.coe_bit1 clashes with [anonymous] -> [anonymous]
-warning: power_series.coe_bit1 -> [anonymous] is a dubious translation:
-lean 3 declaration is
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- forall {R : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> R -> _inst_1) -> Nat -> (List.{u} R) -> (List.{v} _inst_1)
Case conversion may be inaccurate. Consider using '#align power_series.coe_bit1 [anonymous]ₓ'. -/
@[simp, norm_cast]
theorem [anonymous] : ((bit1 f : PowerSeries R) : LaurentSeries R) = bit1 f :=
(ofPowerSeries ℤ R).map_bit1 _
#align power_series.coe_bit1 [anonymous]
-/- warning: power_series.coe_pow -> PowerSeries.coe_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align power_series.coe_pow PowerSeries.coe_powₓ'. -/
@[simp, norm_cast]
theorem coe_pow (n : ℕ) : ((f ^ n : PowerSeries R) : LaurentSeries R) = f ^ n :=
(ofPowerSeries ℤ R).map_pow _ _
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -106,10 +106,7 @@ but is expected to have type
forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (PowerSeries.{u1} R) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 (OfNat.ofNat.{u1} (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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 laurent_series.power_series_part_zero LaurentSeries.powerSeriesPart_zeroₓ'. -/
@[simp]
-theorem powerSeriesPart_zero : powerSeriesPart (0 : LaurentSeries R) = 0 :=
- by
- ext
- simp
+theorem powerSeriesPart_zero : powerSeriesPart (0 : LaurentSeries R) = 0 := by ext; simp
#align laurent_series.power_series_part_zero LaurentSeries.powerSeriesPart_zero
/- warning: laurent_series.power_series_part_eq_zero -> LaurentSeries.powerSeriesPart_eq_zero is a dubious translation:
@@ -328,9 +325,7 @@ theorem coe_X : ((X : PowerSeries R) : LaurentSeries R) = single 1 1 :=
Case conversion may be inaccurate. Consider using '#align power_series.coe_smul PowerSeries.coe_smulₓ'. -/
@[simp, norm_cast]
theorem coe_smul {S : Type _} [Semiring S] [Module R S] (r : R) (x : PowerSeries S) :
- ((r • x : PowerSeries S) : LaurentSeries S) = r • x :=
- by
- ext
+ ((r • x : PowerSeries S) : LaurentSeries S) = r • x := by ext;
simp [coeff_coe, coeff_smul, smul_ite]
#align power_series.coe_smul PowerSeries.coe_smul
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -54,16 +54,19 @@ variable [Semiring R]
instance : Coe (PowerSeries R) (LaurentSeries R) :=
⟨HahnSeries.ofPowerSeries ℤ R⟩
-theorem coe_powerSeries (x : PowerSeries R) :
- (x : LaurentSeries R) = HahnSeries.ofPowerSeries ℤ R x :=
+/- warning: laurent_series.coe_power_series clashes with [anonymous] -> [anonymous]
+warning: laurent_series.coe_power_series -> [anonymous] is a dubious translation:
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(Semiring.toNonAssocSemiring.{u} R _inst_1))))) (Semiring.toNonAssocSemiring.{u} (PowerSeries.{u} R) (PowerSeries.semiring.{u} R _inst_1)) (HahnSeries.nonAssocSemiring.{0, u} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u} R _inst_1))) (fun (_x : RingHom.{u, u} (PowerSeries.{u} R) (HahnSeries.{0, u} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (Semiring.toNonAssocSemiring.{u} (PowerSeries.{u} R) (PowerSeries.semiring.{u} R _inst_1)) (HahnSeries.nonAssocSemiring.{0, u} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u} R _inst_1))) => (PowerSeries.{u} R) -> (HahnSeries.{0, u} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1)))))) (RingHom.hasCoeToFun.{u, u} (PowerSeries.{u} R) (HahnSeries.{0, u} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (Semiring.toNonAssocSemiring.{u} (PowerSeries.{u} R) (PowerSeries.semiring.{u} R _inst_1)) (HahnSeries.nonAssocSemiring.{0, u} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u} R _inst_1))) (HahnSeries.ofPowerSeries.{0, u} Int R _inst_1 (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) x)
+but is expected to have type
+ forall {R : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> R -> _inst_1) -> Nat -> (List.{u} R) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align laurent_series.coe_power_series [anonymous]ₓ'. -/
+theorem [anonymous] (x : PowerSeries R) : (x : LaurentSeries R) = HahnSeries.ofPowerSeries ℤ R x :=
rfl
-#align laurent_series.coe_power_series LaurentSeries.coe_powerSeries
+#align laurent_series.coe_power_series [anonymous]
/- warning: laurent_series.coeff_coe_power_series -> LaurentSeries.coeff_coe_powerSeries is a dubious translation:
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Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) x) (Nat.cast.{0} Int instNatCastInt 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) x)
+<too large>
Case conversion may be inaccurate. Consider using '#align laurent_series.coeff_coe_power_series LaurentSeries.coeff_coe_powerSeriesₓ'. -/
@[simp]
theorem coeff_coe_powerSeries (x : PowerSeries R) (n : ℕ) :
@@ -129,10 +132,7 @@ theorem powerSeriesPart_eq_zero (x : LaurentSeries R) : x.powerSeriesPart = 0
#align laurent_series.power_series_part_eq_zero LaurentSeries.powerSeriesPart_eq_zero
/- warning: laurent_series.single_order_mul_power_series_part -> LaurentSeries.single_order_mul_powerSeriesPart is a dubious translation:
-lean 3 declaration is
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(NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x))) x
+<too large>
Case conversion may be inaccurate. Consider using '#align laurent_series.single_order_mul_power_series_part LaurentSeries.single_order_mul_powerSeriesPartₓ'. -/
@[simp]
theorem single_order_mul_powerSeriesPart (x : LaurentSeries R) :
@@ -156,10 +156,7 @@ theorem single_order_mul_powerSeriesPart (x : LaurentSeries R) :
#align laurent_series.single_order_mul_power_series_part LaurentSeries.single_order_mul_powerSeriesPart
/- warning: laurent_series.of_power_series_power_series_part -> LaurentSeries.ofPowerSeries_powerSeriesPart is a dubious translation:
-lean 3 declaration is
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (instHMul.{u1} (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.hasMul.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HahnSeries.hasZero.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (_x : ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HahnSeries.hasZero.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => R -> (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (ZeroHom.hasCoeToFun.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HahnSeries.hasZero.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int 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(LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) Int.hasZero x))) (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)))))))) x)
-but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.124 : R) => HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.124 : R) => HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (HahnSeries.instMulHahnSeriesToPartialOrderToZeroToMulZeroClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.124 : R) => HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (ZeroHomClass.toFunLike.{u1, u1, u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) R (HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (ZeroHom.zeroHomClass.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (HahnSeries.single.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (Neg.neg.{0} Int Int.instNegInt (HahnSeries.order.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) x))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) x)
+<too large>
Case conversion may be inaccurate. Consider using '#align laurent_series.of_power_series_power_series_part LaurentSeries.ofPowerSeries_powerSeriesPartₓ'. -/
theorem ofPowerSeries_powerSeriesPart (x : LaurentSeries R) :
ofPowerSeries ℤ R x.powerSeriesPart = single (-x.order) 1 * x :=
@@ -175,10 +172,7 @@ instance [CommSemiring R] : Algebra (PowerSeries R) (LaurentSeries R) :=
(HahnSeries.ofPowerSeries ℤ R).toAlgebra
/- warning: laurent_series.coe_algebra_map -> LaurentSeries.coe_algebraMap is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R], Eq.{succ u1} ((PowerSeries.{u1} R) -> (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HahnSeries.semiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HahnSeries.semiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1)))) => (PowerSeries.{u1} R) -> (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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))) (HahnSeries.nonAssocSemiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int 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(MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (HahnSeries.ofPowerSeries.{0, u1} Int R (CommSemiring.toSemiring.{u1} R _inst_1) (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))
+<too large>
Case conversion may be inaccurate. Consider using '#align laurent_series.coe_algebra_map LaurentSeries.coe_algebraMapₓ'. -/
@[simp]
theorem coe_algebraMap [CommSemiring R] :
@@ -248,10 +242,7 @@ open LaurentSeries
variable {R' : Type _} [Semiring R] [Ring R'] (f g : PowerSeries R) (f' g' : PowerSeries R')
/- warning: power_series.coe_zero -> PowerSeries.coe_zero is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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(LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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)))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))))) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))
+<too large>
Case conversion may be inaccurate. Consider using '#align power_series.coe_zero PowerSeries.coe_zeroₓ'. -/
@[simp, norm_cast]
theorem coe_zero : ((0 : PowerSeries R) : LaurentSeries R) = 0 :=
@@ -259,10 +250,7 @@ theorem coe_zero : ((0 : PowerSeries R) : LaurentSeries R) = 0 :=
#align power_series.coe_zero PowerSeries.coe_zero
/- warning: power_series.coe_one -> PowerSeries.coe_one is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align power_series.coe_one PowerSeries.coe_oneₓ'. -/
@[simp, norm_cast]
theorem coe_one : ((1 : PowerSeries R) : LaurentSeries R) = 1 :=
@@ -270,10 +258,7 @@ theorem coe_one : ((1 : PowerSeries R) : LaurentSeries R) = 1 :=
#align power_series.coe_one PowerSeries.coe_one
/- warning: power_series.coe_add -> PowerSeries.coe_add is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align power_series.coe_add PowerSeries.coe_addₓ'. -/
@[simp, norm_cast]
theorem coe_add : ((f + g : PowerSeries R) : LaurentSeries R) = f + g :=
@@ -281,10 +266,7 @@ theorem coe_add : ((f + g : PowerSeries R) : LaurentSeries R) = f + g :=
#align power_series.coe_add PowerSeries.coe_add
/- warning: power_series.coe_sub -> PowerSeries.coe_sub is a dubious translation:
-lean 3 declaration is
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(PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) 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_inst_2))))))) (HahnSeries.ofPowerSeries.{0, u1} Int R' (Ring.toSemiring.{u1} R' _inst_2) (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) g'))
+<too large>
Case conversion may be inaccurate. Consider using '#align power_series.coe_sub PowerSeries.coe_subₓ'. -/
@[simp, norm_cast]
theorem coe_sub : ((f' - g' : PowerSeries R') : LaurentSeries R') = f' - g' :=
@@ -292,10 +274,7 @@ theorem coe_sub : ((f' - g' : PowerSeries R') : LaurentSeries R') = f' - g' :=
#align power_series.coe_sub PowerSeries.coe_sub
/- warning: power_series.coe_neg -> PowerSeries.coe_neg is a dubious translation:
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(LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))))) (HahnSeries.ofPowerSeries.{0, u1} Int R' (Ring.toSemiring.{u1} R' _inst_2) (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Neg.neg.{u1} (PowerSeries.{u1} R') (Ring.toNeg.{u1} (PowerSeries.{u1} R') (PowerSeries.instRingPowerSeries.{u1} R' _inst_2)) f')) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R') => HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) f') (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R') => HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) f') (HahnSeries.instRingHahnSeriesToPartialOrderToZeroToMonoidWithZeroToSemiring.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) _inst_2)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (fun (a : PowerSeries.{u1} R') => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R') => HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (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_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R') (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))))) (HahnSeries.ofPowerSeries.{0, u1} Int R' (Ring.toSemiring.{u1} R' _inst_2) (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) f'))
