topology.algebra.polynomial ⟷ Mathlib.Topology.Algebra.Polynomial

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

@@ -3,9 +3,9 @@ Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis
 -/
-import Data.Polynomial.AlgebraMap
-import Data.Polynomial.Inductions
-import Data.Polynomial.Splits
+import Algebra.Polynomial.AlgebraMap
+import Algebra.Polynomial.Inductions
+import Algebra.Polynomial.Splits
 import RingTheory.Polynomial.Vieta
 import Analysis.Normed.Field.Basic
 

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

@@ -126,13 +126,13 @@ theorem tendsto_abv_eval₂_atTop {R S k α : Type _} [Semiring R] [Ring S] [Lin
   by
   revert hf; refine' degree_pos_induction_on p hd _ _ _ <;> clear hd p
   · rintro c - hc
-    rw [leading_coeff_mul_X, leading_coeff_C] at hc 
+    rw [leading_coeff_mul_X, leading_coeff_C] at hc
     simpa [abv_mul abv] using hz.const_mul_at_top ((abv_pos abv).2 hc)
   · intro p hpd ihp hf
-    rw [leading_coeff_mul_X] at hf 
+    rw [leading_coeff_mul_X] at hf
     simpa [abv_mul abv] using (ihp hf).atTop_mul_atTop hz
   · intro p a hd ihp hf
-    rw [add_comm, leading_coeff_add_of_degree_lt (degree_C_le.trans_lt hd)] at hf 
+    rw [add_comm, leading_coeff_add_of_degree_lt (degree_C_le.trans_lt hd)] at hf
     refine' tendsto_at_top_of_add_const_right (abv (-f a)) _
     refine' tendsto_at_top_mono (fun _ => abv_add abv _ _) _
     simpa using ihp hf
@@ -187,7 +187,7 @@ theorem eq_one_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (hB : B < 0) (h1
   h1.natDegree_eq_zero_iff_eq_one.mp
     (by
       contrapose! hB
-      rw [← h1.nat_degree_map f, nat_degree_eq_card_roots' h2] at hB 
+      rw [← h1.nat_degree_map f, nat_degree_eq_card_roots' h2] at hB
       obtain ⟨z, hz⟩ := card_pos_iff_exists_mem.mp (zero_lt_iff.mpr hB)
       exact le_trans (norm_nonneg _) (h3 z hz))
 #align polynomial.eq_one_of_roots_le Polynomial.eq_one_of_roots_le
@@ -211,9 +211,9 @@ theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1
   ·
     rw [Multiset.map_map, card_map, card_powerset_len, ← nat_degree_eq_card_roots' h2,
       Nat.choose_symm hi, mul_comm, nsmul_eq_mul]
-  simp_rw [Multiset.mem_map] at hr 
+  simp_rw [Multiset.mem_map] at hr
   obtain ⟨_, ⟨s, hs, rfl⟩, rfl⟩ := hr
-  rw [mem_powerset_len] at hs 
+  rw [mem_powerset_len] at hs
   lift B to ℝ≥0 using hB
   rw [← coe_nnnorm, ← NNReal.coe_pow, NNReal.coe_le_coe, ← nnnormHom_apply, ← MonoidHom.coe_coe,
     MonoidHom.map_multiset_prod]

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

@@ -234,10 +234,10 @@ theorem coeff_bdd_of_roots_le {B : ℝ} {d : ℕ} (f : F →+* K) {p : F[X]} (h1
   · apply (coeff_le_of_roots_le i h1 h2 h4).trans
     calc
       _ ≤ max B 1 ^ (p.nat_degree - i) * p.nat_degree.choose i :=
-        mul_le_mul_of_nonneg_right (pow_le_pow_of_le_left hB (le_max_left _ _) _) _
+        mul_le_mul_of_nonneg_right (pow_le_pow_left hB (le_max_left _ _) _) _
       _ ≤ max B 1 ^ d * p.nat_degree.choose i :=
-        (mul_le_mul_of_nonneg_right ((pow_mono (le_max_right _ _)) (le_trans (Nat.sub_le _ _) h3))
-          _)
+        (mul_le_mul_of_nonneg_right
+          ((pow_right_mono (le_max_right _ _)) (le_trans (Nat.sub_le _ _) h3)) _)
       _ ≤ max B 1 ^ d * d.choose (d / 2) :=
         mul_le_mul_of_nonneg_left
           (nat.cast_le.mpr ((i.choose_mono h3).trans (i.choose_le_middle d))) _

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

@@ -3,11 +3,11 @@ Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis
 -/
-import Mathbin.Data.Polynomial.AlgebraMap
-import Mathbin.Data.Polynomial.Inductions
-import Mathbin.Data.Polynomial.Splits
-import Mathbin.RingTheory.Polynomial.Vieta
-import Mathbin.Analysis.Normed.Field.Basic
+import Data.Polynomial.AlgebraMap
+import Data.Polynomial.Inductions
+import Data.Polynomial.Splits
+import RingTheory.Polynomial.Vieta
+import Analysis.Normed.Field.Basic
 
 #align_import topology.algebra.polynomial from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis
-
-! This file was ported from Lean 3 source module topology.algebra.polynomial
-! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.AlgebraMap
 import Mathbin.Data.Polynomial.Inductions
@@ -14,6 +9,8 @@ import Mathbin.Data.Polynomial.Splits
 import Mathbin.RingTheory.Polynomial.Vieta
 import Mathbin.Analysis.Normed.Field.Basic
 
+#align_import topology.algebra.polynomial from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
+
 /-!
 # Polynomials and limits
 

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

@@ -93,26 +93,35 @@ section TopologicalAlgebra
 variable {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A] [TopologicalSpace A]
   [TopologicalSemiring A] (p : R[X])
 
+#print Polynomial.continuous_aeval /-
 @[continuity]
 protected theorem continuous_aeval : Continuous fun x : A => aeval x p :=
   p.continuous_eval₂ _
 #align polynomial.continuous_aeval Polynomial.continuous_aeval
+-/
 
+#print Polynomial.continuousAt_aeval /-
 protected theorem continuousAt_aeval {a : A} : ContinuousAt (fun x : A => aeval x p) a :=
   p.continuous_aeval.ContinuousAt
 #align polynomial.continuous_at_aeval Polynomial.continuousAt_aeval
+-/
 
+#print Polynomial.continuousWithinAt_aeval /-
 protected theorem continuousWithinAt_aeval {s a} :
     ContinuousWithinAt (fun x : A => aeval x p) s a :=
   p.continuous_aeval.ContinuousWithinAt
 #align polynomial.continuous_within_at_aeval Polynomial.continuousWithinAt_aeval
+-/
 
+#print Polynomial.continuousOn_aeval /-
 protected theorem continuousOn_aeval {s} : ContinuousOn (fun x : A => aeval x p) s :=
   p.continuous_aeval.ContinuousOn
 #align polynomial.continuous_on_aeval Polynomial.continuousOn_aeval
+-/
 
 end TopologicalAlgebra
 
+#print Polynomial.tendsto_abv_eval₂_atTop /-
 theorem tendsto_abv_eval₂_atTop {R S k α : Type _} [Semiring R] [Ring S] [LinearOrderedField k]
     (f : R →+* S) (abv : S → k) [IsAbsoluteValue abv] (p : R[X]) (hd : 0 < degree p)
     (hf : f p.leadingCoeff ≠ 0) {l : Filter α} {z : α → S} (hz : Tendsto (abv ∘ z) l atTop) :
@@ -131,19 +140,24 @@ theorem tendsto_abv_eval₂_atTop {R S k α : Type _} [Semiring R] [Ring S] [Lin
     refine' tendsto_at_top_mono (fun _ => abv_add abv _ _) _
     simpa using ihp hf
 #align polynomial.tendsto_abv_eval₂_at_top Polynomial.tendsto_abv_eval₂_atTop
+-/
 
+#print Polynomial.tendsto_abv_atTop /-
 theorem tendsto_abv_atTop {R k α : Type _} [Ring R] [LinearOrderedField k] (abv : R → k)
     [IsAbsoluteValue abv] (p : R[X]) (h : 0 < degree p) {l : Filter α} {z : α → R}
     (hz : Tendsto (abv ∘ z) l atTop) : Tendsto (fun x => abv (p.eval (z x))) l atTop :=
   tendsto_abv_eval₂_atTop _ _ _ h (mt leadingCoeff_eq_zero.1 <| ne_zero_of_degree_gt h) hz
 #align polynomial.tendsto_abv_at_top Polynomial.tendsto_abv_atTop
+-/
 
+#print Polynomial.tendsto_abv_aeval_atTop /-
 theorem tendsto_abv_aeval_atTop {R A k α : Type _} [CommSemiring R] [Ring A] [Algebra R A]
     [LinearOrderedField k] (abv : A → k) [IsAbsoluteValue abv] (p : R[X]) (hd : 0 < degree p)
     (h₀ : algebraMap R A p.leadingCoeff ≠ 0) {l : Filter α} {z : α → A}
     (hz : Tendsto (abv ∘ z) l atTop) : Tendsto (fun x => abv (aeval (z x) p)) l atTop :=
   tendsto_abv_eval₂_atTop _ abv p hd h₀ hz
 #align polynomial.tendsto_abv_aeval_at_top Polynomial.tendsto_abv_aeval_atTop
+-/
 
 variable {α R : Type _} [NormedRing R] [IsAbsoluteValue (norm : R → ℝ)]
 
@@ -154,11 +168,13 @@ theorem tendsto_norm_atTop (p : R[X]) (h : 0 < degree p) {l : Filter α} {z : α
 #align polynomial.tendsto_norm_at_top Polynomial.tendsto_norm_atTop
 -/
 
+#print Polynomial.exists_forall_norm_le /-
 theorem exists_forall_norm_le [ProperSpace R] (p : R[X]) : ∃ x, ∀ y, ‖p.eval x‖ ≤ ‖p.eval y‖ :=
   if hp0 : 0 < degree p then
     p.Continuous.norm.exists_forall_le <| p.tendsto_norm_atTop hp0 tendsto_norm_cocompact_atTop
   else ⟨p.coeff 0, by rw [eq_C_of_degree_le_zero (le_of_not_gt hp0)] <;> simp⟩
 #align polynomial.exists_forall_norm_le Polynomial.exists_forall_norm_le
+-/
 
 section Roots
 
@@ -168,6 +184,7 @@ variable {F K : Type _} [CommRing F] [NormedField K]
 
 open Multiset
 
+#print Polynomial.eq_one_of_roots_le /-
 theorem eq_one_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (hB : B < 0) (h1 : p.Monic)
     (h2 : Splits f p) (h3 : ∀ z ∈ (map f p).roots, ‖z‖ ≤ B) : p = 1 :=
   h1.natDegree_eq_zero_iff_eq_one.mp
@@ -177,7 +194,9 @@ theorem eq_one_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (hB : B < 0) (h1
       obtain ⟨z, hz⟩ := card_pos_iff_exists_mem.mp (zero_lt_iff.mpr hB)
       exact le_trans (norm_nonneg _) (h3 z hz))
 #align polynomial.eq_one_of_roots_le Polynomial.eq_one_of_roots_le
+-/
 
+#print Polynomial.coeff_le_of_roots_le /-
 theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1 : p.Monic)
     (h2 : Splits f p) (h3 : ∀ z ∈ (map f p).roots, ‖z‖ ≤ B) :
     ‖(map f p).coeff i‖ ≤ B ^ (p.natDegree - i) * p.natDegree.choose i :=
@@ -205,7 +224,9 @@ theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1
   obtain ⟨z, hz, rfl⟩ := Multiset.mem_map.1 hx
   exact h3 z (mem_of_le hs.1 hz)
 #align polynomial.coeff_le_of_roots_le Polynomial.coeff_le_of_roots_le
+-/
 
+#print Polynomial.coeff_bdd_of_roots_le /-
 /-- The coefficients of the monic polynomials of bounded degree with bounded roots are
 uniformely bounded. -/
 theorem coeff_bdd_of_roots_le {B : ℝ} {d : ℕ} (f : F →+* K) {p : F[X]} (h1 : p.Monic)
@@ -229,6 +250,7 @@ theorem coeff_bdd_of_roots_le {B : ℝ} {d : ℕ} (f : F →+* K) {p : F[X]} (h1
     · split_ifs <;> norm_num
     · exact_mod_cast nat.succ_le_iff.mpr (Nat.choose_pos (d.div_le_self 2))
 #align polynomial.coeff_bdd_of_roots_le Polynomial.coeff_bdd_of_roots_le
+-/
 
 end Roots
 

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

@@ -223,7 +223,6 @@ theorem coeff_bdd_of_roots_le {B : ℝ} {d : ℕ} (f : F →+* K) {p : F[X]} (h1
       _ ≤ max B 1 ^ d * d.choose (d / 2) :=
         mul_le_mul_of_nonneg_left
           (nat.cast_le.mpr ((i.choose_mono h3).trans (i.choose_le_middle d))) _
-      
     all_goals positivity
   · rw [eq_one_of_roots_le hB h1 h2 h4, Polynomial.map_one, coeff_one]
     refine' trans _ (one_le_mul_of_one_le_of_one_le (one_le_pow_of_one_le (le_max_right B 1) d) _)

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

@@ -120,13 +120,13 @@ theorem tendsto_abv_eval₂_atTop {R S k α : Type _} [Semiring R] [Ring S] [Lin
   by
   revert hf; refine' degree_pos_induction_on p hd _ _ _ <;> clear hd p
   · rintro c - hc
-    rw [leading_coeff_mul_X, leading_coeff_C] at hc
+    rw [leading_coeff_mul_X, leading_coeff_C] at hc 
     simpa [abv_mul abv] using hz.const_mul_at_top ((abv_pos abv).2 hc)
   · intro p hpd ihp hf
-    rw [leading_coeff_mul_X] at hf
+    rw [leading_coeff_mul_X] at hf 
     simpa [abv_mul abv] using (ihp hf).atTop_mul_atTop hz
   · intro p a hd ihp hf
-    rw [add_comm, leading_coeff_add_of_degree_lt (degree_C_le.trans_lt hd)] at hf
+    rw [add_comm, leading_coeff_add_of_degree_lt (degree_C_le.trans_lt hd)] at hf 
     refine' tendsto_at_top_of_add_const_right (abv (-f a)) _
     refine' tendsto_at_top_mono (fun _ => abv_add abv _ _) _
     simpa using ihp hf
@@ -173,7 +173,7 @@ theorem eq_one_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (hB : B < 0) (h1
   h1.natDegree_eq_zero_iff_eq_one.mp
     (by
       contrapose! hB
-      rw [← h1.nat_degree_map f, nat_degree_eq_card_roots' h2] at hB
+      rw [← h1.nat_degree_map f, nat_degree_eq_card_roots' h2] at hB 
       obtain ⟨z, hz⟩ := card_pos_iff_exists_mem.mp (zero_lt_iff.mpr hB)
       exact le_trans (norm_nonneg _) (h3 z hz))
 #align polynomial.eq_one_of_roots_le Polynomial.eq_one_of_roots_le
@@ -195,9 +195,9 @@ theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1
   ·
     rw [Multiset.map_map, card_map, card_powerset_len, ← nat_degree_eq_card_roots' h2,
       Nat.choose_symm hi, mul_comm, nsmul_eq_mul]
-  simp_rw [Multiset.mem_map] at hr
+  simp_rw [Multiset.mem_map] at hr 
   obtain ⟨_, ⟨s, hs, rfl⟩, rfl⟩ := hr
-  rw [mem_powerset_len] at hs
+  rw [mem_powerset_len] at hs 
   lift B to ℝ≥0 using hB
   rw [← coe_nnnorm, ← NNReal.coe_pow, NNReal.coe_le_coe, ← nnnormHom_apply, ← MonoidHom.coe_coe,
     MonoidHom.map_multiset_prod]

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

@@ -93,31 +93,23 @@ section TopologicalAlgebra
 variable {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A] [TopologicalSpace A]
   [TopologicalSemiring A] (p : R[X])
 
-#print Polynomial.continuous_aeval /-
 @[continuity]
 protected theorem continuous_aeval : Continuous fun x : A => aeval x p :=
   p.continuous_eval₂ _
 #align polynomial.continuous_aeval Polynomial.continuous_aeval
--/
 
-#print Polynomial.continuousAt_aeval /-
 protected theorem continuousAt_aeval {a : A} : ContinuousAt (fun x : A => aeval x p) a :=
   p.continuous_aeval.ContinuousAt
 #align polynomial.continuous_at_aeval Polynomial.continuousAt_aeval
--/
 
-#print Polynomial.continuousWithinAt_aeval /-
 protected theorem continuousWithinAt_aeval {s a} :
     ContinuousWithinAt (fun x : A => aeval x p) s a :=
   p.continuous_aeval.ContinuousWithinAt
 #align polynomial.continuous_within_at_aeval Polynomial.continuousWithinAt_aeval
--/
 
-#print Polynomial.continuousOn_aeval /-
 protected theorem continuousOn_aeval {s} : ContinuousOn (fun x : A => aeval x p) s :=
   p.continuous_aeval.ContinuousOn
 #align polynomial.continuous_on_aeval Polynomial.continuousOn_aeval
--/
 
 end TopologicalAlgebra
 

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

@@ -45,7 +45,7 @@ open IsAbsoluteValue Filter
 
 namespace Polynomial
 
-open Polynomial
+open scoped Polynomial
 
 section TopologicalSemiring
 
@@ -155,10 +155,12 @@ theorem tendsto_abv_aeval_atTop {R A k α : Type _} [CommSemiring R] [Ring A] [A
 
 variable {α R : Type _} [NormedRing R] [IsAbsoluteValue (norm : R → ℝ)]
 
+#print Polynomial.tendsto_norm_atTop /-
 theorem tendsto_norm_atTop (p : R[X]) (h : 0 < degree p) {l : Filter α} {z : α → R}
     (hz : Tendsto (fun x => ‖z x‖) l atTop) : Tendsto (fun x => ‖p.eval (z x)‖) l atTop :=
   p.tendsto_abv_atTop norm h hz
 #align polynomial.tendsto_norm_at_top Polynomial.tendsto_norm_atTop
+-/
 
 theorem exists_forall_norm_le [ProperSpace R] (p : R[X]) : ∃ x, ∀ y, ‖p.eval x‖ ≤ ‖p.eval y‖ :=
   if hp0 : 0 < degree p then
@@ -168,7 +170,7 @@ theorem exists_forall_norm_le [ProperSpace R] (p : R[X]) : ∃ x, ∀ y, ‖p.ev
 
 section Roots
 
-open Polynomial NNReal
+open scoped Polynomial NNReal
 
 variable {F K : Type _} [CommRing F] [NormedField K]
 

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

@@ -121,12 +121,6 @@ protected theorem continuousOn_aeval {s} : ContinuousOn (fun x : A => aeval x p)
 
 end TopologicalAlgebra
 
-/- warning: polynomial.tendsto_abv_eval₂_at_top -> Polynomial.tendsto_abv_eval₂_atTop is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_eval₂_at_top Polynomial.tendsto_abv_eval₂_atTopₓ'. -/
 theorem tendsto_abv_eval₂_atTop {R S k α : Type _} [Semiring R] [Ring S] [LinearOrderedField k]
     (f : R →+* S) (abv : S → k) [IsAbsoluteValue abv] (p : R[X]) (hd : 0 < degree p)
     (hf : f p.leadingCoeff ≠ 0) {l : Filter α} {z : α → S} (hz : Tendsto (abv ∘ z) l atTop) :
@@ -146,21 +140,12 @@ theorem tendsto_abv_eval₂_atTop {R S k α : Type _} [Semiring R] [Ring S] [Lin
     simpa using ihp hf
 #align polynomial.tendsto_abv_eval₂_at_top Polynomial.tendsto_abv_eval₂_atTop
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_at_top Polynomial.tendsto_abv_atTopₓ'. -/
 theorem tendsto_abv_atTop {R k α : Type _} [Ring R] [LinearOrderedField k] (abv : R → k)
     [IsAbsoluteValue abv] (p : R[X]) (h : 0 < degree p) {l : Filter α} {z : α → R}
     (hz : Tendsto (abv ∘ z) l atTop) : Tendsto (fun x => abv (p.eval (z x))) l atTop :=
   tendsto_abv_eval₂_atTop _ _ _ h (mt leadingCoeff_eq_zero.1 <| ne_zero_of_degree_gt h) hz
 #align polynomial.tendsto_abv_at_top Polynomial.tendsto_abv_atTop
 
-/- warning: polynomial.tendsto_abv_aeval_at_top -> Polynomial.tendsto_abv_aeval_atTop is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_aeval_at_top Polynomial.tendsto_abv_aeval_atTopₓ'. -/
 theorem tendsto_abv_aeval_atTop {R A k α : Type _} [CommSemiring R] [Ring A] [Algebra R A]
     [LinearOrderedField k] (abv : A → k) [IsAbsoluteValue abv] (p : R[X]) (hd : 0 < degree p)
     (h₀ : algebraMap R A p.leadingCoeff ≠ 0) {l : Filter α} {z : α → A}
@@ -170,23 +155,11 @@ theorem tendsto_abv_aeval_atTop {R A k α : Type _} [CommSemiring R] [Ring A] [A
 
 variable {α R : Type _} [NormedRing R] [IsAbsoluteValue (norm : R → ℝ)]
 
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 theorem tendsto_norm_atTop (p : R[X]) (h : 0 < degree p) {l : Filter α} {z : α → R}
     (hz : Tendsto (fun x => ‖z x‖) l atTop) : Tendsto (fun x => ‖p.eval (z x)‖) l atTop :=
   p.tendsto_abv_atTop norm h hz
 #align polynomial.tendsto_norm_at_top Polynomial.tendsto_norm_atTop
 
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 theorem exists_forall_norm_le [ProperSpace R] (p : R[X]) : ∃ x, ∀ y, ‖p.eval x‖ ≤ ‖p.eval y‖ :=
   if hp0 : 0 < degree p then
     p.Continuous.norm.exists_forall_le <| p.tendsto_norm_atTop hp0 tendsto_norm_cocompact_atTop
@@ -201,12 +174,6 @@ variable {F K : Type _} [CommRing F] [NormedField K]
 
 open Multiset
 
-/- warning: polynomial.eq_one_of_roots_le -> Polynomial.eq_one_of_roots_le is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} {K : Type.{u2}} [_inst_3 : CommRing.{u1} F] [_inst_4 : NormedField.{u2} K] {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))} {f : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (CommRing.toRing.{u1} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))))} {B : Real}, (LT.lt.{0} Real Real.hasLt B (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Polynomial.Monic.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) -> (Polynomial.Splits.{u1, u2} F K _inst_3 (NormedField.toField.{u2} K _inst_4) f p) -> (forall (z : K), (Membership.Mem.{u2, u2} K (Multiset.{u2} K) (Multiset.hasMem.{u2} K) z (Polynomial.roots.{u2} K (SeminormedCommRing.toCommRing.{u2} K (NormedCommRing.toSeminormedCommRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4))) (Field.isDomain.{u2} K (NormedField.toField.{u2} K _inst_4)) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) z) B)) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) p (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) 1 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) 1 (One.one.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) (Polynomial.hasOne.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)))))))
-but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {p : Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))} {f : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))))} {B : Real}, (LT.lt.{0} Real Real.instLTReal B (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Polynomial.Monic.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Field.isDomain.{u1} K (NormedField.toField.{u1} K _inst_4)) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (Eq.{succ u2} (Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) 1 (One.toOfNat1.{u2} (Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Polynomial.one.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))))))
-Case conversion may be inaccurate. Consider using '#align polynomial.eq_one_of_roots_le Polynomial.eq_one_of_roots_leₓ'. -/
 theorem eq_one_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (hB : B < 0) (h1 : p.Monic)
     (h2 : Splits f p) (h3 : ∀ z ∈ (map f p).roots, ‖z‖ ≤ B) : p = 1 :=
   h1.natDegree_eq_zero_iff_eq_one.mp
@@ -217,12 +184,6 @@ theorem eq_one_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (hB : B < 0) (h1
       exact le_trans (norm_nonneg _) (h3 z hz))
 #align polynomial.eq_one_of_roots_le Polynomial.eq_one_of_roots_le
 
-/- warning: polynomial.coeff_le_of_roots_le -> Polynomial.coeff_le_of_roots_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align polynomial.coeff_le_of_roots_le Polynomial.coeff_le_of_roots_leₓ'. -/
 theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1 : p.Monic)
     (h2 : Splits f p) (h3 : ∀ z ∈ (map f p).roots, ‖z‖ ≤ B) :
     ‖(map f p).coeff i‖ ≤ B ^ (p.natDegree - i) * p.natDegree.choose i :=
@@ -251,12 +212,6 @@ theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1
   exact h3 z (mem_of_le hs.1 hz)
 #align polynomial.coeff_le_of_roots_le Polynomial.coeff_le_of_roots_le
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.coeff_bdd_of_roots_le Polynomial.coeff_bdd_of_roots_leₓ'. -/
 /-- The coefficients of the monic polynomials of bounded degree with bounded roots are
 uniformely bounded. -/
 theorem coeff_bdd_of_roots_le {B : ℝ} {d : ℕ} (f : F →+* K) {p : F[X]} (h1 : p.Monic)

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

@@ -233,8 +233,7 @@ theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1
     split_ifs <;> norm_num [h]
   rw [← h1.nat_degree_map f]
   obtain hi | hi := lt_or_le (map f p).natDegree i
-  · rw [coeff_eq_zero_of_nat_degree_lt hi, norm_zero]
-    positivity
+  · rw [coeff_eq_zero_of_nat_degree_lt hi, norm_zero]; positivity
   rw [coeff_eq_esymm_roots_of_splits ((splits_id_iff_splits f).2 h2) hi, (h1.map _).leadingCoeff,
     one_mul, norm_mul, norm_pow, norm_neg, norm_one, one_pow, one_mul]
   apply ((norm_multiset_sum_le _).trans <| sum_le_card_nsmul _ _ fun r hr => _).trans

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

@@ -159,10 +159,7 @@ theorem tendsto_abv_atTop {R k α : Type _} [Ring R] [LinearOrderedField k] (abv
 #align polynomial.tendsto_abv_at_top Polynomial.tendsto_abv_atTop
 
 /- warning: polynomial.tendsto_abv_aeval_at_top -> Polynomial.tendsto_abv_aeval_atTop is a dubious translation:
-lean 3 declaration is
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(AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u4, u3, max u3 u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3 (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) (AlgHom.algHomClass.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3))))) (Polynomial.aeval.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3 (z x)) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_4))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_aeval_at_top Polynomial.tendsto_abv_aeval_atTopₓ'. -/
 theorem tendsto_abv_aeval_atTop {R A k α : Type _} [CommSemiring R] [Ring A] [Algebra R A]
     [LinearOrderedField k] (abv : A → k) [IsAbsoluteValue abv] (p : R[X]) (hd : 0 < degree p)