+<too large>
Case conversion may be inaccurate. Consider using '#align power_series.coe_neg PowerSeries.coe_negₓ'. -/
@[simp, norm_cast]
theorem coe_neg : ((-f' : PowerSeries R') : LaurentSeries R') = -f' :=
@@ -303,10 +282,7 @@ theorem coe_neg : ((-f' : PowerSeries R') : LaurentSeries R') = -f' :=
#align power_series.coe_neg PowerSeries.coe_neg
/- warning: power_series.coe_mul -> PowerSeries.coe_mul is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : PowerSeries.{u1} R) (g : PowerSeries.{u1} R), Eq.{succ u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{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)))))) f g)) (HMul.hMul.{u1, u1, u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (instHMul.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.hasMul.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R 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Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R 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(StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int 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R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) g))
+<too large>
Case conversion may be inaccurate. Consider using '#align power_series.coe_mul PowerSeries.coe_mulₓ'. -/
@[simp, norm_cast]
theorem coe_mul : ((f * g : PowerSeries R) : LaurentSeries R) = f * g :=
@@ -314,10 +290,7 @@ theorem coe_mul : ((f * g : PowerSeries R) : LaurentSeries R) = f * g :=
#align power_series.coe_mul PowerSeries.coe_mul
/- warning: power_series.coeff_coe -> PowerSeries.coeff_coe 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_coe PowerSeries.coeff_coeₓ'. -/
theorem coeff_coe (i : ℤ) :
((f : PowerSeries R) : LaurentSeries R).coeff i =
@@ -335,10 +308,7 @@ theorem coeff_coe (i : ℤ) :
#align power_series.coeff_coe PowerSeries.coeff_coe
/- warning: power_series.coe_C -> PowerSeries.coe_C is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align power_series.coe_C PowerSeries.coe_Cₓ'. -/
@[simp, norm_cast]
theorem coe_C (r : R) : ((C R r : PowerSeries R) : LaurentSeries R) = HahnSeries.C r :=
@@ -346,10 +316,7 @@ theorem coe_C (r : R) : ((C R r : PowerSeries R) : LaurentSeries R) = HahnSeries
#align power_series.coe_C PowerSeries.coe_C
/- warning: power_series.coe_X -> PowerSeries.coe_X is a dubious translation:
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-but is expected to have type
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(PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (PowerSeries.X.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.124 : R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (ZeroHomClass.toFunLike.{u1, u1, u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) R (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (ZeroHom.zeroHomClass.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (HahnSeries.single.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
+<too large>
Case conversion may be inaccurate. Consider using '#align power_series.coe_X PowerSeries.coe_Xₓ'. -/
@[simp]
theorem coe_X : ((X : PowerSeries R) : LaurentSeries R) = single 1 1 :=
@@ -357,10 +324,7 @@ theorem coe_X : ((X : PowerSeries R) : LaurentSeries R) = single 1 1 :=
#align power_series.coe_X PowerSeries.coe_X
/- warning: power_series.coe_smul -> PowerSeries.coe_smul is a dubious translation:
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(NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (CoeTCₓ.coe.{succ u2, succ u2} (PowerSeries.{u2} S) (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (coeBase.{succ u2, succ u2} (PowerSeries.{u2} S) (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (LaurentSeries.hasCoe.{u2} S _inst_3)))) (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_3))))))) (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_3))))))) (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_3))))))) (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_3)))) (PowerSeries.module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))) _inst_4))))) r x)) (SMul.smul.{u1, u2} R (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (HahnSeries.hasSmul.{0, u1, u2} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int 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(PowerSeries.{u2} S) (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (CoeTCₓ.coe.{succ u2, succ u2} (PowerSeries.{u2} S) (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (coeBase.{succ u2, succ u2} (PowerSeries.{u2} S) (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (LaurentSeries.hasCoe.{u2} S _inst_3)))) x))
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(Semiring.toMonoidWithZero.{u1} S _inst_3))) (SMulWithZero.toSMulZeroClass.{u2, u1} R (PowerSeries.{u1} S) (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (PowerSeries.instZeroPowerSeries.{u1} S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R (PowerSeries.{u1} S) (Semiring.toMonoidWithZero.{u2} R _inst_1) (PowerSeries.instZeroPowerSeries.{u1} S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Module.toMulActionWithZero.{u2, u1} R (PowerSeries.{u1} S) _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_3)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u1} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_3))) _inst_4)))))) r x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S 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(HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3))) (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3))) (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3)))))) (HahnSeries.ofPowerSeries.{0, u1} Int S _inst_3 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) x))
+<too large>
Case conversion may be inaccurate. Consider using '#align power_series.coe_smul PowerSeries.coe_smulₓ'. -/
@[simp, norm_cast]
theorem coe_smul {S : Type _} [Semiring S] [Module R S] (r : R) (x : PowerSeries S) :
@@ -370,21 +334,32 @@ theorem coe_smul {S : Type _} [Semiring S] [Module R S] (r : R) (x : PowerSeries
simp [coeff_coe, coeff_smul, smul_ite]
#align power_series.coe_smul PowerSeries.coe_smul
+/- warning: power_series.coe_bit0 clashes with [anonymous] -> [anonymous]
+warning: power_series.coe_bit0 -> [anonymous] is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u}} [_inst_1 : Semiring.{u} R] (f : PowerSeries.{u} R), Eq.{max 1 (succ u)} (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) ((fun (a : Sort.{max 1 (succ u)}) (b : Sort.{max 1 (succ u)}) [self : HasLiftT.{max 1 (succ u), max 1 (succ u)} a b] => self.0) (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (HasLiftT.mk.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (CoeTCₓ.coe.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (coeBase.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (LaurentSeries.hasCoe.{u} R _inst_1)))) (bit0.{u} (PowerSeries.{u} R) (Distrib.toHasAdd.{u} (PowerSeries.{u} R) (NonUnitalNonAssocSemiring.toDistrib.{u} (PowerSeries.{u} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} (PowerSeries.{u} R) (Semiring.toNonAssocSemiring.{u} (PowerSeries.{u} R) (PowerSeries.semiring.{u} R _inst_1))))) f)) (bit0.{u} (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (HahnSeries.hasAdd.{0, u} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (AddMonoidWithOne.toAddMonoid.{u} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u} R (NonAssocSemiring.toAddCommMonoidWithOne.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) ((fun (a : Sort.{max 1 (succ u)}) (b : Sort.{max 1 (succ u)}) [self : HasLiftT.{max 1 (succ u), max 1 (succ u)} a b] => self.0) (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (HasLiftT.mk.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (CoeTCₓ.coe.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (coeBase.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (LaurentSeries.hasCoe.{u} R _inst_1)))) f))
+but is expected to have type
+ forall {R : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> R -> _inst_1) -> Nat -> (List.{u} R) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align power_series.coe_bit0 [anonymous]ₓ'. -/
@[simp, norm_cast]
-theorem coe_bit0 : ((bit0 f : PowerSeries R) : LaurentSeries R) = bit0 f :=
+theorem [anonymous] : ((bit0 f : PowerSeries R) : LaurentSeries R) = bit0 f :=
(ofPowerSeries ℤ R).map_bit0 _
-#align power_series.coe_bit0 PowerSeries.coe_bit0
+#align power_series.coe_bit0 [anonymous]
+/- warning: power_series.coe_bit1 clashes with [anonymous] -> [anonymous]
+warning: power_series.coe_bit1 -> [anonymous] is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u}} [_inst_1 : Semiring.{u} R] (f : PowerSeries.{u} R), Eq.{max 1 (succ u)} (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) ((fun (a : Sort.{max 1 (succ u)}) (b : Sort.{max 1 (succ u)}) [self : HasLiftT.{max 1 (succ u), max 1 (succ u)} a b] => self.0) (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (HasLiftT.mk.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (CoeTCₓ.coe.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (coeBase.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (LaurentSeries.hasCoe.{u} R _inst_1)))) (bit1.{u} (PowerSeries.{u} R) (AddMonoidWithOne.toOne.{u} (PowerSeries.{u} R) (AddCommMonoidWithOne.toAddMonoidWithOne.{u} (PowerSeries.{u} R) (NonAssocSemiring.toAddCommMonoidWithOne.{u} (PowerSeries.{u} R) (Semiring.toNonAssocSemiring.{u} (PowerSeries.{u} R) (PowerSeries.semiring.{u} R _inst_1))))) (Distrib.toHasAdd.{u} (PowerSeries.{u} R) (NonUnitalNonAssocSemiring.toDistrib.{u} (PowerSeries.{u} R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} (PowerSeries.{u} R) (Semiring.toNonAssocSemiring.{u} (PowerSeries.{u} R) (PowerSeries.semiring.{u} R _inst_1))))) f)) (bit1.{u} (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (HahnSeries.hasOne.{0, u} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1)))) (AddMonoidWithOne.toOne.{u} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u} R (NonAssocSemiring.toAddCommMonoidWithOne.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (HahnSeries.hasAdd.{0, u} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (AddMonoidWithOne.toAddMonoid.{u} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u} R (NonAssocSemiring.toAddCommMonoidWithOne.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) ((fun (a : Sort.{max 1 (succ u)}) (b : Sort.{max 1 (succ u)}) [self : HasLiftT.{max 1 (succ u), max 1 (succ u)} a b] => self.0) (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (HasLiftT.mk.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (CoeTCₓ.coe.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (coeBase.{max 1 (succ u), max 1 (succ u)} (PowerSeries.{u} R) (LaurentSeries.{u} R (MulZeroClass.toHasZero.{u} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} R (Semiring.toNonAssocSemiring.{u} R _inst_1))))) (LaurentSeries.hasCoe.{u} R _inst_1)))) f))
+but is expected to have type
+ forall {R : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> R -> _inst_1) -> Nat -> (List.{u} R) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align power_series.coe_bit1 [anonymous]ₓ'. -/
@[simp, norm_cast]
-theorem coe_bit1 : ((bit1 f : PowerSeries R) : LaurentSeries R) = bit1 f :=
+theorem [anonymous] : ((bit1 f : PowerSeries R) : LaurentSeries R) = bit1 f :=
(ofPowerSeries ℤ R).map_bit1 _
-#align power_series.coe_bit1 PowerSeries.coe_bit1
+#align power_series.coe_bit1 [anonymous]
/- warning: power_series.coe_pow -> PowerSeries.coe_pow is a dubious translation:
-lean 3 declaration is
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(HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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))))) f n)) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) f) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) f) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R 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Int Int.linearOrderedCommRing)))) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) f) n)
+<too large>
Case conversion may be inaccurate. Consider using '#align power_series.coe_pow PowerSeries.coe_powₓ'. -/
@[simp, norm_cast]
theorem coe_pow (n : ℕ) : ((f ^ n : PowerSeries R) : LaurentSeries R) = f ^ n :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
! This file was ported from Lean 3 source module ring_theory.laurent_series
-! leanprover-community/mathlib commit 831c494092374cfe9f50591ed0ac81a25efc5b86
+! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.Localization.FractionRing
/-!