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

@@ -162,7 +162,7 @@ theorem tendsto_abv_atTop {R k α : Type _} [Ring R] [LinearOrderedField k] (abv
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {k : Type.{u3}} {α : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (Ring.toSemiring.{u2} A _inst_2)] [_inst_4 : LinearOrderedField.{u3} k] (abv : A -> k) [_inst_5 : IsAbsoluteValue.{u3, u2} k (StrictOrderedSemiring.toOrderedSemiring.{u3} k (StrictOrderedRing.toStrictOrderedSemiring.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_4))))) A (Ring.toSemiring.{u2} A _inst_2) abv] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p)) -> (Ne.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) (algebraMap.{u1, u2} R A _inst_1 (Ring.toSemiring.{u2} A _inst_2) _inst_3) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p)) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_2))))))))) -> (forall {l : Filter.{u4} α} {z : α -> A}, (Filter.Tendsto.{u4, u3} α k (Function.comp.{succ u4, succ u2, succ u3} α A k abv z) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_4)))))))) -> (Filter.Tendsto.{u4, u3} α k (fun (x : α) => abv (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (Polynomial.aeval.{u1, u2} R A _inst_1 (Ring.toSemiring.{u2} A _inst_2) _inst_3 (z x)) p)) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_4)))))))))
 but is expected to have type
-  forall {R : Type.{u4}} {A : Type.{u3}} {k : Type.{u2}} {α : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : Ring.{u3} A] [_inst_3 : Algebra.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2)] [_inst_4 : LinearOrderedField.{u2} k] (abv : A -> k) [_inst_5 : IsAbsoluteValue.{u2, u3} k (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_4))))) A (Ring.toSemiring.{u3} A _inst_2) abv] (p : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) -> (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)) (RingHom.instRingHomClassRingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (algebraMap.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (Ring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) _inst_2)))))) -> (forall {l : Filter.{u1} α} {z : α -> A}, (Filter.Tendsto.{u1, u2} α k (Function.comp.{succ u1, succ u3, succ u2} α A k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_4))))))) -> (Filter.Tendsto.{u1, u2} α k (fun (x : α) => abv (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (fun (_x : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (SMulZeroClass.toSMul.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toAddZeroClass.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1))))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u4, u3, max u3 u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3 (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) (AlgHom.algHomClass.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3))))) (Polynomial.aeval.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3 (z x)) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_4))))))))
+  forall {R : Type.{u4}} {A : Type.{u3}} {k : Type.{u2}} {α : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : Ring.{u3} A] [_inst_3 : Algebra.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2)] [_inst_4 : LinearOrderedField.{u2} k] (abv : A -> k) [_inst_5 : IsAbsoluteValue.{u2, u3} k (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_4))))) A (Ring.toSemiring.{u3} A _inst_2) abv] (p : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) -> (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)) (RingHom.instRingHomClassRingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (algebraMap.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (Ring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) _inst_2)))))) -> (forall {l : Filter.{u1} α} {z : α -> A}, (Filter.Tendsto.{u1, u2} α k (Function.comp.{succ u1, succ u3, succ u2} α A k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_4))))))) -> (Filter.Tendsto.{u1, u2} α k (fun (x : α) => abv (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (fun (_x : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (SMulZeroClass.toSMul.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toAddZeroClass.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1))))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u4, u3, max u3 u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3 (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) (AlgHom.algHomClass.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3))))) (Polynomial.aeval.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3 (z x)) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_4))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_aeval_at_top Polynomial.tendsto_abv_aeval_atTopₓ'. -/
 theorem tendsto_abv_aeval_atTop {R A k α : Type _} [CommSemiring R] [Ring A] [Algebra R A]
     [LinearOrderedField k] (abv : A → k) [IsAbsoluteValue abv] (p : R[X]) (hd : 0 < degree p)

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

@@ -125,7 +125,7 @@ end TopologicalAlgebra
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {k : Type.{u3}} {α : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Ring.{u2} S] [_inst_3 : LinearOrderedField.{u3} k] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (abv : S -> k) [_inst_4 : IsAbsoluteValue.{u3, u2} k (StrictOrderedSemiring.toOrderedSemiring.{u3} k (StrictOrderedRing.toStrictOrderedSemiring.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3))))) S (Ring.toSemiring.{u2} S _inst_2) abv] (p : Polynomial.{u1} R _inst_1), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R _inst_1 p)) -> (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))))))))) -> (forall {l : Filter.{u4} α} {z : α -> S}, (Filter.Tendsto.{u4, u3} α k (Function.comp.{succ u4, succ u2, succ u3} α S k abv z) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3)))))))) -> (Filter.Tendsto.{u4, u3} α k (fun (x : α) => abv (Polynomial.eval₂.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S _inst_2) f (z x) p)) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3)))))))))
 but is expected to have type
-  forall {R : Type.{u4}} {S : Type.{u3}} {k : Type.{u2}} {α : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : Ring.{u3} S] [_inst_3 : LinearOrderedField.{u2} k] (f : RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) (abv : S -> k) [_inst_4 : IsAbsoluteValue.{u2, u3} k (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_3))))) S (Ring.toSemiring.{u3} S _inst_2) abv] (p : Polynomial.{u4} R _inst_1), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u4} R _inst_1 p)) -> (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))))) f (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (Ring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) _inst_2)))))) -> (forall {l : Filter.{u1} α} {z : α -> S}, (Filter.Tendsto.{u1, u2} α k (Function.comp.{succ u1, succ u3, succ u2} α S k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_3))))))) -> (Filter.Tendsto.{u1, u2} α k (fun (x : α) => abv (Polynomial.eval₂.{u4, u3} R S _inst_1 (Ring.toSemiring.{u3} S _inst_2) f (z x) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_3))))))))
+  forall {R : Type.{u4}} {S : Type.{u3}} {k : Type.{u2}} {α : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : Ring.{u3} S] [_inst_3 : LinearOrderedField.{u2} k] (f : RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) (abv : S -> k) [_inst_4 : IsAbsoluteValue.{u2, u3} k (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_3))))) S (Ring.toSemiring.{u3} S _inst_2) abv] (p : Polynomial.{u4} R _inst_1), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u4} R _inst_1 p)) -> (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))))) f (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (Ring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) _inst_2)))))) -> (forall {l : Filter.{u1} α} {z : α -> S}, (Filter.Tendsto.{u1, u2} α k (Function.comp.{succ u1, succ u3, succ u2} α S k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_3))))))) -> (Filter.Tendsto.{u1, u2} α k (fun (x : α) => abv (Polynomial.eval₂.{u4, u3} R S _inst_1 (Ring.toSemiring.{u3} S _inst_2) f (z x) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_3))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_eval₂_at_top Polynomial.tendsto_abv_eval₂_atTopₓ'. -/
 theorem tendsto_abv_eval₂_atTop {R S k α : Type _} [Semiring R] [Ring S] [LinearOrderedField k]
     (f : R →+* S) (abv : S → k) [IsAbsoluteValue abv] (p : R[X]) (hd : 0 < degree p)
@@ -162,7 +162,7 @@ theorem tendsto_abv_atTop {R k α : Type _} [Ring R] [LinearOrderedField k] (abv
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {k : Type.{u3}} {α : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (Ring.toSemiring.{u2} A _inst_2)] [_inst_4 : LinearOrderedField.{u3} k] (abv : A -> k) [_inst_5 : IsAbsoluteValue.{u3, u2} k (StrictOrderedSemiring.toOrderedSemiring.{u3} k (StrictOrderedRing.toStrictOrderedSemiring.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_4))))) A (Ring.toSemiring.{u2} A _inst_2) abv] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p)) -> (Ne.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) (algebraMap.{u1, u2} R A _inst_1 (Ring.toSemiring.{u2} A _inst_2) _inst_3) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p)) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_2))))))))) -> (forall {l : Filter.{u4} α} {z : α -> A}, (Filter.Tendsto.{u4, u3} α k (Function.comp.{succ u4, succ u2, succ u3} α A k abv z) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_4)))))))) -> (Filter.Tendsto.{u4, u3} α k (fun (x : α) => abv (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (Polynomial.aeval.{u1, u2} R A _inst_1 (Ring.toSemiring.{u2} A _inst_2) _inst_3 (z x)) p)) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_4)))))))))
 but is expected to have type
-  forall {R : Type.{u4}} {A : Type.{u3}} {k : Type.{u2}} {α : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : Ring.{u3} A] [_inst_3 : Algebra.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2)] [_inst_4 : LinearOrderedField.{u2} k] (abv : A -> k) [_inst_5 : IsAbsoluteValue.{u2, u3} k (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_4))))) A (Ring.toSemiring.{u3} A _inst_2) abv] (p : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) -> (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)) (RingHom.instRingHomClassRingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (algebraMap.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (Ring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) _inst_2)))))) -> (forall {l : Filter.{u1} α} {z : α -> A}, (Filter.Tendsto.{u1, u2} α k (Function.comp.{succ u1, succ u3, succ u2} α A k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_4))))))) -> (Filter.Tendsto.{u1, u2} α k (fun (x : α) => abv (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (fun (_x : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (SMulZeroClass.toSMul.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toAddZeroClass.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1))))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u4, u3, max u3 u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3 (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) (AlgHom.algHomClass.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3))))) (Polynomial.aeval.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3 (z x)) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_4))))))))
+  forall {R : Type.{u4}} {A : Type.{u3}} {k : Type.{u2}} {α : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : Ring.{u3} A] [_inst_3 : Algebra.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2)] [_inst_4 : LinearOrderedField.{u2} k] (abv : A -> k) [_inst_5 : IsAbsoluteValue.{u2, u3} k (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_4))))) A (Ring.toSemiring.{u3} A _inst_2) abv] (p : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) -> (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)) (RingHom.instRingHomClassRingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (algebraMap.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (Ring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) _inst_2)))))) -> (forall {l : Filter.{u1} α} {z : α -> A}, (Filter.Tendsto.{u1, u2} α k (Function.comp.{succ u1, succ u3, succ u2} α A k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_4))))))) -> (Filter.Tendsto.{u1, u2} α k (fun (x : α) => abv (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 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(Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toAddZeroClass.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1))))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 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(Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u4, u3, max u3 u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3 (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) (AlgHom.algHomClass.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3))))) (Polynomial.aeval.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3 (z x)) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_4))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_aeval_at_top Polynomial.tendsto_abv_aeval_atTopₓ'. -/
 theorem tendsto_abv_aeval_atTop {R A k α : Type _} [CommSemiring R] [Ring A] [Algebra R A]
     [LinearOrderedField k] (abv : A → k) [IsAbsoluteValue abv] (p : R[X]) (hd : 0 < degree p)

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

@@ -123,7 +123,7 @@ end TopologicalAlgebra
 
 /- warning: polynomial.tendsto_abv_eval₂_at_top -> Polynomial.tendsto_abv_eval₂_atTop is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} {k : Type.{u3}} {α : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Ring.{u2} S] [_inst_3 : LinearOrderedField.{u3} k] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (abv : S -> k) [_inst_4 : IsAbsoluteValue.{u3, u2} k (StrictOrderedSemiring.toOrderedSemiring.{u3} k (StrictOrderedRing.toStrictOrderedSemiring.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3))))) S (Ring.toSemiring.{u2} S _inst_2) abv] (p : Polynomial.{u1} R _inst_1), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R _inst_1 p)) -> (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))))))))) -> (forall {l : Filter.{u4} α} {z : α -> S}, (Filter.Tendsto.{u4, u3} α k (Function.comp.{succ u4, succ u2, succ u3} α S k abv z) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3)))))))) -> (Filter.Tendsto.{u4, u3} α k (fun (x : α) => abv (Polynomial.eval₂.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S _inst_2) f (z x) p)) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3)))))))))
+  forall {R : Type.{u1}} {S : Type.{u2}} {k : Type.{u3}} {α : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Ring.{u2} S] [_inst_3 : LinearOrderedField.{u3} k] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (abv : S -> k) [_inst_4 : IsAbsoluteValue.{u3, u2} k (StrictOrderedSemiring.toOrderedSemiring.{u3} k (StrictOrderedRing.toStrictOrderedSemiring.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3))))) S (Ring.toSemiring.{u2} S _inst_2) abv] (p : Polynomial.{u1} R _inst_1), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R _inst_1 p)) -> (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))))))))) -> (forall {l : Filter.{u4} α} {z : α -> S}, (Filter.Tendsto.{u4, u3} α k (Function.comp.{succ u4, succ u2, succ u3} α S k abv z) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3)))))))) -> (Filter.Tendsto.{u4, u3} α k (fun (x : α) => abv (Polynomial.eval₂.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S _inst_2) f (z x) p)) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3)))))))))
 but is expected to have type
   forall {R : Type.{u4}} {S : Type.{u3}} {k : Type.{u2}} {α : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : Ring.{u3} S] [_inst_3 : LinearOrderedField.{u2} k] (f : RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) (abv : S -> k) [_inst_4 : IsAbsoluteValue.{u2, u3} k (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_3))))) S (Ring.toSemiring.{u3} S _inst_2) abv] (p : Polynomial.{u4} R _inst_1), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u4} R _inst_1 p)) -> (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))))) f (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (Ring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) _inst_2)))))) -> (forall {l : Filter.{u1} α} {z : α -> S}, (Filter.Tendsto.{u1, u2} α k (Function.comp.{succ u1, succ u3, succ u2} α S k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_3))))))) -> (Filter.Tendsto.{u1, u2} α k (fun (x : α) => abv (Polynomial.eval₂.{u4, u3} R S _inst_1 (Ring.toSemiring.{u3} S _inst_2) f (z x) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_3))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_eval₂_at_top Polynomial.tendsto_abv_eval₂_atTopₓ'. -/
@@ -148,7 +148,7 @@ theorem tendsto_abv_eval₂_atTop {R S k α : Type _} [Semiring R] [Ring S] [Lin
 
 /- warning: polynomial.tendsto_abv_at_top -> Polynomial.tendsto_abv_atTop is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {k : Type.{u2}} {α : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : LinearOrderedField.{u2} k] (abv : R -> k) [_inst_3 : IsAbsoluteValue.{u2, u1} k (StrictOrderedSemiring.toOrderedSemiring.{u2} k (StrictOrderedRing.toStrictOrderedSemiring.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_2))))) R (Ring.toSemiring.{u1} R _inst_1) abv] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) -> (forall {l : Filter.{u3} α} {z : α -> R}, (Filter.Tendsto.{u3, u2} α k (Function.comp.{succ u3, succ u1, succ u2} α R k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedAddCommGroup.toPartialOrder.{u2} k (StrictOrderedRing.toOrderedAddCommGroup.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_2)))))))) -> (Filter.Tendsto.{u3, u2} α k (fun (x : α) => abv (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) (z x) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedAddCommGroup.toPartialOrder.{u2} k (StrictOrderedRing.toOrderedAddCommGroup.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_2)))))))))
+  forall {R : Type.{u1}} {k : Type.{u2}} {α : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : LinearOrderedField.{u2} k] (abv : R -> k) [_inst_3 : IsAbsoluteValue.{u2, u1} k (StrictOrderedSemiring.toOrderedSemiring.{u2} k (StrictOrderedRing.toStrictOrderedSemiring.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_2))))) R (Ring.toSemiring.{u1} R _inst_1) abv] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) -> (forall {l : Filter.{u3} α} {z : α -> R}, (Filter.Tendsto.{u3, u2} α k (Function.comp.{succ u3, succ u1, succ u2} α R k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedAddCommGroup.toPartialOrder.{u2} k (StrictOrderedRing.toOrderedAddCommGroup.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_2)))))))) -> (Filter.Tendsto.{u3, u2} α k (fun (x : α) => abv (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) (z x) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedAddCommGroup.toPartialOrder.{u2} k (StrictOrderedRing.toOrderedAddCommGroup.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_2)))))))))
 but is expected to have type
   forall {R : Type.{u3}} {k : Type.{u2}} {α : Type.{u1}} [_inst_1 : Ring.{u3} R] [_inst_2 : LinearOrderedField.{u2} k] (abv : R -> k) [_inst_3 : IsAbsoluteValue.{u2, u3} k (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_2))))) R (Ring.toSemiring.{u3} R _inst_1) abv] (p : Polynomial.{u3} R (Ring.toSemiring.{u3} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u3} R (Ring.toSemiring.{u3} R _inst_1) p)) -> (forall {l : Filter.{u1} α} {z : α -> R}, (Filter.Tendsto.{u1, u2} α k (Function.comp.{succ u1, succ u3, succ u2} α R k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_2))))))) -> (Filter.Tendsto.{u1, u2} α k (fun (x : α) => abv (Polynomial.eval.{u3} R (Ring.toSemiring.{u3} R _inst_1) (z x) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_at_top Polynomial.tendsto_abv_atTopₓ'. -/
@@ -160,7 +160,7 @@ theorem tendsto_abv_atTop {R k α : Type _} [Ring R] [LinearOrderedField k] (abv
 
 /- warning: polynomial.tendsto_abv_aeval_at_top -> Polynomial.tendsto_abv_aeval_atTop is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} {k : Type.{u3}} {α : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (Ring.toSemiring.{u2} A _inst_2)] [_inst_4 : LinearOrderedField.{u3} k] (abv : A -> k) [_inst_5 : IsAbsoluteValue.{u3, u2} k (StrictOrderedSemiring.toOrderedSemiring.{u3} k (StrictOrderedRing.toStrictOrderedSemiring.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_4))))) A (Ring.toSemiring.{u2} A _inst_2) abv] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p)) -> (Ne.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) (algebraMap.{u1, u2} R A _inst_1 (Ring.toSemiring.{u2} A _inst_2) _inst_3) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p)) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_2))))))))) -> (forall {l : Filter.{u4} α} {z : α -> A}, (Filter.Tendsto.{u4, u3} α k (Function.comp.{succ u4, succ u2, succ u3} α A k abv z) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_4)))))))) -> (Filter.Tendsto.{u4, u3} α k (fun (x : α) => abv (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (Polynomial.aeval.{u1, u2} R A _inst_1 (Ring.toSemiring.{u2} A _inst_2) _inst_3 (z x)) p)) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_4)))))))))
+  forall {R : Type.{u1}} {A : Type.{u2}} {k : Type.{u3}} {α : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (Ring.toSemiring.{u2} A _inst_2)] [_inst_4 : LinearOrderedField.{u3} k] (abv : A -> k) [_inst_5 : IsAbsoluteValue.{u3, u2} k (StrictOrderedSemiring.toOrderedSemiring.{u3} k (StrictOrderedRing.toStrictOrderedSemiring.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_4))))) A (Ring.toSemiring.{u2} A _inst_2) abv] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p)) -> (Ne.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) (algebraMap.{u1, u2} R A _inst_1 (Ring.toSemiring.{u2} A _inst_2) _inst_3) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p)) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_2))))))))) -> (forall {l : Filter.{u4} α} {z : α -> A}, (Filter.Tendsto.{u4, u3} α k (Function.comp.{succ u4, succ u2, succ u3} α A k abv z) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_4)))))))) -> (Filter.Tendsto.{u4, u3} α k (fun (x : α) => abv (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (Polynomial.aeval.{u1, u2} R A _inst_1 (Ring.toSemiring.{u2} A _inst_2) _inst_3 (z x)) p)) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_4)))))))))
 but is expected to have type
   forall {R : Type.{u4}} {A : Type.{u3}} {k : Type.{u2}} {α : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : Ring.{u3} A] [_inst_3 : Algebra.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2)] [_inst_4 : LinearOrderedField.{u2} k] (abv : A -> k) [_inst_5 : IsAbsoluteValue.{u2, u3} k (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_4))))) A (Ring.toSemiring.{u3} A _inst_2) abv] (p : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) -> (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)) (RingHom.instRingHomClassRingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (algebraMap.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (Ring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) _inst_2)))))) -> (forall {l : Filter.{u1} α} {z : α -> A}, (Filter.Tendsto.{u1, u2} α k (Function.comp.{succ u1, succ u3, succ u2} α A k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_4))))))) -> (Filter.Tendsto.{u1, u2} α k (fun (x : α) => abv (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (fun (_x : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (SMulZeroClass.toSMul.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toAddZeroClass.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1))))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u4, u3, max u3 u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3 (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) (AlgHom.algHomClass.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3))))) (Polynomial.aeval.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3 (z x)) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_4))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_aeval_at_top Polynomial.tendsto_abv_aeval_atTopₓ'. -/
@@ -173,12 +173,16 @@ theorem tendsto_abv_aeval_atTop {R A k α : Type _} [CommSemiring R] [Ring A] [A
 
 variable {α R : Type _} [NormedRing R] [IsAbsoluteValue (norm : R → ℝ)]
 
-#print Polynomial.tendsto_norm_atTop /-
+/- warning: polynomial.tendsto_norm_at_top -> Polynomial.tendsto_norm_atTop is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {R : Type.{u2}} [_inst_1 : NormedRing.{u2} R] [_inst_2 : IsAbsoluteValue.{0, u2} Real Real.orderedSemiring R (Ring.toSemiring.{u2} R (NormedRing.toRing.{u2} R _inst_1)) (Norm.norm.{u2} R (NormedRing.toHasNorm.{u2} R _inst_1))] (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (NormedRing.toRing.{u2} R _inst_1))), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u2} R (Ring.toSemiring.{u2} R (NormedRing.toRing.{u2} R _inst_1)) p)) -> (forall {l : Filter.{u1} α} {z : α -> R}, (Filter.Tendsto.{u1, 0} α Real (fun (x : α) => Norm.norm.{u2} R (NormedRing.toHasNorm.{u2} R _inst_1) (z x)) l (Filter.atTop.{0} Real Real.preorder)) -> (Filter.Tendsto.{u1, 0} α Real (fun (x : α) => Norm.norm.{u2} R (NormedRing.toHasNorm.{u2} R _inst_1) (Polynomial.eval.{u2} R (Ring.toSemiring.{u2} R (NormedRing.toRing.{u2} R _inst_1)) (z x) p)) l (Filter.atTop.{0} Real Real.preorder)))
+but is expected to have type
+  forall {α : Type.{u1}} {R : Type.{u2}} [_inst_1 : NormedRing.{u2} R] [_inst_2 : IsAbsoluteValue.{0, u2} Real Real.orderedSemiring R (Ring.toSemiring.{u2} R (NormedRing.toRing.{u2} R _inst_1)) (Norm.norm.{u2} R (NormedRing.toNorm.{u2} R _inst_1))] (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (NormedRing.toRing.{u2} R _inst_1))), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u2} R (Ring.toSemiring.{u2} R (NormedRing.toRing.{u2} R _inst_1)) p)) -> (forall {l : Filter.{u1} α} {z : α -> R}, (Filter.Tendsto.{u1, 0} α Real (fun (x : α) => Norm.norm.{u2} R (NormedRing.toNorm.{u2} R _inst_1) (z x)) l (Filter.atTop.{0} Real Real.instPreorderReal)) -> (Filter.Tendsto.{u1, 0} α Real (fun (x : α) => Norm.norm.{u2} R (NormedRing.toNorm.{u2} R _inst_1) (Polynomial.eval.{u2} R (Ring.toSemiring.{u2} R (NormedRing.toRing.{u2} R _inst_1)) (z x) p)) l (Filter.atTop.{0} Real Real.instPreorderReal)))
+Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_norm_at_top Polynomial.tendsto_norm_atTopₓ'. -/
 theorem tendsto_norm_atTop (p : R[X]) (h : 0 < degree p) {l : Filter α} {z : α → R}
     (hz : Tendsto (fun x => ‖z x‖) l atTop) : Tendsto (fun x => ‖p.eval (z x)‖) l atTop :=
   p.tendsto_abv_atTop norm h hz
 #align polynomial.tendsto_norm_at_top Polynomial.tendsto_norm_atTop
--/
 
 /- warning: polynomial.exists_forall_norm_le -> Polynomial.exists_forall_norm_le is a dubious translation:
 lean 3 declaration is

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

@@ -204,7 +204,7 @@ open Multiset
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} [_inst_3 : CommRing.{u1} F] [_inst_4 : NormedField.{u2} K] {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))} {f : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (CommRing.toRing.{u1} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))))} {B : Real}, (LT.lt.{0} Real Real.hasLt B (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Polynomial.Monic.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) -> (Polynomial.Splits.{u1, u2} F K _inst_3 (NormedField.toField.{u2} K _inst_4) f p) -> (forall (z : K), (Membership.Mem.{u2, u2} K (Multiset.{u2} K) (Multiset.hasMem.{u2} K) z (Polynomial.roots.{u2} K (SeminormedCommRing.toCommRing.{u2} K (NormedCommRing.toSeminormedCommRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4))) (Field.isDomain.{u2} K (NormedField.toField.{u2} K _inst_4)) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) z) B)) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) p (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) 1 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) 1 (One.one.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) (Polynomial.hasOne.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)))))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {p : Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))} {f : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))))} {B : Real}, (LT.lt.{0} Real Real.instLTReal B (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Polynomial.Monic.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (Eq.{succ u2} (Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) 1 (One.toOfNat1.{u2} (Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Polynomial.one.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))))))
+  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {p : Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))} {f : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))))} {B : Real}, (LT.lt.{0} Real Real.instLTReal B (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Polynomial.Monic.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Field.isDomain.{u1} K (NormedField.toField.{u1} K _inst_4)) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (Eq.{succ u2} (Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) 1 (One.toOfNat1.{u2} (Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Polynomial.one.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_one_of_roots_le Polynomial.eq_one_of_roots_leₓ'. -/
 theorem eq_one_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (hB : B < 0) (h1 : p.Monic)
     (h2 : Splits f p) (h3 : ∀ z ∈ (map f p).roots, ‖z‖ ≤ B) : p = 1 :=
@@ -220,7 +220,7 @@ theorem eq_one_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (hB : B < 0) (h1
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} [_inst_3 : CommRing.{u1} F] [_inst_4 : NormedField.{u2} K] {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))} {f : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (CommRing.toRing.{u1} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))))} {B : Real} (i : Nat), (Polynomial.Monic.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) -> (Polynomial.Splits.{u1, u2} F K _inst_3 (NormedField.toField.{u2} K _inst_4) f p) -> (forall (z : K), (Membership.Mem.{u2, u2} K (Multiset.{u2} K) (Multiset.hasMem.{u2} K) z (Polynomial.roots.{u2} K (SeminormedCommRing.toCommRing.{u2} K (NormedCommRing.toSeminormedCommRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4))) (Field.isDomain.{u2} K (NormedField.toField.{u2} K _inst_4)) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) z) B)) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) (Polynomial.coeff.{u2} K (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) B (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) (Nat.choose (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) i))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {p : Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))} {f : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))))} {B : Real} (i : Nat), (Polynomial.Monic.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) B (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) i)) (Nat.cast.{0} Real Real.natCast (Nat.choose (Polynomial.natDegree.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) i))))
+  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {p : Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))} {f : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))))} {B : Real} (i : Nat), (Polynomial.Monic.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Field.isDomain.{u1} K (NormedField.toField.{u1} K _inst_4)) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) B (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) i)) (Nat.cast.{0} Real Real.natCast (Nat.choose (Polynomial.natDegree.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) i))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_le_of_roots_le Polynomial.coeff_le_of_roots_leₓ'. -/
 theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1 : p.Monic)
     (h2 : Splits f p) (h3 : ∀ z ∈ (map f p).roots, ‖z‖ ≤ B) :
@@ -255,7 +255,7 @@ theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} [_inst_3 : CommRing.{u1} F] [_inst_4 : NormedField.{u2} K] {B : Real} {d : Nat} (f : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (CommRing.toRing.{u1} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))))) {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))}, (Polynomial.Monic.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) -> (Polynomial.Splits.{u1, u2} F K _inst_3 (NormedField.toField.{u2} K _inst_4) f p) -> (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) d) -> (forall (z : K), (Membership.Mem.{u2, u2} K (Multiset.{u2} K) (Multiset.hasMem.{u2} K) z (Polynomial.roots.{u2} K (SeminormedCommRing.toCommRing.{u2} K (NormedCommRing.toSeminormedCommRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4))) (Field.isDomain.{u2} K (NormedField.toField.{u2} K _inst_4)) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) z) B)) -> (forall (i : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) (Polynomial.coeff.{u2} K (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (LinearOrder.max.{0} Real Real.linearOrder B (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) d) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) (Nat.choose d (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.hasDiv) d (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {B : Real} {d : Nat} (f : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))))) {p : Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))}, (Polynomial.Monic.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) d) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (forall (i : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) B (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) d) (Nat.cast.{0} Real Real.natCast (Nat.choose d (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.instDivNat) d (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
+  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {B : Real} {d : Nat} (f : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))))) {p : Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))}, (Polynomial.Monic.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) d) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Field.isDomain.{u1} K (NormedField.toField.{u1} K _inst_4)) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (forall (i : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) B (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) d) (Nat.cast.{0} Real Real.natCast (Nat.choose d (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.instDivNat) d (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_bdd_of_roots_le Polynomial.coeff_bdd_of_roots_leₓ'. -/
 /-- The coefficients of the monic polynomials of bounded degree with bounded roots are
 uniformely bounded. -/