# Laurent Series
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
## Main Definitions
* Defines `laurent_series` as an abbreviation for `hahn_series ℤ`.
* Provides a coercion `power_series R` into `laurent_series R` given by
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -33,10 +33,12 @@ noncomputable section
universe u
+#print LaurentSeries /-
/-- A `laurent_series` is implemented as a `hahn_series` with value group `ℤ`. -/
abbrev LaurentSeries (R : Type _) [Zero R] :=
HahnSeries ℤ R
#align laurent_series LaurentSeries
+-/
variable {R : Type u}
@@ -54,12 +56,24 @@ theorem coe_powerSeries (x : PowerSeries R) :
rfl
#align laurent_series.coe_power_series LaurentSeries.coe_powerSeries
+/- warning: laurent_series.coeff_coe_power_series -> LaurentSeries.coeff_coe_powerSeries is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : PowerSeries.{u1} R) (n : Nat), Eq.{succ u1} R (HahnSeries.coeff.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{u1} R _inst_1)))) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)) (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) x)
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : PowerSeries.{u1} R) (n : Nat), Eq.{succ u1} R (HahnSeries.coeff.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) x) (Nat.cast.{0} Int instNatCastInt 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) x)
+Case conversion may be inaccurate. Consider using '#align laurent_series.coeff_coe_power_series LaurentSeries.coeff_coe_powerSeriesₓ'. -/
@[simp]
theorem coeff_coe_powerSeries (x : PowerSeries R) (n : ℕ) :
HahnSeries.coeff (x : LaurentSeries R) n = PowerSeries.coeff R n x := by
rw [coe_power_series, of_power_series_apply_coeff]
#align laurent_series.coeff_coe_power_series LaurentSeries.coeff_coe_powerSeries
+/- warning: laurent_series.power_series_part -> LaurentSeries.powerSeriesPart is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> (PowerSeries.{u1} R)
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) -> (PowerSeries.{u1} R)
+Case conversion may be inaccurate. Consider using '#align laurent_series.power_series_part LaurentSeries.powerSeriesPartₓ'. -/
/-- This is a power series that can be multiplied by an integer power of `X` to give our
Laurent series. If the Laurent series is nonzero, `power_series_part` has a nonzero
constant term. -/
@@ -67,12 +81,24 @@ def powerSeriesPart (x : LaurentSeries R) : PowerSeries R :=
PowerSeries.mk fun n => x.coeff (x.order + n)
#align laurent_series.power_series_part LaurentSeries.powerSeriesPart
+/- warning: laurent_series.power_series_part_coeff -> LaurentSeries.powerSeriesPart_coeff is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (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) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x)) (HahnSeries.coeff.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) (HahnSeries.order.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) Int.hasZero x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)))
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x)) (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) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x)) (HahnSeries.coeff.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) x (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HahnSeries.order.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) x) (Nat.cast.{0} Int instNatCastInt n)))
+Case conversion may be inaccurate. Consider using '#align laurent_series.power_series_part_coeff LaurentSeries.powerSeriesPart_coeffₓ'. -/
@[simp]
theorem powerSeriesPart_coeff (x : LaurentSeries R) (n : ℕ) :
PowerSeries.coeff R n x.powerSeriesPart = x.coeff (x.order + n) :=
PowerSeries.coeff_mk _ _
#align laurent_series.power_series_part_coeff LaurentSeries.powerSeriesPart_coeff
+/- warning: laurent_series.power_series_part_zero -> LaurentSeries.powerSeriesPart_zero is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (PowerSeries.{u1} R) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 (OfNat.ofNat.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 0 (OfNat.mk.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 0 (Zero.zero.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.hasZero.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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], Eq.{succ u1} (PowerSeries.{u1} R) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 (OfNat.ofNat.{u1} (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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 laurent_series.power_series_part_zero LaurentSeries.powerSeriesPart_zeroₓ'. -/
@[simp]
theorem powerSeriesPart_zero : powerSeriesPart (0 : LaurentSeries R) = 0 :=
by
@@ -80,6 +106,12 @@ theorem powerSeriesPart_zero : powerSeriesPart (0 : LaurentSeries R) = 0 :=
simp
#align laurent_series.power_series_part_zero LaurentSeries.powerSeriesPart_zero
+/- warning: laurent_series.power_series_part_eq_zero -> LaurentSeries.powerSeriesPart_eq_zero is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))), Iff (Eq.{succ u1} (PowerSeries.{u1} R) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x) (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))))))))) (Eq.{succ u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x (OfNat.ofNat.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 0 (OfNat.mk.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 0 (Zero.zero.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.hasZero.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (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] (x : LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))), Iff (Eq.{succ u1} (PowerSeries.{u1} R) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x) (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)))))) (Eq.{succ u1} (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) x (OfNat.ofNat.{u1} (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align laurent_series.power_series_part_eq_zero LaurentSeries.powerSeriesPart_eq_zeroₓ'. -/
@[simp]
theorem powerSeriesPart_eq_zero (x : LaurentSeries R) : x.powerSeriesPart = 0 ↔ x = 0 :=
by
@@ -93,6 +125,12 @@ theorem powerSeriesPart_eq_zero (x : LaurentSeries R) : x.powerSeriesPart = 0
simp
#align laurent_series.power_series_part_eq_zero LaurentSeries.powerSeriesPart_eq_zero
+/- warning: laurent_series.single_order_mul_power_series_part -> LaurentSeries.single_order_mul_powerSeriesPart is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))), Eq.{succ u1} (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HMul.hMul.{u1, u1, u1} (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (instHMul.{u1} (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.hasMul.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HahnSeries.hasZero.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (_x : ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HahnSeries.hasZero.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => R -> (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (ZeroHom.hasCoeToFun.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HahnSeries.hasZero.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.single.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HahnSeries.order.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) Int.hasZero x)) (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)))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{u1} R _inst_1)))) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x))) x
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.124 : R) => HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.124 : R) => HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.124 : R) => HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.124 : R) => HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (HahnSeries.instMulHahnSeriesToPartialOrderToZeroToMulZeroClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.124 : R) => HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (ZeroHomClass.toFunLike.{u1, u1, u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) R (HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (ZeroHom.zeroHomClass.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (HahnSeries.single.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.order.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) x)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int 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(LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) 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(StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x))) x
+Case conversion may be inaccurate. Consider using '#align laurent_series.single_order_mul_power_series_part LaurentSeries.single_order_mul_powerSeriesPartₓ'. -/
@[simp]
theorem single_order_mul_powerSeriesPart (x : LaurentSeries R) :
(single x.order 1 : LaurentSeries R) * x.powerSeriesPart = x :=
@@ -114,6 +152,12 @@ theorem single_order_mul_powerSeriesPart (x : LaurentSeries R) :
exact Int.zero_le_ofNat _
#align laurent_series.single_order_mul_power_series_part LaurentSeries.single_order_mul_powerSeriesPart
+/- warning: laurent_series.of_power_series_power_series_part -> LaurentSeries.ofPowerSeries_powerSeriesPart is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))), Eq.{succ u1} (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (HahnSeries.nonAssocSemiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (HahnSeries.nonAssocSemiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) => (PowerSeries.{u1} R) -> (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.semiring.{u1} R _inst_1)) (HahnSeries.nonAssocSemiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x)) (HMul.hMul.{u1, u1, u1} (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (instHMul.{u1} (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.hasMul.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HahnSeries.hasZero.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (_x : ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HahnSeries.hasZero.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => R -> (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (ZeroHom.hasCoeToFun.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HahnSeries.hasZero.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.single.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Neg.neg.{0} Int Int.hasNeg (HahnSeries.order.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) Int.hasZero x))) (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)))))))) x)
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.124 : R) => HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (LaurentSeries.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (LaurentSeries.powerSeriesPart.{u1} R _inst_1 x)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.124 : R) => HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (HahnSeries.instMulHahnSeriesToPartialOrderToZeroToMulZeroClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.124 : R) => HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (ZeroHomClass.toFunLike.{u1, u1, u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) R (HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (ZeroHom.zeroHomClass.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (HahnSeries.single.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (Neg.neg.{0} Int Int.instNegInt (HahnSeries.order.{0, u1} Int R (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) x))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) x)
+Case conversion may be inaccurate. Consider using '#align laurent_series.of_power_series_power_series_part LaurentSeries.ofPowerSeries_powerSeriesPartₓ'. -/
theorem ofPowerSeries_powerSeriesPart (x : LaurentSeries R) :
ofPowerSeries ℤ R x.powerSeriesPart = single (-x.order) 1 * x :=
by
@@ -127,12 +171,24 @@ end Semiring
instance [CommSemiring R] : Algebra (PowerSeries R) (LaurentSeries R) :=
(HahnSeries.ofPowerSeries ℤ R).toAlgebra
+/- warning: laurent_series.coe_algebra_map -> LaurentSeries.coe_algebraMap is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R], Eq.{succ u1} ((PowerSeries.{u1} R) -> (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HahnSeries.semiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HahnSeries.semiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1)))) => (PowerSeries.{u1} R) -> (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HahnSeries.semiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1)))) (algebraMap.{u1, u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (PowerSeries.commSemiring.{u1} R _inst_1) (HahnSeries.semiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentSeries.algebra.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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))) (HahnSeries.nonAssocSemiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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))) (HahnSeries.nonAssocSemiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (PowerSeries.{u1} R) -> (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (RingHom.hasCoeToFun.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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))) (HahnSeries.nonAssocSemiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (HahnSeries.ofPowerSeries.{0, u1} Int R (CommSemiring.toSemiring.{u1} R _inst_1) (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R], Eq.{succ u1} (forall (ᾰ : PowerSeries.{u1} R), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instSemiringHahnSeriesToPartialOrderToZeroToMonoidWithZero.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instSemiringHahnSeriesToPartialOrderToZeroToMonoidWithZero.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (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.{u1} (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instSemiringHahnSeriesToPartialOrderToZeroToMonoidWithZero.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instSemiringHahnSeriesToPartialOrderToZeroToMonoidWithZero.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (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.{u1} (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instSemiringHahnSeriesToPartialOrderToZeroToMonoidWithZero.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instSemiringHahnSeriesToPartialOrderToZeroToMonoidWithZero.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instSemiringHahnSeriesToPartialOrderToZeroToMonoidWithZero.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (CommSemiring.toSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instSemiringHahnSeriesToPartialOrderToZeroToMonoidWithZero.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1))))))) (algebraMap.{u1, u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (PowerSeries.instCommSemiringPowerSeries.{u1} R _inst_1) (HahnSeries.instSemiringHahnSeriesToPartialOrderToZeroToMonoidWithZero.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentSeries.instAlgebraPowerSeriesLaurentSeriesToZeroToCommMonoidWithZeroInstCommSemiringPowerSeriesInstSemiringHahnSeriesToPartialOrderToZeroToMonoidWithZeroIntToOrderedCancelAddCommMonoidToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringLinearOrderedCommRingToSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (HahnSeries.ofPowerSeries.{0, u1} Int R (CommSemiring.toSemiring.{u1} R _inst_1) (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))
+Case conversion may be inaccurate. Consider using '#align laurent_series.coe_algebra_map LaurentSeries.coe_algebraMapₓ'. -/
@[simp]
theorem coe_algebraMap [CommSemiring R] :
⇑(algebraMap (PowerSeries R) (LaurentSeries R)) = HahnSeries.ofPowerSeries ℤ R :=
rfl
#align laurent_series.coe_algebra_map LaurentSeries.coe_algebraMap
+/- warning: laurent_series.of_power_series_localization -> LaurentSeries.of_powerSeries_localization is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], IsLocalization.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submonoid.powers.{u1} (PowerSeries.{u1} R) (Ring.toMonoid.{u1} (PowerSeries.{u1} R) (PowerSeries.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PowerSeries.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LaurentSeries.{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))))))) (HahnSeries.commSemiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (CommRing.toCommSemiring.{u1} R _inst_1)) (LaurentSeries.algebra.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], IsLocalization.{u1, u1} (PowerSeries.{u1} R) (PowerSeries.instCommSemiringPowerSeries.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submonoid.powers.{u1} (PowerSeries.{u1} R) (MonoidWithZero.toMonoid.{u1} (PowerSeries.{u1} R) (Semiring.toMonoidWithZero.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (PowerSeries.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LaurentSeries.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HahnSeries.instCommSemiringHahnSeriesToPartialOrderToZeroToCommMonoidWithZero.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (CommRing.toCommSemiring.{u1} R _inst_1)) (LaurentSeries.instAlgebraPowerSeriesLaurentSeriesToZeroToCommMonoidWithZeroInstCommSemiringPowerSeriesInstSemiringHahnSeriesToPartialOrderToZeroToMonoidWithZeroIntToOrderedCancelAddCommMonoidToStrictOrderedSemiringToLinearOrderedSemiringToLinearOrderedCommSemiringLinearOrderedCommRingToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))
+Case conversion may be inaccurate. Consider using '#align laurent_series.of_power_series_localization LaurentSeries.of_powerSeries_localizationₓ'. -/
/-- The localization map from power series to Laurent series. -/
@[simps]
instance of_powerSeries_localization [CommRing R] :
@@ -188,36 +244,78 @@ open LaurentSeries
variable {R' : Type _} [Semiring R] [Ring R'] (f g : PowerSeries R) (f' g' : PowerSeries R')
+/- warning: power_series.coe_zero -> PowerSeries.coe_zero is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{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))))))))) (OfNat.ofNat.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 0 (OfNat.mk.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 0 (Zero.zero.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.hasZero.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (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.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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)))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))))) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align power_series.coe_zero PowerSeries.coe_zeroₓ'. -/
@[simp, norm_cast]
theorem coe_zero : ((0 : PowerSeries R) : LaurentSeries R) = 0 :=
(ofPowerSeries ℤ R).map_zero
#align power_series.coe_zero PowerSeries.coe_zero
+/- warning: power_series.coe_one -> PowerSeries.coe_one is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{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.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 1 (OfNat.mk.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 1 (One.one.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.hasOne.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (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.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R 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(LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int 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Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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))))) (HahnSeries.instOneHahnSeriesToPartialOrder.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (Semiring.toOne.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align power_series.coe_one PowerSeries.coe_oneₓ'. -/
@[simp, norm_cast]
theorem coe_one : ((1 : PowerSeries R) : LaurentSeries R) = 1 :=
(ofPowerSeries ℤ R).map_one
#align power_series.coe_one PowerSeries.coe_one
+/- warning: power_series.coe_add -> PowerSeries.coe_add is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : PowerSeries.{u1} R) (g : PowerSeries.{u1} R), Eq.{succ u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{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)))))) f g)) (HAdd.hAdd.{u1, u1, u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (instHAdd.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.hasAdd.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{u1} R _inst_1)))) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{u1} R _inst_1)))) g))
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : PowerSeries.{u1} R) (g : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))))) f g)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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)))))) f g)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) f) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) f) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) f) (HahnSeries.instAddHahnSeriesToZero.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) 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R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) g))
+Case conversion may be inaccurate. Consider using '#align power_series.coe_add PowerSeries.coe_addₓ'. -/
@[simp, norm_cast]
theorem coe_add : ((f + g : PowerSeries R) : LaurentSeries R) = f + g :=
(ofPowerSeries ℤ R).map_add _ _
#align power_series.coe_add PowerSeries.coe_add
+/- warning: power_series.coe_sub -> PowerSeries.coe_sub is a dubious translation:
+lean 3 declaration is
+ forall {R' : Type.{u1}} [_inst_2 : Ring.{u1} R'] (f' : PowerSeries.{u1} R') (g' : PowerSeries.{u1} R'), Eq.{succ u1} (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (LaurentSeries.hasCoe.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))) (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_2))))))) f' g')) (HSub.hSub.{u1, u1, u1} (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (instHSub.{u1} (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (SubNegMonoid.toHasSub.{u1} (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (AddGroup.toSubNegMonoid.{u1} (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (HahnSeries.addGroup.{0, u1} Int R' (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (AddGroupWithOne.toAddGroup.{u1} R' (AddCommGroupWithOne.toAddGroupWithOne.{u1} R' (Ring.toAddCommGroupWithOne.{u1} R' _inst_2))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (LaurentSeries.hasCoe.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))) f') ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (LaurentSeries.hasCoe.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))) g'))
+but is expected to have type
+ forall {R' : Type.{u1}} [_inst_2 : Ring.{u1} R'] (f' : PowerSeries.{u1} R') (g' : PowerSeries.{u1} R'), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R') => HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (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' _inst_2))) f' g')) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (fun (a : PowerSeries.{u1} R') => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R') => HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (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_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R') (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))))) (HahnSeries.ofPowerSeries.{0, u1} Int R' (Ring.toSemiring.{u1} R' _inst_2) (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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' _inst_2))) f' g')) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R') => HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) f') ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R') => HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) g') ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R') => HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) f') (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R') => 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' 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(StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R') (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) 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R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))))) (HahnSeries.ofPowerSeries.{0, u1} Int R' (Ring.toSemiring.{u1} R' _inst_2) (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) f') (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int 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(PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) 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R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R') (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))))) (HahnSeries.ofPowerSeries.{0, u1} Int R' (Ring.toSemiring.{u1} R' _inst_2) (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) g'))