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

@@ -125,7 +125,7 @@ end TopologicalAlgebra
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {k : Type.{u3}} {α : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Ring.{u2} S] [_inst_3 : LinearOrderedField.{u3} k] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (abv : S -> k) [_inst_4 : IsAbsoluteValue.{u3, u2} k (StrictOrderedSemiring.toOrderedSemiring.{u3} k (StrictOrderedRing.toStrictOrderedSemiring.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3))))) S (Ring.toSemiring.{u2} S _inst_2) abv] (p : Polynomial.{u1} R _inst_1), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R _inst_1 p)) -> (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))))))))) -> (forall {l : Filter.{u4} α} {z : α -> S}, (Filter.Tendsto.{u4, u3} α k (Function.comp.{succ u4, succ u2, succ u3} α S k abv z) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3)))))))) -> (Filter.Tendsto.{u4, u3} α k (fun (x : α) => abv (Polynomial.eval₂.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S _inst_2) f (z x) p)) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3)))))))))
 but is expected to have type
-  forall {R : Type.{u4}} {S : Type.{u3}} {k : Type.{u2}} {α : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : Ring.{u3} S] [_inst_3 : LinearOrderedField.{u2} k] (f : RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S _inst_2))) (abv : S -> k) [_inst_4 : IsAbsoluteValue.{u2, u3} k (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_3))))) S (Ring.toSemiring.{u3} S _inst_2) abv] (p : Polynomial.{u4} R _inst_1), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u4} R _inst_1 p)) -> (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S _inst_2)))))) f (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (Ring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) _inst_2)))))) -> (forall {l : Filter.{u1} α} {z : α -> S}, (Filter.Tendsto.{u1, u2} α k (Function.comp.{succ u1, succ u3, succ u2} α S k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_3))))))) -> (Filter.Tendsto.{u1, u2} α k (fun (x : α) => abv (Polynomial.eval₂.{u4, u3} R S _inst_1 (Ring.toSemiring.{u3} S _inst_2) f (z x) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_3))))))))
+  forall {R : Type.{u4}} {S : Type.{u3}} {k : Type.{u2}} {α : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : Ring.{u3} S] [_inst_3 : LinearOrderedField.{u2} k] (f : RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) (abv : S -> k) [_inst_4 : IsAbsoluteValue.{u2, u3} k (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_3))))) S (Ring.toSemiring.{u3} S _inst_2) abv] (p : Polynomial.{u4} R _inst_1), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u4} R _inst_1 p)) -> (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))))) f (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) (Ring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u4} R _inst_1 p)) _inst_2)))))) -> (forall {l : Filter.{u1} α} {z : α -> S}, (Filter.Tendsto.{u1, u2} α k (Function.comp.{succ u1, succ u3, succ u2} α S k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_3))))))) -> (Filter.Tendsto.{u1, u2} α k (fun (x : α) => abv (Polynomial.eval₂.{u4, u3} R S _inst_1 (Ring.toSemiring.{u3} S _inst_2) f (z x) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_3))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_eval₂_at_top Polynomial.tendsto_abv_eval₂_atTopₓ'. -/
 theorem tendsto_abv_eval₂_atTop {R S k α : Type _} [Semiring R] [Ring S] [LinearOrderedField k]
     (f : R →+* S) (abv : S → k) [IsAbsoluteValue abv] (p : R[X]) (hd : 0 < degree p)
@@ -204,7 +204,7 @@ open Multiset
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} [_inst_3 : CommRing.{u1} F] [_inst_4 : NormedField.{u2} K] {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))} {f : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (CommRing.toRing.{u1} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))))} {B : Real}, (LT.lt.{0} Real Real.hasLt B (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Polynomial.Monic.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) -> (Polynomial.Splits.{u1, u2} F K _inst_3 (NormedField.toField.{u2} K _inst_4) f p) -> (forall (z : K), (Membership.Mem.{u2, u2} K (Multiset.{u2} K) (Multiset.hasMem.{u2} K) z (Polynomial.roots.{u2} K (SeminormedCommRing.toCommRing.{u2} K (NormedCommRing.toSeminormedCommRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4))) (Field.isDomain.{u2} K (NormedField.toField.{u2} K _inst_4)) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) z) B)) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) p (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) 1 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) 1 (One.one.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) (Polynomial.hasOne.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)))))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {p : Polynomial.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))} {f : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (CommRing.toRing.{u2} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_4)))))} {B : Real}, (LT.lt.{0} Real Real.instLTReal B (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Polynomial.Monic.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Polynomial.map.{u2, u1} F K (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (Eq.{succ u2} (Polynomial.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))) 1 (One.toOfNat1.{u2} (Polynomial.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))) (Polynomial.one.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))))))
+  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {p : Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))} {f : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))))} {B : Real}, (LT.lt.{0} Real Real.instLTReal B (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Polynomial.Monic.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (Eq.{succ u2} (Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) 1 (One.toOfNat1.{u2} (Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Polynomial.one.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_one_of_roots_le Polynomial.eq_one_of_roots_leₓ'. -/
 theorem eq_one_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (hB : B < 0) (h1 : p.Monic)
     (h2 : Splits f p) (h3 : ∀ z ∈ (map f p).roots, ‖z‖ ≤ B) : p = 1 :=
@@ -220,7 +220,7 @@ theorem eq_one_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (hB : B < 0) (h1
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} [_inst_3 : CommRing.{u1} F] [_inst_4 : NormedField.{u2} K] {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))} {f : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (CommRing.toRing.{u1} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))))} {B : Real} (i : Nat), (Polynomial.Monic.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) -> (Polynomial.Splits.{u1, u2} F K _inst_3 (NormedField.toField.{u2} K _inst_4) f p) -> (forall (z : K), (Membership.Mem.{u2, u2} K (Multiset.{u2} K) (Multiset.hasMem.{u2} K) z (Polynomial.roots.{u2} K (SeminormedCommRing.toCommRing.{u2} K (NormedCommRing.toSeminormedCommRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4))) (Field.isDomain.{u2} K (NormedField.toField.{u2} K _inst_4)) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) z) B)) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) (Polynomial.coeff.{u2} K (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) B (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) (Nat.choose (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) i))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {p : Polynomial.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))} {f : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (CommRing.toRing.{u2} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_4)))))} {B : Real} (i : Nat), (Polynomial.Monic.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Polynomial.map.{u2, u1} F K (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) (Polynomial.map.{u2, u1} F K (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) B (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) p) i)) (Nat.cast.{0} Real Real.natCast (Nat.choose (Polynomial.natDegree.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) p) i))))
+  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {p : Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))} {f : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))))} {B : Real} (i : Nat), (Polynomial.Monic.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) B (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) i)) (Nat.cast.{0} Real Real.natCast (Nat.choose (Polynomial.natDegree.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) i))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_le_of_roots_le Polynomial.coeff_le_of_roots_leₓ'. -/
 theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1 : p.Monic)
     (h2 : Splits f p) (h3 : ∀ z ∈ (map f p).roots, ‖z‖ ≤ B) :
@@ -255,7 +255,7 @@ theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} [_inst_3 : CommRing.{u1} F] [_inst_4 : NormedField.{u2} K] {B : Real} {d : Nat} (f : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (CommRing.toRing.{u1} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))))) {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))}, (Polynomial.Monic.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) -> (Polynomial.Splits.{u1, u2} F K _inst_3 (NormedField.toField.{u2} K _inst_4) f p) -> (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) d) -> (forall (z : K), (Membership.Mem.{u2, u2} K (Multiset.{u2} K) (Multiset.hasMem.{u2} K) z (Polynomial.roots.{u2} K (SeminormedCommRing.toCommRing.{u2} K (NormedCommRing.toSeminormedCommRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4))) (Field.isDomain.{u2} K (NormedField.toField.{u2} K _inst_4)) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) z) B)) -> (forall (i : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) (Polynomial.coeff.{u2} K (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (LinearOrder.max.{0} Real Real.linearOrder B (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) d) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) (Nat.choose d (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.hasDiv) d (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {B : Real} {d : Nat} (f : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (CommRing.toRing.{u2} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_4)))))) {p : Polynomial.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))}, (Polynomial.Monic.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) p) d) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Polynomial.map.{u2, u1} F K (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (forall (i : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) (Polynomial.map.{u2, u1} F K (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) B (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) d) (Nat.cast.{0} Real Real.natCast (Nat.choose d (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.instDivNat) d (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
+  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {B : Real} {d : Nat} (f : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))))) {p : Polynomial.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3))}, (Polynomial.Monic.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} F (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) p) d) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (forall (i : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) (Polynomial.map.{u2, u1} F K (CommSemiring.toSemiring.{u2} F (CommRing.toCommSemiring.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) B (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) d) (Nat.cast.{0} Real Real.natCast (Nat.choose d (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.instDivNat) d (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_bdd_of_roots_le Polynomial.coeff_bdd_of_roots_leₓ'. -/
 /-- The coefficients of the monic polynomials of bounded degree with bounded roots are
 uniformely bounded. -/

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis
 
 ! This file was ported from Lean 3 source module topology.algebra.polynomial
-! leanprover-community/mathlib commit 565eb991e264d0db702722b4bde52ee5173c9950
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Analysis.Normed.Field.Basic
 /-!
 # Polynomials and limits
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove the following lemmas.
 