+Case conversion may be inaccurate. Consider using '#align power_series.coe_sub PowerSeries.coe_subₓ'. -/
@[simp, norm_cast]
theorem coe_sub : ((f' - g' : PowerSeries R') : LaurentSeries R') = f' - g' :=
(ofPowerSeries ℤ R').map_sub _ _
#align power_series.coe_sub PowerSeries.coe_sub
+/- warning: power_series.coe_neg -> PowerSeries.coe_neg is a dubious translation:
+lean 3 declaration is
+ forall {R' : Type.{u1}} [_inst_2 : Ring.{u1} R'] (f' : PowerSeries.{u1} R'), Eq.{succ u1} (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (LaurentSeries.hasCoe.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))) (Neg.neg.{u1} (PowerSeries.{u1} R') (SubNegMonoid.toHasNeg.{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_2)))))) f')) (Neg.neg.{u1} (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (SubNegMonoid.toHasNeg.{u1} (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (AddGroup.toSubNegMonoid.{u1} (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (HahnSeries.addGroup.{0, u1} Int R' (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (AddGroupWithOne.toAddGroup.{u1} R' (AddCommGroupWithOne.toAddGroupWithOne.{u1} R' (Ring.toAddCommGroupWithOne.{u1} R' _inst_2)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R') (LaurentSeries.{u1} R' (MulZeroClass.toHasZero.{u1} R' (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R' (NonAssocRing.toNonUnitalNonAssocRing.{u1} R' (Ring.toNonAssocRing.{u1} R' _inst_2)))))) (LaurentSeries.hasCoe.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))) f'))
+but is expected to have type
+ forall {R' : Type.{u1}} [_inst_2 : Ring.{u1} R'] (f' : PowerSeries.{u1} R'), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R') => HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Neg.neg.{u1} (PowerSeries.{u1} R') (Ring.toNeg.{u1} (PowerSeries.{u1} R') (PowerSeries.instRingPowerSeries.{u1} R' _inst_2)) f')) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (fun (a : PowerSeries.{u1} R') => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R') => HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int 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Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (fun (a : PowerSeries.{u1} R') => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R') => HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int 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(LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (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_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R') (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R') (HahnSeries.{0, u1} Int R' (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (Ring.toSemiring.{u1} R' _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R') (PowerSeries.instSemiringPowerSeries.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R' (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R' (Ring.toSemiring.{u1} R' _inst_2))))))) (HahnSeries.ofPowerSeries.{0, u1} Int R' (Ring.toSemiring.{u1} R' _inst_2) (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) f'))
+Case conversion may be inaccurate. Consider using '#align power_series.coe_neg PowerSeries.coe_negₓ'. -/
@[simp, norm_cast]
theorem coe_neg : ((-f' : PowerSeries R') : LaurentSeries R') = -f' :=
(ofPowerSeries ℤ R').map_neg _
#align power_series.coe_neg PowerSeries.coe_neg
+/- warning: power_series.coe_mul -> PowerSeries.coe_mul is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : PowerSeries.{u1} R) (g : PowerSeries.{u1} R), Eq.{succ u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{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)))))) f g)) (HMul.hMul.{u1, u1, u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (instHMul.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.hasMul.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{u1} R _inst_1)))) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{u1} R _inst_1)))) g))
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : PowerSeries.{u1} R) (g : PowerSeries.{u1} R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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))))) f g)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int 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R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) g))
+Case conversion may be inaccurate. Consider using '#align power_series.coe_mul PowerSeries.coe_mulₓ'. -/
@[simp, norm_cast]
theorem coe_mul : ((f * g : PowerSeries R) : LaurentSeries R) = f * g :=
(ofPowerSeries ℤ R).map_mul _ _
#align power_series.coe_mul PowerSeries.coe_mul
+/- warning: power_series.coeff_coe -> PowerSeries.coeff_coe is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : PowerSeries.{u1} R) (i : Int), Eq.{succ u1} R (HahnSeries.coeff.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{u1} R _inst_1)))) f) i) (ite.{succ u1} R (LT.lt.{0} Int Int.hasLt i (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (Int.decLt i (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (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))))))) (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 (Int.natAbs i)) f))
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : PowerSeries.{u1} R) (i : Int), Eq.{succ u1} R (HahnSeries.coeff.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) f) i) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) f) (LT.lt.{0} Int Int.instLTInt i (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (Int.decLt i (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) f) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) f) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) f) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : PowerSeries.{u1} R) => R) f) _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 (Int.natAbs i)) f))
+Case conversion may be inaccurate. Consider using '#align power_series.coeff_coe PowerSeries.coeff_coeₓ'. -/
theorem coeff_coe (i : ℤ) :
((f : PowerSeries R) : LaurentSeries R).coeff i =
if i < 0 then 0 else PowerSeries.coeff R i.natAbs f :=
@@ -233,16 +331,34 @@ theorem coeff_coe (i : ℤ) :
not_false_iff]
#align power_series.coeff_coe PowerSeries.coeff_coe
+/- warning: power_series.coe_C -> PowerSeries.coe_C is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{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) r)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (HahnSeries.nonAssocSemiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (HahnSeries.nonAssocSemiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) => R -> (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (RingHom.hasCoeToFun.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (HahnSeries.nonAssocSemiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (HahnSeries.C.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) r)
+but is expected to have type
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(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) 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Int.linearOrderedCommRing))))) (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedCancelAddCommMonoid.toPartialOrder.{0} Int (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.C.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) r)
+Case conversion may be inaccurate. Consider using '#align power_series.coe_C PowerSeries.coe_Cₓ'. -/
@[simp, norm_cast]
-theorem coe_c (r : R) : ((C R r : PowerSeries R) : LaurentSeries R) = HahnSeries.C r :=
+theorem coe_C (r : R) : ((C R r : PowerSeries R) : LaurentSeries R) = HahnSeries.C r :=
ofPowerSeries_C _
-#align power_series.coe_C PowerSeries.coe_c
-
+#align power_series.coe_C PowerSeries.coe_C
+
+/- warning: power_series.coe_X -> PowerSeries.coe_X is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{u1} R _inst_1)))) (PowerSeries.X.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HahnSeries.hasZero.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (_x : ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HahnSeries.hasZero.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => R -> (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (ZeroHom.hasCoeToFun.{u1, u1} R (HahnSeries.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HahnSeries.hasZero.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.single.{0, u1} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.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} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (PowerSeries.X.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (PowerSeries.X.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.124 : R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _x) (ZeroHomClass.toFunLike.{u1, u1, u1} (ZeroHom.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) R (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (ZeroHom.zeroHomClass.{u1, u1} R (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HahnSeries.instZeroHahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (HahnSeries.single.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (OfNat.ofNat.{0} Int 1 (instOfNatInt 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.coe_X PowerSeries.coe_Xₓ'. -/
@[simp]
-theorem coe_x : ((X : PowerSeries R) : LaurentSeries R) = single 1 1 :=
+theorem coe_X : ((X : PowerSeries R) : LaurentSeries R) = single 1 1 :=
ofPowerSeries_X
-#align power_series.coe_X PowerSeries.coe_x
-
+#align power_series.coe_X PowerSeries.coe_X
+
+/- warning: power_series.coe_smul -> PowerSeries.coe_smul is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_3 : Semiring.{u2} S] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3)))] (r : R) (x : PowerSeries.{u2} S), Eq.{succ u2} (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (PowerSeries.{u2} S) (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (HasLiftT.mk.{succ u2, succ u2} (PowerSeries.{u2} S) (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (CoeTCₓ.coe.{succ u2, succ u2} (PowerSeries.{u2} S) (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (coeBase.{succ u2, succ u2} (PowerSeries.{u2} S) (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (LaurentSeries.hasCoe.{u2} S _inst_3)))) (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_3))))))) (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_3))))))) (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_3))))))) (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_3)))) (PowerSeries.module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))) _inst_4))))) r x)) (SMul.smul.{u1, u2} R (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (HahnSeries.hasSmul.{0, u1, u2} Int R (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) S (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoidWithOne.toAddMonoid.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3)))) (Module.toDistribMulAction.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))) _inst_4)) r ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (PowerSeries.{u2} S) (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (HasLiftT.mk.{succ u2, succ u2} (PowerSeries.{u2} S) (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (CoeTCₓ.coe.{succ u2, succ u2} (PowerSeries.{u2} S) (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (coeBase.{succ u2, succ u2} (PowerSeries.{u2} S) (LaurentSeries.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_3))))) (LaurentSeries.hasCoe.{u2} S _inst_3)))) x))
+but is expected to have type
+ forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {S : Type.{u1}} [_inst_3 : Semiring.{u1} S] [_inst_4 : Module.{u2, u1} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_3)))] (r : R) (x : PowerSeries.{u1} S), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} S) => HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (HSMul.hSMul.{u2, u1, u1} R (PowerSeries.{u1} S) (PowerSeries.{u1} S) (instHSMul.{u2, u1} R (PowerSeries.{u1} S) (SMulZeroClass.toSMul.{u2, u1} R (PowerSeries.{u1} S) (PowerSeries.instZeroPowerSeries.{u1} S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (SMulWithZero.toSMulZeroClass.{u2, u1} R (PowerSeries.{u1} S) (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (PowerSeries.instZeroPowerSeries.{u1} S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} R (PowerSeries.{u1} S) (Semiring.toMonoidWithZero.{u2} R _inst_1) (PowerSeries.instZeroPowerSeries.{u1} S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Module.toMulActionWithZero.{u2, u1} R (PowerSeries.{u1} S) _inst_1 (PowerSeries.instAddCommMonoidPowerSeries.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_3)))) (PowerSeries.instModulePowerSeriesInstAddCommMonoidPowerSeries.{u2, u1} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_3))) _inst_4)))))) r x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3))) (PowerSeries.{u1} S) (fun (a : PowerSeries.{u1} S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} S) => HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3))) (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S 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S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3)))))) (HahnSeries.ofPowerSeries.{0, u1} Int S _inst_3 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (HSMul.hSMul.{u2, u1, u1} R (PowerSeries.{u1} S) (PowerSeries.{u1} S) (instHSMul.{u2, u1} R (PowerSeries.{u1} S) (SMulZeroClass.toSMul.{u2, u1} R (PowerSeries.{u1} S) (PowerSeries.instZeroPowerSeries.{u1} S 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_3))) _inst_4)))))) r x)) (HSMul.hSMul.{u2, u1, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} S) => HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} S) => HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) x) (instHSMul.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} S) => HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) x) (HahnSeries.instSMulHahnSeriesToZero.{0, u2, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoidWithOne.toAddMonoid.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_3)))) (Module.toDistribMulAction.{u2, u1} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_3))) _inst_4))) r (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3))) (PowerSeries.{u1} S) (fun (a : PowerSeries.{u1} S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} S) => HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3))) (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} (PowerSeries.{u1} S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3))) (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} S) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3))) (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} S) (HahnSeries.{0, u1} Int S (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_3))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} S) (PowerSeries.instSemiringPowerSeries.{u1} S _inst_3)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int S (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} S _inst_3)))))) (HahnSeries.ofPowerSeries.{0, u1} Int S _inst_3 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) x))
+Case conversion may be inaccurate. Consider using '#align power_series.coe_smul PowerSeries.coe_smulₓ'. -/
@[simp, norm_cast]
theorem coe_smul {S : Type _} [Semiring S] [Module R S] (r : R) (x : PowerSeries S) :
((r • x : PowerSeries S) : LaurentSeries S) = r • x :=
@@ -261,6 +377,12 @@ theorem coe_bit1 : ((bit1 f : PowerSeries R) : LaurentSeries R) = bit1 f :=
(ofPowerSeries ℤ R).map_bit1 _
#align power_series.coe_bit1 PowerSeries.coe_bit1
+/- warning: power_series.coe_pow -> PowerSeries.coe_pow is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : PowerSeries.{u1} R) (n : Nat), Eq.{succ u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{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))))) f n)) (HPow.hPow.{u1, 0, u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) Nat (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (instHPow.{u1, 0} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) Nat (Monoid.Pow.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Semiring.toMonoidWithZero.{u1} (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HahnSeries.semiring.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) _inst_1))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (CoeTCₓ.coe.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeBase.{succ u1, succ u1} (PowerSeries.{u1} R) (LaurentSeries.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (LaurentSeries.hasCoe.{u1} R _inst_1)))) f) n)
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : PowerSeries.{u1} R) (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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))))) f n)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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))))) f n)) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) f) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) f) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) f) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) f) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) f) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : PowerSeries.{u1} R) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) f) (HahnSeries.instSemiringHahnSeriesToPartialOrderToZeroToMonoidWithZero.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (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) => HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (PowerSeries.{u1} R) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (PowerSeries.{u1} R) (HahnSeries.{0, u1} Int R (StrictOrderedSemiring.toPartialOrder.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (PowerSeries.{u1} R) (PowerSeries.instSemiringPowerSeries.{u1} R _inst_1)) (HahnSeries.instNonAssocSemiringHahnSeriesToPartialOrderToZeroToMulZeroOneClass.{0, u1} Int R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (HahnSeries.ofPowerSeries.{0, u1} Int R _inst_1 (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))) f) n)
+Case conversion may be inaccurate. Consider using '#align power_series.coe_pow PowerSeries.coe_powₓ'. -/
@[simp, norm_cast]
theorem coe_pow (n : ℕ) : ((f ^ n : PowerSeries R) : LaurentSeries R) = f ^ n :=
(ofPowerSeries ℤ R).map_pow _ _
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -234,13 +234,13 @@ theorem coeff_coe (i : ℤ) :
#align power_series.coeff_coe PowerSeries.coeff_coe
@[simp, norm_cast]
-theorem coe_c (r : R) : ((C R r : PowerSeries R) : LaurentSeries R) = HahnSeries.c r :=
- ofPowerSeries_c _
+theorem coe_c (r : R) : ((C R r : PowerSeries R) : LaurentSeries R) = HahnSeries.C r :=
+ ofPowerSeries_C _
#align power_series.coe_C PowerSeries.coe_c
@[simp]
theorem coe_x : ((X : PowerSeries R) : LaurentSeries R) = single 1 1 :=
- ofPowerSeries_x
+ ofPowerSeries_X
#align power_series.coe_X PowerSeries.coe_x
@[simp, norm_cast]
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -136,7 +136,7 @@ theorem coe_algebraMap [CommSemiring R] :
/-- The localization map from power series to Laurent series. -/
@[simps]
instance of_powerSeries_localization [CommRing R] :
- IsLocalization (Submonoid.powers (PowerSeries.x : PowerSeries R)) (LaurentSeries R)
+ IsLocalization (Submonoid.powers (PowerSeries.X : PowerSeries R)) (LaurentSeries R)
where
map_units := by
rintro ⟨_, n, rfl⟩
@@ -149,11 +149,11 @@ instance of_powerSeries_localization [CommRing R] :
surj := by
intro z
by_cases h : 0 ≤ z.order
- · refine' ⟨⟨PowerSeries.x ^ Int.natAbs z.order * power_series_part z, 1⟩, _⟩
+ · refine' ⟨⟨PowerSeries.X ^ Int.natAbs z.order * power_series_part z, 1⟩, _⟩
simp only [RingHom.map_one, mul_one, RingHom.map_mul, coe_algebra_map, of_power_series_X_pow,
Submonoid.coe_one]
rw [Int.natAbs_of_nonneg h, ← coe_power_series, single_order_mul_power_series_part]
- · refine' ⟨⟨power_series_part z, PowerSeries.x ^ Int.natAbs z.order, ⟨_, rfl⟩⟩, _⟩
+ · refine' ⟨⟨power_series_part z, PowerSeries.X ^ Int.natAbs z.order, ⟨_, rfl⟩⟩, _⟩
simp only [coe_algebra_map, of_power_series_power_series_part]
rw [mul_comm _ z]
refine' congr rfl _
@@ -170,14 +170,14 @@ instance of_powerSeries_localization [CommRing R] :
rw [← sub_eq_zero, PowerSeries.ext_iff]
intro m
have h := hc (m + n)
- rwa [LinearMap.map_zero, Subtype.coe_mk, PowerSeries.x_pow_eq, PowerSeries.monomial,
+ rwa [LinearMap.map_zero, Subtype.coe_mk, PowerSeries.X_pow_eq, PowerSeries.monomial,
add_comm m, PowerSeries.coeff, Finsupp.single_add, MvPowerSeries.coeff_add_monomial_mul,
one_mul] at h
#align laurent_series.of_power_series_localization LaurentSeries.of_powerSeries_localization
instance {K : Type u} [Field K] : IsFractionRing (PowerSeries K) (LaurentSeries K) :=
- IsLocalization.of_le (Submonoid.powers (PowerSeries.x : PowerSeries K)) _
- (powers_le_nonZeroDivisors_of_noZeroDivisors PowerSeries.x_ne_zero) fun f hf =>
+ IsLocalization.of_le (Submonoid.powers (PowerSeries.X : PowerSeries K)) _
+ (powers_le_nonZeroDivisors_of_noZeroDivisors PowerSeries.X_ne_zero) fun f hf =>
isUnit_of_mem_nonZeroDivisors <| map_mem_nonZeroDivisors _ HahnSeries.ofPowerSeries_injective hf
end LaurentSeries
@@ -234,12 +234,12 @@ theorem coeff_coe (i : ℤ) :
#align power_series.coeff_coe PowerSeries.coeff_coe
@[simp, norm_cast]
-theorem coe_c (r : R) : ((c R r : PowerSeries R) : LaurentSeries R) = HahnSeries.c r :=
+theorem coe_c (r : R) : ((C R r : PowerSeries R) : LaurentSeries R) = HahnSeries.c r :=
ofPowerSeries_c _
#align power_series.coe_C PowerSeries.coe_c
@[simp]
-theorem coe_x : ((x : PowerSeries R) : LaurentSeries R) = single 1 1 :=
+theorem coe_x : ((X : PowerSeries R) : LaurentSeries R) = single 1 1 :=
ofPowerSeries_x
#align power_series.coe_X PowerSeries.coe_x
mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba
@@ -108,7 +108,7 @@ theorem single_order_mul_powerSeriesPart (x : LaurentSeries R) :
· contrapose! h
exact order_le_of_coeff_ne_zero h.symm
· contrapose! h
- simp only [Set.mem_range, RelEmbedding.coeFn_mk, Function.Embedding.coeFn_mk] at h
+ simp only [Set.mem_range, RelEmbedding.coe_mk, Function.Embedding.coeFn_mk] at h
obtain ⟨m, hm⟩ := h
rw [← sub_nonneg, ← hm]
exact Int.zero_le_ofNat _
@@ -228,9 +228,9 @@ theorem coeff_coe (i : ℤ) :
if_neg (Int.coe_nat_nonneg _).not_lt]
· rw [coe_power_series, of_power_series_apply, emb_domain_notin_image_support,
if_pos (Int.negSucc_lt_zero _)]
- simp only [not_exists, RelEmbedding.coeFn_mk, Set.mem_image, not_and,
- Function.Embedding.coeFn_mk, Ne.def, to_power_series_symm_apply_coeff, mem_support,
- Int.coe_nat_eq, imp_true_iff, not_false_iff]
+ simp only [not_exists, RelEmbedding.coe_mk, Set.mem_image, not_and, Function.Embedding.coeFn_mk,
+ Ne.def, to_power_series_symm_apply_coeff, mem_support, Int.coe_nat_eq, imp_true_iff,
+ not_false_iff]
#align power_series.coeff_coe PowerSeries.coeff_coe
@[simp, norm_cast]
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -51,8 +51,8 @@ def hasseDeriv (R : Type*) {V : Type*} [AddCommGroup V] [Semiring R] [Module R V
(forallLTEqZero_supp_BddBelow _ (f.order - k : ℤ)
(fun _ h_lt ↦ by rw [coeff_eq_zero_of_lt_order <| lt_sub_iff_add_lt.mp h_lt, smul_zero]))
map_add' f g := by
+ ext
simp only [ofSuppBddBelow, add_coeff', Pi.add_apply, smul_add]
- exact rfl
map_smul' r f := by
ext
simp only [ofSuppBddBelow, smul_coeff, RingHom.id_apply, smul_comm r]
This PR defines Hasse derivatives of formal Laurent series using integer binomial coefficients, and proves some basic properties.
@@ -3,9 +3,10 @@ Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
+import Mathlib.Data.Int.Interval
+import Mathlib.RingTheory.Binomial
import Mathlib.RingTheory.HahnSeries.PowerSeries
import Mathlib.RingTheory.HahnSeries.Summable
-import Mathlib.RingTheory.Localization.FractionRing
#align_import ring_theory.laurent_series from "leanprover-community/mathlib"@"831c494092374cfe9f50591ed0ac81a25efc5b86"
@@ -14,12 +15,16 @@ import Mathlib.RingTheory.Localization.FractionRing
## Main Definitions
* Defines `LaurentSeries` as an abbreviation for `HahnSeries ℤ`.
+* Defines `hasseDeriv` of a Laurent series with coefficients in a module over a ring.
* Provides a coercion `PowerSeries R` into `LaurentSeries R` given by
`HahnSeries.ofPowerSeries`.
* Defines `LaurentSeries.powerSeriesPart`
* Defines the localization map `LaurentSeries.of_powerSeries_localization` which evaluates to
`HahnSeries.ofPowerSeries`.