 * `polynomial.continuous_eval₂: `polynomial.eval₂` defines a continuous function.

mathlib commit https://github.com/leanprover-community/mathlib/commit/0148d455199ed64bf8eb2f493a1e7eb9211ce170

@@ -48,6 +48,7 @@ section TopologicalSemiring
 
 variable {R S : Type _} [Semiring R] [TopologicalSpace R] [TopologicalSemiring R] (p : R[X])
 
+#print Polynomial.continuous_eval₂ /-
 @[continuity]
 protected theorem continuous_eval₂ [Semiring S] (p : S[X]) (f : S →+* R) :
     Continuous fun x => p.eval₂ f x :=
@@ -55,23 +56,32 @@ protected theorem continuous_eval₂ [Semiring S] (p : S[X]) (f : S →+* R) :
   simp only [eval₂_eq_sum, Finsupp.sum]
   exact continuous_finset_sum _ fun c hc => continuous_const.mul (continuous_pow _)
 #align polynomial.continuous_eval₂ Polynomial.continuous_eval₂
+-/
 
+#print Polynomial.continuous /-
 @[continuity]
 protected theorem continuous : Continuous fun x => p.eval x :=
   p.continuous_eval₂ _
 #align polynomial.continuous Polynomial.continuous
+-/
 
+#print Polynomial.continuousAt /-
 protected theorem continuousAt {a : R} : ContinuousAt (fun x => p.eval x) a :=
   p.Continuous.ContinuousAt
 #align polynomial.continuous_at Polynomial.continuousAt
+-/
 
+#print Polynomial.continuousWithinAt /-
 protected theorem continuousWithinAt {s a} : ContinuousWithinAt (fun x => p.eval x) s a :=
   p.Continuous.ContinuousWithinAt
 #align polynomial.continuous_within_at Polynomial.continuousWithinAt
+-/
 
+#print Polynomial.continuousOn /-
 protected theorem continuousOn {s} : ContinuousOn (fun x => p.eval x) s :=
   p.Continuous.ContinuousOn
 #align polynomial.continuous_on Polynomial.continuousOn
+-/
 
 end TopologicalSemiring
 
@@ -80,26 +90,40 @@ section TopologicalAlgebra
 variable {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A] [TopologicalSpace A]
   [TopologicalSemiring A] (p : R[X])
 
+#print Polynomial.continuous_aeval /-
 @[continuity]
 protected theorem continuous_aeval : Continuous fun x : A => aeval x p :=
   p.continuous_eval₂ _
 #align polynomial.continuous_aeval Polynomial.continuous_aeval
+-/
 
+#print Polynomial.continuousAt_aeval /-
 protected theorem continuousAt_aeval {a : A} : ContinuousAt (fun x : A => aeval x p) a :=
   p.continuous_aeval.ContinuousAt
 #align polynomial.continuous_at_aeval Polynomial.continuousAt_aeval
+-/
 
+#print Polynomial.continuousWithinAt_aeval /-
 protected theorem continuousWithinAt_aeval {s a} :
     ContinuousWithinAt (fun x : A => aeval x p) s a :=
   p.continuous_aeval.ContinuousWithinAt
 #align polynomial.continuous_within_at_aeval Polynomial.continuousWithinAt_aeval
+-/
 
+#print Polynomial.continuousOn_aeval /-
 protected theorem continuousOn_aeval {s} : ContinuousOn (fun x : A => aeval x p) s :=
   p.continuous_aeval.ContinuousOn
 #align polynomial.continuous_on_aeval Polynomial.continuousOn_aeval
+-/
 
 end TopologicalAlgebra
 
+/- warning: polynomial.tendsto_abv_eval₂_at_top -> Polynomial.tendsto_abv_eval₂_atTop is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} {k : Type.{u3}} {α : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Ring.{u2} S] [_inst_3 : LinearOrderedField.{u3} k] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (abv : S -> k) [_inst_4 : IsAbsoluteValue.{u3, u2} k (StrictOrderedSemiring.toOrderedSemiring.{u3} k (StrictOrderedRing.toStrictOrderedSemiring.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3))))) S (Ring.toSemiring.{u2} S _inst_2) abv] (p : Polynomial.{u1} R _inst_1), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R _inst_1 p)) -> (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))))))))) -> (forall {l : Filter.{u4} α} {z : α -> S}, (Filter.Tendsto.{u4, u3} α k (Function.comp.{succ u4, succ u2, succ u3} α S k abv z) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3)))))))) -> (Filter.Tendsto.{u4, u3} α k (fun (x : α) => abv (Polynomial.eval₂.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S _inst_2) f (z x) p)) l (Filter.atTop.{u3} k (PartialOrder.toPreorder.{u3} k (OrderedAddCommGroup.toPartialOrder.{u3} k (StrictOrderedRing.toOrderedAddCommGroup.{u3} k (LinearOrderedRing.toStrictOrderedRing.{u3} k (LinearOrderedCommRing.toLinearOrderedRing.{u3} k (LinearOrderedField.toLinearOrderedCommRing.{u3} k _inst_3)))))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_eval₂_at_top Polynomial.tendsto_abv_eval₂_atTopₓ'. -/
 theorem tendsto_abv_eval₂_atTop {R S k α : Type _} [Semiring R] [Ring S] [LinearOrderedField k]
     (f : R →+* S) (abv : S → k) [IsAbsoluteValue abv] (p : R[X]) (hd : 0 < degree p)
     (hf : f p.leadingCoeff ≠ 0) {l : Filter α} {z : α → S} (hz : Tendsto (abv ∘ z) l atTop) :
@@ -119,12 +143,24 @@ theorem tendsto_abv_eval₂_atTop {R S k α : Type _} [Semiring R] [Ring S] [Lin
     simpa using ihp hf
 #align polynomial.tendsto_abv_eval₂_at_top Polynomial.tendsto_abv_eval₂_atTop
 
+/- warning: polynomial.tendsto_abv_at_top -> Polynomial.tendsto_abv_atTop is a dubious translation:
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+  forall {R : Type.{u1}} {k : Type.{u2}} {α : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : LinearOrderedField.{u2} k] (abv : R -> k) [_inst_3 : IsAbsoluteValue.{u2, u1} k (StrictOrderedSemiring.toOrderedSemiring.{u2} k (StrictOrderedRing.toStrictOrderedSemiring.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_2))))) R (Ring.toSemiring.{u1} R _inst_1) abv] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) -> (forall {l : Filter.{u3} α} {z : α -> R}, (Filter.Tendsto.{u3, u2} α k (Function.comp.{succ u3, succ u1, succ u2} α R k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedAddCommGroup.toPartialOrder.{u2} k (StrictOrderedRing.toOrderedAddCommGroup.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_2)))))))) -> (Filter.Tendsto.{u3, u2} α k (fun (x : α) => abv (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) (z x) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedAddCommGroup.toPartialOrder.{u2} k (StrictOrderedRing.toOrderedAddCommGroup.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_2)))))))))
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+Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_at_top Polynomial.tendsto_abv_atTopₓ'. -/
 theorem tendsto_abv_atTop {R k α : Type _} [Ring R] [LinearOrderedField k] (abv : R → k)
     [IsAbsoluteValue abv] (p : R[X]) (h : 0 < degree p) {l : Filter α} {z : α → R}
     (hz : Tendsto (abv ∘ z) l atTop) : Tendsto (fun x => abv (p.eval (z x))) l atTop :=
   tendsto_abv_eval₂_atTop _ _ _ h (mt leadingCoeff_eq_zero.1 <| ne_zero_of_degree_gt h) hz
 #align polynomial.tendsto_abv_at_top Polynomial.tendsto_abv_atTop
 
+/- warning: polynomial.tendsto_abv_aeval_at_top -> Polynomial.tendsto_abv_aeval_atTop is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u4}} {A : Type.{u3}} {k : Type.{u2}} {α : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : Ring.{u3} A] [_inst_3 : Algebra.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2)] [_inst_4 : LinearOrderedField.{u2} k] (abv : A -> k) [_inst_5 : IsAbsoluteValue.{u2, u3} k (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_4))))) A (Ring.toSemiring.{u3} A _inst_2) abv] (p : Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) -> (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))) R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)) (RingHom.instRingHomClassRingHom.{u4, u3} R A (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (algebraMap.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) (Ring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.leadingCoeff.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1) p)) _inst_2)))))) -> (forall {l : Filter.{u1} α} {z : α -> A}, (Filter.Tendsto.{u1, u2} α k (Function.comp.{succ u1, succ u3, succ u2} α A k abv z) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_4))))))) -> (Filter.Tendsto.{u1, u2} α k (fun (x : α) => abv (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 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(Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Algebra.toModule.{u4, u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1))))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 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(Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u4, u4, u3} (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} 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(Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u4, u3, max u3 u4} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3 (AlgHom.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3) (AlgHom.algHomClass.{u4, u4, u3} R (Polynomial.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) A _inst_1 (Polynomial.semiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Ring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u4, u4} R R _inst_1 (CommSemiring.toSemiring.{u4} R _inst_1) (Algebra.id.{u4} R _inst_1)) _inst_3))))) (Polynomial.aeval.{u4, u3} R A _inst_1 (Ring.toSemiring.{u3} A _inst_2) _inst_3 (z x)) p)) l (Filter.atTop.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_4))))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.tendsto_abv_aeval_at_top Polynomial.tendsto_abv_aeval_atTopₓ'. -/
 theorem tendsto_abv_aeval_atTop {R A k α : Type _} [CommSemiring R] [Ring A] [Algebra R A]
     [LinearOrderedField k] (abv : A → k) [IsAbsoluteValue abv] (p : R[X]) (hd : 0 < degree p)
     (h₀ : algebraMap R A p.leadingCoeff ≠ 0) {l : Filter α} {z : α → A}
@@ -134,11 +170,19 @@ theorem tendsto_abv_aeval_atTop {R A k α : Type _} [CommSemiring R] [Ring A] [A
 
 variable {α R : Type _} [NormedRing R] [IsAbsoluteValue (norm : R → ℝ)]
 
+#print Polynomial.tendsto_norm_atTop /-
 theorem tendsto_norm_atTop (p : R[X]) (h : 0 < degree p) {l : Filter α} {z : α → R}
     (hz : Tendsto (fun x => ‖z x‖) l atTop) : Tendsto (fun x => ‖p.eval (z x)‖) l atTop :=
   p.tendsto_abv_atTop norm h hz
 #align polynomial.tendsto_norm_at_top Polynomial.tendsto_norm_atTop
+-/
 
+/- warning: polynomial.exists_forall_norm_le -> Polynomial.exists_forall_norm_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : IsAbsoluteValue.{0, u1} Real Real.orderedSemiring R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)) (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1))] [_inst_3 : ProperSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1))), Exists.{succ u1} R (fun (x : R) => forall (y : R), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)) x p)) (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)) y p)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : IsAbsoluteValue.{0, u1} Real Real.orderedSemiring R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)) (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1))] [_inst_3 : ProperSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1))), Exists.{succ u1} R (fun (x : R) => forall (y : R), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)) x p)) (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)) y p)))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_forall_norm_le Polynomial.exists_forall_norm_leₓ'. -/
 theorem exists_forall_norm_le [ProperSpace R] (p : R[X]) : ∃ x, ∀ y, ‖p.eval x‖ ≤ ‖p.eval y‖ :=
   if hp0 : 0 < degree p then
     p.Continuous.norm.exists_forall_le <| p.tendsto_norm_atTop hp0 tendsto_norm_cocompact_atTop
@@ -153,6 +197,12 @@ variable {F K : Type _} [CommRing F] [NormedField K]
 
 open Multiset
 
+/- warning: polynomial.eq_one_of_roots_le -> Polynomial.eq_one_of_roots_le is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {K : Type.{u2}} [_inst_3 : CommRing.{u1} F] [_inst_4 : NormedField.{u2} K] {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))} {f : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (CommRing.toRing.{u1} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))))} {B : Real}, (LT.lt.{0} Real Real.hasLt B (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Polynomial.Monic.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) -> (Polynomial.Splits.{u1, u2} F K _inst_3 (NormedField.toField.{u2} K _inst_4) f p) -> (forall (z : K), (Membership.Mem.{u2, u2} K (Multiset.{u2} K) (Multiset.hasMem.{u2} K) z (Polynomial.roots.{u2} K (SeminormedCommRing.toCommRing.{u2} K (NormedCommRing.toSeminormedCommRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4))) (Field.isDomain.{u2} K (NormedField.toField.{u2} K _inst_4)) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) z) B)) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) p (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) 1 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) 1 (One.one.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))) (Polynomial.hasOne.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)))))))
+but is expected to have type
+  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {p : Polynomial.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))} {f : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (CommRing.toRing.{u2} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_4)))))} {B : Real}, (LT.lt.{0} Real Real.instLTReal B (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Polynomial.Monic.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Polynomial.map.{u2, u1} F K (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (Eq.{succ u2} (Polynomial.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))) 1 (One.toOfNat1.{u2} (Polynomial.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))) (Polynomial.one.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.eq_one_of_roots_le Polynomial.eq_one_of_roots_leₓ'. -/
 theorem eq_one_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (hB : B < 0) (h1 : p.Monic)
     (h2 : Splits f p) (h3 : ∀ z ∈ (map f p).roots, ‖z‖ ≤ B) : p = 1 :=
   h1.natDegree_eq_zero_iff_eq_one.mp
@@ -163,6 +213,12 @@ theorem eq_one_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (hB : B < 0) (h1
       exact le_trans (norm_nonneg _) (h3 z hz))
 #align polynomial.eq_one_of_roots_le Polynomial.eq_one_of_roots_le
 
+/- warning: polynomial.coeff_le_of_roots_le -> Polynomial.coeff_le_of_roots_le is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {K : Type.{u2}} [_inst_3 : CommRing.{u1} F] [_inst_4 : NormedField.{u2} K] {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))} {f : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (CommRing.toRing.{u1} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))))} {B : Real} (i : Nat), (Polynomial.Monic.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) -> (Polynomial.Splits.{u1, u2} F K _inst_3 (NormedField.toField.{u2} K _inst_4) f p) -> (forall (z : K), (Membership.Mem.{u2, u2} K (Multiset.{u2} K) (Multiset.hasMem.{u2} K) z (Polynomial.roots.{u2} K (SeminormedCommRing.toCommRing.{u2} K (NormedCommRing.toSeminormedCommRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4))) (Field.isDomain.{u2} K (NormedField.toField.{u2} K _inst_4)) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) z) B)) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) (Polynomial.coeff.{u2} K (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) B (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) (Nat.choose (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) i))))
+but is expected to have type
+  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {p : Polynomial.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))} {f : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (CommRing.toRing.{u2} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_4)))))} {B : Real} (i : Nat), (Polynomial.Monic.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Polynomial.map.{u2, u1} F K (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) (Polynomial.map.{u2, u1} F K (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) B (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) p) i)) (Nat.cast.{0} Real Real.natCast (Nat.choose (Polynomial.natDegree.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) p) i))))
+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_le_of_roots_le Polynomial.coeff_le_of_roots_leₓ'. -/
 theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1 : p.Monic)
     (h2 : Splits f p) (h3 : ∀ z ∈ (map f p).roots, ‖z‖ ≤ B) :
     ‖(map f p).coeff i‖ ≤ B ^ (p.natDegree - i) * p.natDegree.choose i :=
@@ -192,6 +248,12 @@ theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1
   exact h3 z (mem_of_le hs.1 hz)
 #align polynomial.coeff_le_of_roots_le Polynomial.coeff_le_of_roots_le
 
+/- warning: polynomial.coeff_bdd_of_roots_le -> Polynomial.coeff_bdd_of_roots_le is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {K : Type.{u2}} [_inst_3 : CommRing.{u1} F] [_inst_4 : NormedField.{u2} K] {B : Real} {d : Nat} (f : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (CommRing.toRing.{u1} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))))) {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3))}, (Polynomial.Monic.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) -> (Polynomial.Splits.{u1, u2} F K _inst_3 (NormedField.toField.{u2} K _inst_4) f p) -> (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) p) d) -> (forall (z : K), (Membership.Mem.{u2, u2} K (Multiset.{u2} K) (Multiset.hasMem.{u2} K) z (Polynomial.roots.{u2} K (SeminormedCommRing.toCommRing.{u2} K (NormedCommRing.toSeminormedCommRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4))) (Field.isDomain.{u2} K (NormedField.toField.{u2} K _inst_4)) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) z) B)) -> (forall (i : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} K (NormedField.toHasNorm.{u2} K _inst_4) (Polynomial.coeff.{u2} K (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (NormedRing.toRing.{u2} K (NormedCommRing.toNormedRing.{u2} K (NormedField.toNormedCommRing.{u2} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (LinearOrder.max.{0} Real Real.linearOrder B (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) d) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) (Nat.choose d (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.hasDiv) d (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))
+but is expected to have type
+  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_3 : CommRing.{u2} F] [_inst_4 : NormedField.{u1} K] {B : Real} {d : Nat} (f : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (CommRing.toRing.{u2} F _inst_3))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_4)))))) {p : Polynomial.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3))}, (Polynomial.Monic.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) p) -> (Polynomial.Splits.{u2, u1} F K _inst_3 (NormedField.toField.{u1} K _inst_4) f p) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} F (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) p) d) -> (forall (z : K), (Membership.mem.{u1, u1} K (Multiset.{u1} K) (Multiset.instMembershipMultiset.{u1} K) z (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K _inst_4))) (Polynomial.map.{u2, u1} F K (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) z) B)) -> (forall (i : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_4) (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) (Polynomial.map.{u2, u1} F K (Ring.toSemiring.{u2} F (CommRing.toRing.{u2} F _inst_3)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_4)))) f p) i)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) B (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) d) (Nat.cast.{0} Real Real.natCast (Nat.choose d (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.instDivNat) d (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_bdd_of_roots_le Polynomial.coeff_bdd_of_roots_leₓ'. -/
 /-- The coefficients of the monic polynomials of bounded degree with bounded roots are
 uniformely bounded. -/
 theorem coeff_bdd_of_roots_le {B : ℝ} {d : ℕ} (f : F →+* K) {p : F[X]} (h1 : p.Monic)

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -204,7 +204,8 @@ theorem coeff_bdd_of_roots_le {B : ℝ} {d : ℕ} (f : F →+* K) {p : F[X]} (h1
       _ ≤ max B 1 ^ (p.nat_degree - i) * p.nat_degree.choose i :=
         mul_le_mul_of_nonneg_right (pow_le_pow_of_le_left hB (le_max_left _ _) _) _
       _ ≤ max B 1 ^ d * p.nat_degree.choose i :=
-        mul_le_mul_of_nonneg_right ((pow_mono (le_max_right _ _)) (le_trans (Nat.sub_le _ _) h3)) _
+        (mul_le_mul_of_nonneg_right ((pow_mono (le_max_right _ _)) (le_trans (Nat.sub_le _ _) h3))
+          _)
       _ ≤ max B 1 ^ d * d.choose (d / 2) :=
         mul_le_mul_of_nonneg_left
           (nat.cast_le.mpr ((i.choose_mono h3).trans (i.choose_le_middle d))) _

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

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

@@ -203,7 +203,9 @@ theorem coeff_bdd_of_roots_le {B : ℝ} {d : ℕ} (f : F →+* K) {p : F[X]} (h1
     calc
       _ ≤ max B 1 ^ (p.natDegree - i) * p.natDegree.choose i := by gcongr; apply le_max_left
       _ ≤ max B 1 ^ d * p.natDegree.choose i := by
-        gcongr; apply le_max_right; exact le_trans (Nat.sub_le _ _) h3
+        gcongr
+        · apply le_max_right
+        · exact le_trans (Nat.sub_le _ _) h3
       _ ≤ max B 1 ^ d * d.choose (d / 2) := by
         gcongr; exact (i.choose_mono h3).trans (i.choose_le_middle d)
   · rw [eq_one_of_roots_le hB h1 h2 h4, Polynomial.map_one, coeff_one]

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

@@ -124,7 +124,7 @@ theorem tendsto_abv_atTop {R k α : Type*} [Ring R] [LinearOrderedField k] (abv
     [IsAbsoluteValue abv] (p : R[X]) (h : 0 < degree p) {l : Filter α} {z : α → R}
     (hz : Tendsto (abv ∘ z) l atTop) : Tendsto (fun x => abv (p.eval (z x))) l atTop := by
   apply tendsto_abv_eval₂_atTop _ _ _ h _ hz
-  exact (mt leadingCoeff_eq_zero.1 (ne_zero_of_degree_gt h))
+  exact mt leadingCoeff_eq_zero.1 (ne_zero_of_degree_gt h)
 #align polynomial.tendsto_abv_at_top Polynomial.tendsto_abv_atTop
 
 theorem tendsto_abv_aeval_atTop {R A k α : Type*} [CommSemiring R] [Ring A] [Algebra R A]

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

@@ -3,11 +3,11 @@ Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis
 -/
-import Mathlib.Data.Polynomial.AlgebraMap
-import Mathlib.Data.Polynomial.Inductions
-import Mathlib.Data.Polynomial.Splits
-import Mathlib.RingTheory.Polynomial.Vieta
+import Mathlib.Algebra.Polynomial.AlgebraMap
+import Mathlib.Algebra.Polynomial.Inductions
+import Mathlib.Algebra.Polynomial.Splits
 import Mathlib.Analysis.Normed.Field.Basic
+import Mathlib.RingTheory.Polynomial.Vieta
 
 #align_import topology.algebra.polynomial from "leanprover-community/mathlib"@"565eb991e264d0db702722b4bde52ee5173c9950"
 

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

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

@@ -209,7 +209,7 @@ theorem coeff_bdd_of_roots_le {B : ℝ} {d : ℕ} (f : F →+* K) {p : F[X]} (h1
   · rw [eq_one_of_roots_le hB h1 h2 h4, Polynomial.map_one, coeff_one]
     refine' _root_.trans _
       (one_le_mul_of_one_le_of_one_le (one_le_pow_of_one_le (le_max_right B 1) d) _)
-    · split_ifs <;> norm_num
+    · split_ifs <;> set_option tactic.skipAssignedInstances false in norm_num
     · exact mod_cast Nat.succ_le_iff.mpr (Nat.choose_pos (d.div_le_self 2))
 #align polynomial.coeff_bdd_of_roots_le Polynomial.coeff_bdd_of_roots_le
 

@@ -23,8 +23,8 @@ In this file we prove the following lemmas.
 * `Polynomial.continuous`:  `Polynomial.eval` defines a continuous functions;
   we also prove convenience lemmas `Polynomial.continuousAt`, `Polynomial.continuousWithinAt`,
   `Polynomial.continuousOn`.
-* `Polynomial.tendsto_norm_atTop`: `fun x ↦‖Polynomial.eval (z x) p‖` tends to infinity
-  provided that `fun x ↦ ‖z x‖` tends to infinity and `0 < degree p`;
+* `Polynomial.tendsto_norm_atTop`: `fun x ↦ ‖Polynomial.eval (z x) p‖` tends to infinity provided
+  that `fun x ↦ ‖z x‖` tends to infinity and `0 < degree p`;
 * `Polynomial.tendsto_abv_eval₂_atTop`, `Polynomial.tendsto_abv_atTop`,
   `Polynomial.tendsto_abv_aeval_atTop`: a few versions of the previous statement for
   `IsAbsoluteValue abv` instead of norm.
@@ -45,26 +45,29 @@ section TopologicalSemiring
 
 variable {R S : Type*} [Semiring R] [TopologicalSpace R] [TopologicalSemiring R] (p : R[X])
 
-@[continuity]
+@[continuity, fun_prop]
 protected theorem continuous_eval₂ [Semiring S] (p : S[X]) (f : S →+* R) :
     Continuous fun x => p.eval₂ f x := by
   simp only [eval₂_eq_sum, Finsupp.sum]
   exact continuous_finset_sum _ fun c _ => continuous_const.mul (continuous_pow _)
 #align polynomial.continuous_eval₂ Polynomial.continuous_eval₂
 
-@[continuity]
+@[continuity, fun_prop]
 protected theorem continuous : Continuous fun x => p.eval x :=
   p.continuous_eval₂ _
 #align polynomial.continuous Polynomial.continuous
 
+@[fun_prop]
 protected theorem continuousAt {a : R} : ContinuousAt (fun x => p.eval x) a :=
   p.continuous.continuousAt
 #align polynomial.continuous_at Polynomial.continuousAt
 
+@[fun_prop]
 protected theorem continuousWithinAt {s a} : ContinuousWithinAt (fun x => p.eval x) s a :=
   p.continuous.continuousWithinAt
 #align polynomial.continuous_within_at Polynomial.continuousWithinAt
 
+@[fun_prop]
 protected theorem continuousOn {s} : ContinuousOn (fun x => p.eval x) s :=
   p.continuous.continuousOn
 #align polynomial.continuous_on Polynomial.continuousOn
@@ -76,20 +79,23 @@ section TopologicalAlgebra
 variable {R A : Type*} [CommSemiring R] [Semiring A] [Algebra R A] [TopologicalSpace A]
   [TopologicalSemiring A] (p : R[X])
 
-@[continuity]
+@[continuity, fun_prop]
 protected theorem continuous_aeval : Continuous fun x : A => aeval x p :=
   p.continuous_eval₂ _
 #align polynomial.continuous_aeval Polynomial.continuous_aeval
 
+@[fun_prop]
 protected theorem continuousAt_aeval {a : A} : ContinuousAt (fun x : A => aeval x p) a :=
   p.continuous_aeval.continuousAt
 #align polynomial.continuous_at_aeval Polynomial.continuousAt_aeval
 
+@[fun_prop]
 protected theorem continuousWithinAt_aeval {s a} :
     ContinuousWithinAt (fun x : A => aeval x p) s a :=
   p.continuous_aeval.continuousWithinAt
 #align polynomial.continuous_within_at_aeval Polynomial.continuousWithinAt_aeval
 
+@[fun_prop]
 protected theorem continuousOn_aeval {s} : ContinuousOn (fun x : A => aeval x p) s :=
   p.continuous_aeval.continuousOn
 #align polynomial.continuous_on_aeval Polynomial.continuousOn_aeval

Use Lean 4 syntax fun x ↦ instead, matching the style guide. This is close to exhaustive for doc comments; mathlib has about 460 remaining uses of λ (not all in Lean 3 syntax).

@@ -23,8 +23,8 @@ In this file we prove the following lemmas.
 * `Polynomial.continuous`:  `Polynomial.eval` defines a continuous functions;
   we also prove convenience lemmas `Polynomial.continuousAt`, `Polynomial.continuousWithinAt`,
   `Polynomial.continuousOn`.
-* `Polynomial.tendsto_norm_atTop`: `λ x, ‖Polynomial.eval (z x) p‖` tends to infinity provided that
-  `fun x ↦ ‖z x‖` tends to infinity and `0 < degree p`;
+* `Polynomial.tendsto_norm_atTop`: `fun x ↦‖Polynomial.eval (z x) p‖` tends to infinity
+  provided that `fun x ↦ ‖z x‖` tends to infinity and `0 < degree p`;
 * `Polynomial.tendsto_abv_eval₂_atTop`, `Polynomial.tendsto_abv_atTop`,
   `Polynomial.tendsto_abv_aeval_atTop`: a few versions of the previous statement for
   `IsAbsoluteValue abv` instead of norm.

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

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

@@ -204,7 +204,7 @@ theorem coeff_bdd_of_roots_le {B : ℝ} {d : ℕ} (f : F →+* K) {p : F[X]} (h1
     refine' _root_.trans _
       (one_le_mul_of_one_le_of_one_le (one_le_pow_of_one_le (le_max_right B 1) d) _)
     · split_ifs <;> norm_num
-    · exact_mod_cast Nat.succ_le_iff.mpr (Nat.choose_pos (d.div_le_self 2))
+    · exact mod_cast Nat.succ_le_iff.mpr (Nat.choose_pos (d.div_le_self 2))
 #align polynomial.coeff_bdd_of_roots_le Polynomial.coeff_bdd_of_roots_le
 
 end Roots

I don't understand why this was ever named powersetLen, there isn't even the notion of the length of a Finset/Multiset.

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

@@ -173,12 +173,12 @@ theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1
   rw [coeff_eq_esymm_roots_of_splits ((splits_id_iff_splits f).2 h2) hi, (h1.map _).leadingCoeff,
     one_mul, norm_mul, norm_pow, norm_neg, norm_one, one_pow, one_mul]
   apply ((norm_multiset_sum_le _).trans <| sum_le_card_nsmul _ _ fun r hr => _).trans
-  · rw [Multiset.map_map, card_map, card_powersetLen, ← natDegree_eq_card_roots' h2,
+  · rw [Multiset.map_map, card_map, card_powersetCard, ← natDegree_eq_card_roots' h2,
       Nat.choose_symm hi, mul_comm, nsmul_eq_mul]
   intro r hr
   simp_rw [Multiset.mem_map] at hr
   obtain ⟨_, ⟨s, hs, rfl⟩, rfl⟩ := hr
-  rw [mem_powersetLen] at hs
+  rw [mem_powersetCard] at hs
   lift B to ℝ≥0 using hB
   rw [← coe_nnnorm, ← NNReal.coe_pow, NNReal.coe_le_coe, ← nnnormHom_apply, ← MonoidHom.coe_coe,
     MonoidHom.map_multiset_prod]

Also rename dimH_image_le_of_locally_lipschitz_on to dimH_image_le_of_locally_lipschitzOn.