+## Main Results
+* Basic properties of Hasse derivatives
+
-/
open scoped Classical
@@ -27,8 +32,6 @@ open HahnSeries BigOperators Polynomial
noncomputable section
-universe u
-
/-- A `LaurentSeries` is implemented as a `HahnSeries` with value group `ℤ`. -/
abbrev LaurentSeries (R : Type*) [Zero R] :=
HahnSeries ℤ R
@@ -38,6 +41,30 @@ variable {R : Type*}
namespace LaurentSeries
+section HasseDeriv
+
+/-- The Hasse derivative of Laurent series, as a linear map. -/
+@[simps]
+def hasseDeriv (R : Type*) {V : Type*} [AddCommGroup V] [Semiring R] [Module R V] (k : ℕ) :
+ LaurentSeries V →ₗ[R] LaurentSeries V where
+ toFun f := HahnSeries.ofSuppBddBelow (fun (n : ℤ) => (Ring.choose (n + k) k) • f.coeff (n + k))
+ (forallLTEqZero_supp_BddBelow _ (f.order - k : ℤ)
+ (fun _ h_lt ↦ by rw [coeff_eq_zero_of_lt_order <| lt_sub_iff_add_lt.mp h_lt, smul_zero]))
+ map_add' f g := by
+ simp only [ofSuppBddBelow, add_coeff', Pi.add_apply, smul_add]
+ exact rfl
+ map_smul' r f := by
+ ext
+ simp only [ofSuppBddBelow, smul_coeff, RingHom.id_apply, smul_comm r]
+
+variable [Semiring R] {V : Type*} [AddCommGroup V] [Module R V]
+
+theorem hasseDeriv_coeff (k : ℕ) (f : LaurentSeries V) (n : ℤ) :
+ (hasseDeriv R k f).coeff n = Ring.choose (n + k) k • f.coeff (n + k) :=
+ rfl
+
+end HasseDeriv
+
section Semiring
variable [Semiring R]
@@ -155,9 +182,7 @@ instance of_powerSeries_localization [CommRing R] :
exact ⟨1, rfl⟩
#align laurent_series.of_power_series_localization LaurentSeries.of_powerSeries_localization
--- Porting note: this instance is needed
-local instance {K : Type u} [Field K] : MonoidWithZero (HahnSeries ℤ K) := inferInstance in
-instance {K : Type u} [Field K] : IsFractionRing (PowerSeries K) (LaurentSeries K) :=
+instance {K : Type*} [Field K] : IsFractionRing (PowerSeries K) (LaurentSeries K) :=
IsLocalization.of_le (Submonoid.powers (PowerSeries.X : PowerSeries K)) _
(powers_le_nonZeroDivisors_of_noZeroDivisors PowerSeries.X_ne_zero) fun _ hf =>
isUnit_of_mem_nonZeroDivisors <| map_mem_nonZeroDivisors _ HahnSeries.ofPowerSeries_injective hf
@@ -236,7 +261,7 @@ theorem coe_smul {S : Type*} [Semiring S] [Module R S] (r : R) (x : PowerSeries
#noalign power_series.coe_bit0
#noalign power_series.coe_bit1
-@[simp, norm_cast]
+@[norm_cast]
theorem coe_pow (n : ℕ) : ((f ^ n : PowerSeries R) : LaurentSeries R) = (ofPowerSeries ℤ R f) ^ n :=
(ofPowerSeries ℤ R).map_pow _ _
#align power_series.coe_pow PowerSeries.coe_pow
coe_nat
to natCast
(#11637)
Reduce the diff of #11499
All in the Int
namespace:
ofNat_eq_cast
→ ofNat_eq_natCast
cast_eq_cast_iff_Nat
→ natCast_inj
natCast_eq_ofNat
→ ofNat_eq_natCast
coe_nat_sub
→ natCast_sub
coe_nat_nonneg
→ natCast_nonneg
sign_coe_add_one
→ sign_natCast_add_one
nat_succ_eq_int_succ
→ natCast_succ
succ_neg_nat_succ
→ succ_neg_natCast_succ
coe_pred_of_pos
→ natCast_pred_of_pos
coe_nat_div
→ natCast_div
coe_nat_ediv
→ natCast_ediv
sign_coe_nat_of_nonzero
→ sign_natCast_of_ne_zero
toNat_coe_nat
→ toNat_natCast
toNat_coe_nat_add_one
→ toNat_natCast_add_one
coe_nat_dvd
→ natCast_dvd_natCast
coe_nat_dvd_left
→ natCast_dvd
coe_nat_dvd_right
→ dvd_natCast
le_coe_nat_sub
→ le_natCast_sub
succ_coe_nat_pos
→ succ_natCast_pos
coe_nat_modEq_iff
→ natCast_modEq_iff
coe_natAbs
→ natCast_natAbs
coe_nat_eq_zero
→ natCast_eq_zero
coe_nat_ne_zero
→ natCast_ne_zero
coe_nat_ne_zero_iff_pos
→ natCast_ne_zero_iff_pos
abs_coe_nat
→ abs_natCast
coe_nat_nonpos_iff
→ natCast_nonpos_iff
Also rename Nat.coe_nat_dvd
to Nat.cast_dvd_cast
@@ -204,7 +204,7 @@ theorem coeff_coe (i : ℤ) :
((f : PowerSeries R) : LaurentSeries R).coeff i =
if i < 0 then 0 else PowerSeries.coeff R i.natAbs f := by
cases i
- · rw [Int.ofNat_eq_coe, coeff_coe_powerSeries, if_neg (Int.coe_nat_nonneg _).not_lt,
+ · rw [Int.ofNat_eq_coe, coeff_coe_powerSeries, if_neg (Int.natCast_nonneg _).not_lt,
Int.natAbs_ofNat]
· rw [ofPowerSeries_apply, embDomain_notin_image_support, if_pos (Int.negSucc_lt_zero _)]
simp only [not_exists, RelEmbedding.coe_mk, Set.mem_image, not_and, Function.Embedding.coeFn_mk,
@@ -208,7 +208,7 @@ theorem coeff_coe (i : ℤ) :
Int.natAbs_ofNat]
· rw [ofPowerSeries_apply, embDomain_notin_image_support, if_pos (Int.negSucc_lt_zero _)]
simp only [not_exists, RelEmbedding.coe_mk, Set.mem_image, not_and, Function.Embedding.coeFn_mk,
- Ne.def, toPowerSeries_symm_apply_coeff, mem_support, imp_true_iff,
+ Ne, toPowerSeries_symm_apply_coeff, mem_support, imp_true_iff,
not_false_iff]
#align power_series.coeff_coe PowerSeries.coeff_coe
mul
-div
cancellation lemmas (#11530)
Lemma names around cancellation of multiplication and division are a mess.
This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero
lemma name, the Group
lemma, the AddGroup
lemma name).
| Statement | New name | Old name | |
@@ -97,7 +97,7 @@ theorem single_order_mul_powerSeriesPart (x : LaurentSeries R) :
by_cases h : x.order ≤ n
· rw [Int.eq_natAbs_of_zero_le (sub_nonneg_of_le h), coeff_coe_powerSeries,
powerSeriesPart_coeff, ← Int.eq_natAbs_of_zero_le (sub_nonneg_of_le h),
- add_sub_cancel'_right]
+ add_sub_cancel]
· rw [ofPowerSeries_apply, embDomain_notin_range]
· contrapose! h
exact order_le_of_coeff_ne_zero h.symm
Given a locally finite linearly ordered set Γ
and a function f
on Γ
whose support is bounded below, we produce a Hahn series whose coefficients are given by f
. We introduce a theorem (borrowing from mathlib3 #18604) for translating the vanishing condition to the partially well-ordered support condition that is used in the definition of Hahn Series.
@@ -22,7 +22,6 @@ import Mathlib.RingTheory.Localization.FractionRing
-/
-
open scoped Classical
open HahnSeries BigOperators Polynomial
@@ -35,7 +34,7 @@ abbrev LaurentSeries (R : Type*) [Zero R] :=
HahnSeries ℤ R
#align laurent_series LaurentSeries
-variable {R : Type u}
+variable {R : Type*}
namespace LaurentSeries
open Classical
(#11199)
We remove all but one open Classical
s, instead preferring to use open scoped Classical
. The only real side-effect this led to is moving a couple declarations to use Exists.choose
instead of Classical.choose
.
The first few commits are explicitly labelled regex replaces for ease of review.
@@ -23,7 +23,8 @@ import Mathlib.RingTheory.Localization.FractionRing
-/
-open HahnSeries BigOperators Classical Polynomial
+open scoped Classical
+open HahnSeries BigOperators Polynomial
noncomputable section
@@ -170,17 +170,17 @@ open LaurentSeries
variable {R' : Type*} [Semiring R] [Ring R'] (f g : PowerSeries R) (f' g' : PowerSeries R')
-@[norm_cast] -- Porting note: simp can prove this
+@[norm_cast] -- Porting note (#10618): simp can prove this
theorem coe_zero : ((0 : PowerSeries R) : LaurentSeries R) = 0 :=
(ofPowerSeries ℤ R).map_zero
#align power_series.coe_zero PowerSeries.coe_zero
-@[norm_cast] -- Porting note: simp can prove this
+@[norm_cast] -- Porting note (#10618): simp can prove this
theorem coe_one : ((1 : PowerSeries R) : LaurentSeries R) = 1 :=
(ofPowerSeries ℤ R).map_one
#align power_series.coe_one PowerSeries.coe_one
-@[norm_cast] -- Porting note: simp can prove this
+@[norm_cast] -- Porting note (#10618): simp can prove this
theorem coe_add : ((f + g : PowerSeries R) : LaurentSeries R) = f + g :=
(ofPowerSeries ℤ R).map_add _ _
#align power_series.coe_add PowerSeries.coe_add
@@ -195,7 +195,7 @@ theorem coe_neg : ((-f' : PowerSeries R') : LaurentSeries R') = -f' :=
(ofPowerSeries ℤ R').map_neg _
#align power_series.coe_neg PowerSeries.coe_neg
-@[norm_cast] -- Porting note: simp can prove this
+@[norm_cast] -- Porting note (#10618): simp can prove this
theorem coe_mul : ((f * g : PowerSeries R) : LaurentSeries R) = f * g :=
(ofPowerSeries ℤ R).map_mul _ _
#align power_series.coe_mul PowerSeries.coe_mul
@@ -212,13 +212,14 @@ theorem coeff_coe (i : ℤ) :
not_false_iff]
#align power_series.coeff_coe PowerSeries.coeff_coe
--- Porting note: simp can prove this, and removed norm_cast attribute
+-- Porting note (#10618): simp can prove this
+-- Porting note: removed norm_cast attribute
theorem coe_C (r : R) : ((C R r : PowerSeries R) : LaurentSeries R) = HahnSeries.C r :=
ofPowerSeries_C _
set_option linter.uppercaseLean3 false in
#align power_series.coe_C PowerSeries.coe_C
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
theorem coe_X : ((X : PowerSeries R) : LaurentSeries R) = single 1 1 :=
ofPowerSeries_X
set_option linter.uppercaseLean3 false in
The HahnSeries file is approaching 2000 lines, and I was hoping to add some more material on Hahn series in the near future. This PR splits the material roughly according to what structure we see in the coefficients: Basic
assumes that the coefficient type R
has zero, Addition
assumes addition, Multiplication
more or less assumes some multiplicative structure.
@@ -3,7 +3,8 @@ Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
-import Mathlib.RingTheory.HahnSeries
+import Mathlib.RingTheory.HahnSeries.PowerSeries
+import Mathlib.RingTheory.HahnSeries.Summable
import Mathlib.RingTheory.Localization.FractionRing
#align_import ring_theory.laurent_series from "leanprover-community/mathlib"@"831c494092374cfe9f50591ed0ac81a25efc5b86"
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.
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]
.
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_param
s, [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 sometimesThis 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.
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 outParam
s 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.)
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>
@@ -72,7 +72,7 @@ theorem powerSeriesPart_coeff (x : LaurentSeries R) (n : ℕ) :
@[simp]
theorem powerSeriesPart_zero : powerSeriesPart (0 : LaurentSeries R) = 0 := by
ext
- simp
+ simp [(PowerSeries.coeff _ _).map_zero] -- Note: this doesn't get picked up any more
#align laurent_series.power_series_part_zero LaurentSeries.powerSeriesPart_zero
@[simp]
@@ -184,12 +184,12 @@ theorem coe_add : ((f + g : PowerSeries R) : LaurentSeries R) = f + g :=
(ofPowerSeries ℤ R).map_add _ _
#align power_series.coe_add PowerSeries.coe_add
-@[simp, norm_cast]
+@[norm_cast]
theorem coe_sub : ((f' - g' : PowerSeries R') : LaurentSeries R') = f' - g' :=
(ofPowerSeries ℤ R').map_sub _ _
#align power_series.coe_sub PowerSeries.coe_sub
-@[simp, norm_cast]
+@[norm_cast]
theorem coe_neg : ((-f' : PowerSeries R') : LaurentSeries R') = -f' :=
(ofPowerSeries ℤ R').map_neg _
#align power_series.coe_neg PowerSeries.coe_neg
The other direction is a consequence of IsLocalization.map_units
.