@@ -22,7 +22,7 @@ In this file we prove the following lemmas.
   `Polynomial.continuousWithinAt_aeval`, `Polynomial.continuousOn_aeval`.
 * `Polynomial.continuous`:  `Polynomial.eval` defines a continuous functions;
   we also prove convenience lemmas `Polynomial.continuousAt`, `Polynomial.continuousWithinAt`,
-  `Polynomial.continuous_on`.
+  `Polynomial.continuousOn`.
 * `Polynomial.tendsto_norm_atTop`: `λ x, ‖Polynomial.eval (z x) p‖` tends to infinity provided that
   `fun x ↦ ‖z x‖` tends to infinity and `0 < degree p`;
 * `Polynomial.tendsto_abv_eval₂_atTop`, `Polynomial.tendsto_abv_atTop`,

norm_num was passing the wrong syntax node to elabSimpArgs when elaborating, which essentially had the effect of ignoring all arguments it was passed, i.e. norm_num [add_comm] would not try to commute addition in the simp step. The fix itself is very simple (though not obvious to debug!), probably using TSyntax more would help avoid such issues in future.

Due to this bug many norm_num [blah] became rw [blah]; norm_num or similar, sometimes with porting notes, sometimes not, we fix these porting notes and other regressions during the port also.

Interestingly cancel_denoms uses norm_num [<- mul_assoc] internally, so cancel_denoms also got stronger with this change.

@@ -165,8 +165,7 @@ theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1
   obtain hB | hB := lt_or_le B 0
   · rw [eq_one_of_roots_le hB h1 h2 h3, Polynomial.map_one, natDegree_one, zero_tsub, pow_zero,
       one_mul, coeff_one]
-    split_ifs <;> norm_num [h]
-    simp [‹0 = i›]
+    split_ifs with h <;> simp [h]
   rw [← h1.natDegree_map f]
   obtain hi | hi := lt_or_le (map f p).natDegree i
   · rw [coeff_eq_zero_of_natDegree_lt hi, norm_zero]

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

This has nice performance benefits.

@@ -43,7 +43,7 @@ open Polynomial
 
 section TopologicalSemiring
 
-variable {R S : Type _} [Semiring R] [TopologicalSpace R] [TopologicalSemiring R] (p : R[X])
+variable {R S : Type*} [Semiring R] [TopologicalSpace R] [TopologicalSemiring R] (p : R[X])
 
 @[continuity]
 protected theorem continuous_eval₂ [Semiring S] (p : S[X]) (f : S →+* R) :
@@ -73,7 +73,7 @@ end TopologicalSemiring
 
 section TopologicalAlgebra
 
-variable {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A] [TopologicalSpace A]
+variable {R A : Type*} [CommSemiring R] [Semiring A] [Algebra R A] [TopologicalSpace A]
   [TopologicalSemiring A] (p : R[X])
 
 @[continuity]
@@ -96,7 +96,7 @@ protected theorem continuousOn_aeval {s} : ContinuousOn (fun x : A => aeval x p)
 
 end TopologicalAlgebra
 
-theorem tendsto_abv_eval₂_atTop {R S k α : Type _} [Semiring R] [Ring S] [LinearOrderedField k]
+theorem tendsto_abv_eval₂_atTop {R S k α : Type*} [Semiring R] [Ring S] [LinearOrderedField k]
     (f : R →+* S) (abv : S → k) [IsAbsoluteValue abv] (p : R[X]) (hd : 0 < degree p)
     (hf : f p.leadingCoeff ≠ 0) {l : Filter α} {z : α → S} (hz : Tendsto (abv ∘ z) l atTop) :
     Tendsto (fun x => abv (p.eval₂ f (z x))) l atTop := by
@@ -114,21 +114,21 @@ theorem tendsto_abv_eval₂_atTop {R S k α : Type _} [Semiring R] [Ring S] [Lin
     simpa using ihp hf
 #align polynomial.tendsto_abv_eval₂_at_top Polynomial.tendsto_abv_eval₂_atTop
 
-theorem tendsto_abv_atTop {R k α : Type _} [Ring R] [LinearOrderedField k] (abv : R → k)
+theorem tendsto_abv_atTop {R k α : Type*} [Ring R] [LinearOrderedField k] (abv : R → k)
     [IsAbsoluteValue abv] (p : R[X]) (h : 0 < degree p) {l : Filter α} {z : α → R}
     (hz : Tendsto (abv ∘ z) l atTop) : Tendsto (fun x => abv (p.eval (z x))) l atTop := by
   apply tendsto_abv_eval₂_atTop _ _ _ h _ hz
   exact (mt leadingCoeff_eq_zero.1 (ne_zero_of_degree_gt h))
 #align polynomial.tendsto_abv_at_top Polynomial.tendsto_abv_atTop
 
-theorem tendsto_abv_aeval_atTop {R A k α : Type _} [CommSemiring R] [Ring A] [Algebra R A]
+theorem tendsto_abv_aeval_atTop {R A k α : Type*} [CommSemiring R] [Ring A] [Algebra R A]
     [LinearOrderedField k] (abv : A → k) [IsAbsoluteValue abv] (p : R[X]) (hd : 0 < degree p)
     (h₀ : algebraMap R A p.leadingCoeff ≠ 0) {l : Filter α} {z : α → A}
     (hz : Tendsto (abv ∘ z) l atTop) : Tendsto (fun x => abv (aeval (z x) p)) l atTop :=
   tendsto_abv_eval₂_atTop _ abv p hd h₀ hz
 #align polynomial.tendsto_abv_aeval_at_top Polynomial.tendsto_abv_aeval_atTop
 
-variable {α R : Type _} [NormedRing R] [IsAbsoluteValue (norm : R → ℝ)]
+variable {α R : Type*} [NormedRing R] [IsAbsoluteValue (norm : R → ℝ)]
 
 theorem tendsto_norm_atTop (p : R[X]) (h : 0 < degree p) {l : Filter α} {z : α → R}
     (hz : Tendsto (fun x => ‖z x‖) l atTop) : Tendsto (fun x => ‖p.eval (z x)‖) l atTop :=
@@ -146,7 +146,7 @@ section Roots
 
 open Polynomial NNReal
 
-variable {F K : Type _} [CommRing F] [NormedField K]
+variable {F K : Type*} [CommRing F] [NormedField K]
 
 open Multiset
 

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis
-
-! This file was ported from Lean 3 source module topology.algebra.polynomial
-! leanprover-community/mathlib commit 565eb991e264d0db702722b4bde52ee5173c9950
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.AlgebraMap
 import Mathlib.Data.Polynomial.Inductions
@@ -14,6 +9,8 @@ import Mathlib.Data.Polynomial.Splits
 import Mathlib.RingTheory.Polynomial.Vieta
 import Mathlib.Analysis.Normed.Field.Basic
 
+#align_import topology.algebra.polynomial from "leanprover-community/mathlib"@"565eb991e264d0db702722b4bde52ee5173c9950"
+
 /-!
 # Polynomials and limits
 

I wrote a script to find lines that contain an odd number of backticks

@@ -19,8 +19,8 @@ import Mathlib.Analysis.Normed.Field.Basic
 
 In this file we prove the following lemmas.
 
-* `Polynomial.continuous_eval₂: `Polynomial.eval₂` defines a continuous function.
-* `Polynomial.continuous_aeval: `Polynomial.aeval` defines a continuous function;
+* `Polynomial.continuous_eval₂`: `Polynomial.eval₂` defines a continuous function.
+* `Polynomial.continuous_aeval`: `Polynomial.aeval` defines a continuous function;
   we also prove convenience lemmas `Polynomial.continuousAt_aeval`,
   `Polynomial.continuousWithinAt_aeval`, `Polynomial.continuousOn_aeval`.
 * `Polynomial.continuous`:  `Polynomial.eval` defines a continuous functions;

Found with git grep -n "λ [a-zA-Z_ ]*,"

@@ -27,7 +27,7 @@ In this file we prove the following lemmas.
   we also prove convenience lemmas `Polynomial.continuousAt`, `Polynomial.continuousWithinAt`,
   `Polynomial.continuous_on`.
 * `Polynomial.tendsto_norm_atTop`: `λ x, ‖Polynomial.eval (z x) p‖` tends to infinity provided that
-  `λ x, ‖z x‖` tends to infinity and `0 < degree p`;
+  `fun x ↦ ‖z x‖` tends to infinity and `0 < degree p`;
 * `Polynomial.tendsto_abv_eval₂_atTop`, `Polynomial.tendsto_abv_atTop`,
   `Polynomial.tendsto_abv_aeval_atTop`: a few versions of the previous statement for
   `IsAbsoluteValue abv` instead of norm.

100 sample uses of the new tactic gcongr, added in #3965.

@@ -199,14 +199,11 @@ theorem coeff_bdd_of_roots_le {B : ℝ} {d : ℕ} (f : F →+* K) {p : F[X]} (h1
   obtain hB | hB := le_or_lt 0 B
   · apply (coeff_le_of_roots_le i h1 h2 h4).trans
     calc
-      _ ≤ max B 1 ^ (p.natDegree - i) * p.natDegree.choose i :=
-        mul_le_mul_of_nonneg_right (pow_le_pow_of_le_left hB (le_max_left _ _) _) (by simp)
-      _ ≤ max B 1 ^ d * p.natDegree.choose i :=
-        (mul_le_mul_of_nonneg_right ((pow_mono (le_max_right _ _)) (le_trans (Nat.sub_le _ _) h3))
-          (by simp))
-      _ ≤ max B 1 ^ d * d.choose (d / 2) :=
-        mul_le_mul_of_nonneg_left
-          (Nat.cast_le.mpr ((i.choose_mono h3).trans (i.choose_le_middle d))) (by simp)
+      _ ≤ max B 1 ^ (p.natDegree - i) * p.natDegree.choose i := by gcongr; apply le_max_left
+      _ ≤ max B 1 ^ d * p.natDegree.choose i := by
+        gcongr; apply le_max_right; exact le_trans (Nat.sub_le _ _) h3
+      _ ≤ max B 1 ^ d * d.choose (d / 2) := by
+        gcongr; exact (i.choose_mono h3).trans (i.choose_le_middle d)
   · rw [eq_one_of_roots_le hB h1 h2 h4, Polynomial.map_one, coeff_one]
     refine' _root_.trans _
       (one_le_mul_of_one_le_of_one_le (one_le_pow_of_one_le (le_max_right B 1) d) _)

Run codespell Mathlib and keep some suggestions.

@@ -192,7 +192,7 @@ theorem coeff_le_of_roots_le {p : F[X]} {f : F →+* K} {B : ℝ} (i : ℕ) (h1
 #align polynomial.coeff_le_of_roots_le Polynomial.coeff_le_of_roots_le
 
 /-- The coefficients of the monic polynomials of bounded degree with bounded roots are
-uniformely bounded. -/
+uniformly bounded. -/
 theorem coeff_bdd_of_roots_le {B : ℝ} {d : ℕ} (f : F →+* K) {p : F[X]} (h1 : p.Monic)
     (h2 : Splits f p) (h3 : p.natDegree ≤ d) (h4 : ∀ z ∈ (map f p).roots, ‖z‖ ≤ B) (i : ℕ) :
     ‖(map f p).coeff i‖ ≤ max B 1 ^ d * d.choose (d / 2) := by

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

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

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

@@ -140,9 +140,9 @@ theorem tendsto_norm_atTop (p : R[X]) (h : 0 < degree p) {l : Filter α} {z : α
 
 theorem exists_forall_norm_le [ProperSpace R] (p : R[X]) : ∃ x, ∀ y, ‖p.eval x‖ ≤ ‖p.eval y‖ :=
   if hp0 : 0 < degree p then
-    set_option synthInstance.etaExperiment true in -- workaround for lean4#2074
-      p.continuous.norm.exists_forall_le <| p.tendsto_norm_atTop hp0 tendsto_norm_cocompact_atTop
-  else ⟨p.coeff 0, by rw [eq_C_of_degree_le_zero (le_of_not_gt hp0)]; simp⟩
+    p.continuous.norm.exists_forall_le <| p.tendsto_norm_atTop hp0 tendsto_norm_cocompact_atTop
+  else
+    ⟨p.coeff 0, by rw [eq_C_of_degree_le_zero (le_of_not_gt hp0)]; simp⟩
 #align polynomial.exists_forall_norm_le Polynomial.exists_forall_norm_le
 
 section Roots

@@ -30,7 +30,7 @@ In this file we prove the following lemmas.
   `λ x, ‖z x‖` tends to infinity and `0 < degree p`;
 * `Polynomial.tendsto_abv_eval₂_atTop`, `Polynomial.tendsto_abv_atTop`,
   `Polynomial.tendsto_abv_aeval_atTop`: a few versions of the previous statement for
-  `is_absolute_value abv` instead of norm.
+  `IsAbsoluteValue abv` instead of norm.
 
 ## Tags
 

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