Also do the same for LocalizationMap
and IsLocalizedModule
.
This means we have one less fact to prove when constructing an IsLocalization
(etc.) instance (thus many proofs are golfed), but once we construct it we still have access to the eq_iff_exists
lemmas (without the prime) so the API doesn't get less powerful.
Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>
@@ -136,8 +136,7 @@ instance of_powerSeries_localization [CommRing R] :
· simp only [single_mul_single, mul_one, add_left_neg]
rfl
· dsimp; rw [ofPowerSeries_X_pow]
- surj' := by
- intro z
+ surj' z := by
by_cases h : 0 ≤ z.order
· refine' ⟨⟨PowerSeries.X ^ Int.natAbs z.order * powerSeriesPart z, 1⟩, _⟩
simp only [RingHom.map_one, mul_one, RingHom.map_mul, coe_algebraMap, ofPowerSeries_X_pow,
@@ -149,23 +148,10 @@ instance of_powerSeries_localization [CommRing R] :
refine' congr rfl _
rw [ofPowerSeries_X_pow, Int.ofNat_natAbs_of_nonpos]
exact le_of_not_ge h
- eq_iff_exists' := by
- intro x y
+ exists_of_eq {x y} := by
rw [coe_algebraMap, ofPowerSeries_injective.eq_iff]
- constructor
- · rintro rfl
- exact ⟨1, rfl⟩
- · rintro ⟨⟨_, n, rfl⟩, hc⟩
- rw [← sub_eq_zero, ← mul_sub, PowerSeries.ext_iff] at hc
- rw [← sub_eq_zero, PowerSeries.ext_iff]
- intro m
- have h := hc (m + n)
- simp only at h
- -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
- erw [LinearMap.map_zero, PowerSeries.X_pow_eq, PowerSeries.monomial,
- add_comm m, PowerSeries.coeff, Finsupp.single_add, MvPowerSeries.coeff_add_monomial_mul,
- one_mul] at h
- assumption
+ rintro rfl
+ exact ⟨1, rfl⟩
#align laurent_series.of_power_series_localization LaurentSeries.of_powerSeries_localization
-- Porting note: this instance is needed
@@ -135,7 +135,7 @@ instance of_powerSeries_localization [CommRing R] :
rfl
· simp only [single_mul_single, mul_one, add_left_neg]
rfl
- · simp
+ · dsimp; rw [ofPowerSeries_X_pow]
surj' := by
intro z
by_cases h : 0 ≤ z.order
@@ -161,9 +161,11 @@ instance of_powerSeries_localization [CommRing R] :
intro m
have h := hc (m + n)
simp only at h
- rwa [LinearMap.map_zero, PowerSeries.X_pow_eq, PowerSeries.monomial,
+ -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+ erw [LinearMap.map_zero, PowerSeries.X_pow_eq, PowerSeries.monomial,
add_comm m, PowerSeries.coeff, Finsupp.single_add, MvPowerSeries.coeff_add_monomial_mul,
one_mul] at h
+ assumption
#align laurent_series.of_power_series_localization LaurentSeries.of_powerSeries_localization
-- Porting note: this instance is needed
@@ -161,11 +161,9 @@ instance of_powerSeries_localization [CommRing R] :
intro m
have h := hc (m + n)
simp only at h
- -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
- erw [LinearMap.map_zero, PowerSeries.X_pow_eq, PowerSeries.monomial,
+ rwa [LinearMap.map_zero, PowerSeries.X_pow_eq, PowerSeries.monomial,
add_comm m, PowerSeries.coeff, Finsupp.single_add, MvPowerSeries.coeff_add_monomial_mul,
one_mul] at h
- assumption
#align laurent_series.of_power_series_localization LaurentSeries.of_powerSeries_localization
-- Porting note: this instance is needed
@@ -161,9 +161,11 @@ instance of_powerSeries_localization [CommRing R] :
intro m
have h := hc (m + n)
simp only at h
- rwa [LinearMap.map_zero, PowerSeries.X_pow_eq, PowerSeries.monomial,
+ -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+ erw [LinearMap.map_zero, PowerSeries.X_pow_eq, PowerSeries.monomial,
add_comm m, PowerSeries.coeff, Finsupp.single_add, MvPowerSeries.coeff_add_monomial_mul,
one_mul] at h
+ assumption
#align laurent_series.of_power_series_localization LaurentSeries.of_powerSeries_localization
-- Porting note: this instance is needed
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -29,7 +29,7 @@ noncomputable section
universe u
/-- A `LaurentSeries` is implemented as a `HahnSeries` with value group `ℤ`. -/
-abbrev LaurentSeries (R : Type _) [Zero R] :=
+abbrev LaurentSeries (R : Type*) [Zero R] :=
HahnSeries ℤ R
#align laurent_series LaurentSeries
@@ -179,7 +179,7 @@ namespace PowerSeries
open LaurentSeries
-variable {R' : Type _} [Semiring R] [Ring R'] (f g : PowerSeries R) (f' g' : PowerSeries R')
+variable {R' : Type*} [Semiring R] [Ring R'] (f g : PowerSeries R) (f' g' : PowerSeries R')
@[norm_cast] -- Porting note: simp can prove this
theorem coe_zero : ((0 : PowerSeries R) : LaurentSeries R) = 0 :=
@@ -236,7 +236,7 @@ set_option linter.uppercaseLean3 false in
#align power_series.coe_X PowerSeries.coe_X
@[simp, norm_cast]
-theorem coe_smul {S : Type _} [Semiring S] [Module R S] (r : R) (x : PowerSeries S) :
+theorem coe_smul {S : Type*} [Semiring S] [Module R S] (r : R) (x : PowerSeries S) :
((r • x : PowerSeries S) : LaurentSeries S) = r • (ofPowerSeries ℤ S x) := by
ext
simp [coeff_coe, coeff_smul, smul_ite]
@@ -2,15 +2,12 @@
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module ring_theory.laurent_series
-! leanprover-community/mathlib commit 831c494092374cfe9f50591ed0ac81a25efc5b86
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.RingTheory.HahnSeries
import Mathlib.RingTheory.Localization.FractionRing
+#align_import ring_theory.laurent_series from "leanprover-community/mathlib"@"831c494092374cfe9f50591ed0ac81a25efc5b86"
+
/-!
# Laurent Series
Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>
@@ -128,7 +128,7 @@ theorem coe_algebraMap [CommSemiring R] :
#align laurent_series.coe_algebra_map LaurentSeries.coe_algebraMap
/-- The localization map from power series to Laurent series. -/
-@[simps!]
+@[simps (config := { rhsMd := .all, simpRhs := true })]
instance of_powerSeries_localization [CommRing R] :
IsLocalization (Submonoid.powers (PowerSeries.X : PowerSeries R)) (LaurentSeries R) where
map_units' := by
@@ -25,9 +25,7 @@ import Mathlib.RingTheory.Localization.FractionRing
-/
-open HahnSeries
-
-open BigOperators Classical Polynomial
+open HahnSeries BigOperators Classical Polynomial
noncomputable section
@@ -49,11 +47,11 @@ variable [Semiring R]
instance : Coe (PowerSeries R) (LaurentSeries R) :=
⟨HahnSeries.ofPowerSeries ℤ R⟩
-/-- Porting note: now a syntactic tautology and not needed elsewhere
+/- Porting note: now a syntactic tautology and not needed elsewhere
theorem coe_powerSeries (x : PowerSeries R) :
(x : LaurentSeries R) = HahnSeries.ofPowerSeries ℤ R x :=
- rfl
-#align laurent_series.coe_power_series LaurentSeries.coe_powerSeries -/
+ rfl -/
+#noalign laurent_series.coe_power_series
@[simp]
theorem coeff_coe_powerSeries (x : PowerSeries R) (n : ℕ) :
@@ -220,8 +218,8 @@ theorem coeff_coe (i : ℤ) :
((f : PowerSeries R) : LaurentSeries R).coeff i =
if i < 0 then 0 else PowerSeries.coeff R i.natAbs f := by
cases i
- · rw [Int.ofNat_eq_coe, coeff_coe_powerSeries,
- if_neg (Int.coe_nat_nonneg _).not_lt, Int.natAbs_ofNat]
+ · rw [Int.ofNat_eq_coe, coeff_coe_powerSeries, if_neg (Int.coe_nat_nonneg _).not_lt,
+ Int.natAbs_ofNat]
· rw [ofPowerSeries_apply, embDomain_notin_image_support, if_pos (Int.negSucc_lt_zero _)]
simp only [not_exists, RelEmbedding.coe_mk, Set.mem_image, not_and, Function.Embedding.coeFn_mk,
Ne.def, toPowerSeries_symm_apply_coeff, mem_support, imp_true_iff,
@@ -247,16 +245,9 @@ theorem coe_smul {S : Type _} [Semiring S] [Module R S] (r : R) (x : PowerSeries
simp [coeff_coe, coeff_smul, smul_ite]
#align power_series.coe_smul PowerSeries.coe_smul
-/-- Porting note: RingHom.map_bit0 and RingHom.map_bit1 no longer exist
-@[simp, norm_cast]
-theorem coe_bit0 : ((bit0 f : PowerSeries R) : LaurentSeries R) = bit0 f :=
- (ofPowerSeries ℤ R).map_bit0 _
-#align power_series.coe_bit0 PowerSeries.coe_bit0
-
-@[simp, norm_cast]
-theorem coe_bit1 : ((bit1 f : PowerSeries R) : LaurentSeries R) = bit1 f :=
- (ofPowerSeries ℤ R).map_bit1 _
-#align power_series.coe_bit1 PowerSeries.coe_bit1 -/
+-- Porting note: RingHom.map_bit0 and RingHom.map_bit1 no longer exist
+#noalign power_series.coe_bit0
+#noalign power_series.coe_bit1
@[simp, norm_cast]
theorem coe_pow (n : ℕ) : ((f ^ n : PowerSeries R) : LaurentSeries R) = (ofPowerSeries ℤ R f) ^ n :=
The unported dependencies are