number_theory.class_number.admissible_card_pow_degree ⟷ Mathlib.NumberTheory.ClassNumber.AdmissibleCardPowDegree

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

@@ -149,7 +149,7 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
   suffices (nat_degree (A i₁ % b - A i₀ % b) : ℝ) < b.nat_degree + log ε / log (Fintype.card Fq) by
     rwa [← Real.log_lt_log_iff (int.cast_pos.mpr (card_pow_degree.pos h')) hbε,
       card_pow_degree_nonzero _ h', card_pow_degree_nonzero _ hb, Algebra.smul_def, eq_intCast,
-      Int.cast_pow, Int.cast_ofNat, Int.cast_pow, Int.cast_ofNat,
+      Int.cast_pow, Int.cast_natCast, Int.cast_pow, Int.cast_natCast,
       log_mul (pow_ne_zero _ q_pos'.ne') hε.ne', ← rpow_nat_cast, ← rpow_nat_cast, log_rpow q_pos',
       log_rpow q_pos', ← lt_div_iff (log_pos one_lt_q'), add_div,
       mul_div_cancel_right₀ _ (log_pos one_lt_q').ne']
@@ -181,7 +181,7 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
   rw [card_pow_degree_nonzero _ hxz', card_pow_degree_nonzero _ hxy',
     card_pow_degree_nonzero _ hyz']
   have : (1 : ℤ) ≤ Fintype.card Fq := by exact_mod_cast (@Fintype.one_lt_card Fq _ _).le
-  simp only [Int.cast_pow, Int.cast_ofNat, le_max_iff]
+  simp only [Int.cast_pow, Int.cast_natCast, le_max_iff]
   refine' Or.imp (pow_le_pow_right this) (pow_le_pow_right this) _
   rw [nat_degree_le_iff_degree_le, nat_degree_le_iff_degree_le, ← le_max_iff, ←
     degree_eq_nat_degree hxy', ← degree_eq_nat_degree hyz']

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

@@ -6,7 +6,7 @@ Authors: Anne Baanen
 import NumberTheory.ClassNumber.AdmissibleAbsoluteValue
 import Analysis.SpecialFunctions.Pow.Real
 import RingTheory.Ideal.LocalRing
-import Data.Polynomial.Degree.CardPowDegree
+import Algebra.Polynomial.Degree.CardPowDegree
 
 #align_import number_theory.class_number.admissible_card_pow_degree from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
 

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

@@ -152,7 +152,7 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
       Int.cast_pow, Int.cast_ofNat, Int.cast_pow, Int.cast_ofNat,
       log_mul (pow_ne_zero _ q_pos'.ne') hε.ne', ← rpow_nat_cast, ← rpow_nat_cast, log_rpow q_pos',
       log_rpow q_pos', ← lt_div_iff (log_pos one_lt_q'), add_div,
-      mul_div_cancel _ (log_pos one_lt_q').ne']
+      mul_div_cancel_right₀ _ (log_pos one_lt_q').ne']
   -- And that result follows from manipulating the result from `exists_approx_polynomial_aux`
   -- to turn the `-⌈-stuff⌉₊` into `+ stuff`.
   refine' lt_of_lt_of_le (nat.cast_lt.mpr (with_bot.coe_lt_coe.mp _)) _

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

@@ -58,7 +58,7 @@ theorem exists_eq_polynomial [Semiring Fq] {d : ℕ} {m : ℕ} (hm : Fintype.car
     rw [coeff_eq_zero_of_degree_lt (lt_of_lt_of_le (hA _) hbj),
       coeff_eq_zero_of_degree_lt (lt_of_lt_of_le (hA _) hbj)]
   -- So we only need to look for the coefficients between `0` and `deg b`.
-  rw [not_le] at hbj 
+  rw [not_le] at hbj
   apply congr_fun i_eq.symm ⟨j, _⟩
   exact lt_of_lt_of_le (coe_lt_degree.mp hbj) hb
 #align polynomial.exists_eq_polynomial Polynomial.exists_eq_polynomial
@@ -75,7 +75,7 @@ theorem exists_approx_polynomial_aux [Ring Fq] {d : ℕ} {m : ℕ} (hm : Fintype
   have hb : b ≠ 0 := by
     rintro rfl
     specialize hA 0
-    rw [degree_zero] at hA 
+    rw [degree_zero] at hA
     exact not_lt_of_le bot_le hA
   -- Since there are > q^d elements of A, and only q^d choices for the highest `d` coefficients,
   -- there must be two elements of A with the same coefficients at
@@ -94,14 +94,14 @@ theorem exists_approx_polynomial_aux [Ring Fq] {d : ℕ} {m : ℕ} (hm : Fintype
     exact lt_of_le_of_lt (degree_sub_le _ _) (max_lt (hA _) (hA _))
   -- So we only need to look for the coefficients between `deg b - d` and `deg b`.
   rw [coeff_sub, sub_eq_zero]
-  rw [not_le, degree_eq_nat_degree hb, WithBot.coe_lt_coe] at hbj 
+  rw [not_le, degree_eq_nat_degree hb, WithBot.coe_lt_coe] at hbj
   have hj : nat_degree b - j.succ < d :=
     by
     by_cases hd : nat_degree b < d
     · exact lt_of_le_of_lt tsub_le_self hd
-    · rw [not_lt] at hd 
+    · rw [not_lt] at hd
       have := lt_of_le_of_lt hj (Nat.lt_succ_self j)
-      rwa [tsub_lt_iff_tsub_lt hd hbj] at this 
+      rwa [tsub_lt_iff_tsub_lt hd hbj] at this
   have : j = b.nat_degree - (nat_degree b - j.succ).succ := by
     rw [← Nat.succ_sub hbj, Nat.succ_sub_succ, tsub_tsub_cancel_of_le hbj.le]
   convert congr_fun i_eq.symm ⟨nat_degree b - j.succ, hj⟩
@@ -131,14 +131,14 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
   · obtain ⟨i₀, i₁, i_ne, mod_eq⟩ :=
       exists_eq_polynomial le_rfl b le_b (fun i => A i % b) fun i => EuclideanDomain.mod_lt (A i) hb
     refine' ⟨i₀, i₁, i_ne, _⟩
-    simp only at mod_eq 
+    simp only at mod_eq
     rwa [mod_eq, sub_self, AbsoluteValue.map_zero, Int.cast_zero]
   -- Otherwise, it suffices to choose two elements whose difference is of small enough degree.
-  rw [not_le] at le_b 
+  rw [not_le] at le_b
   obtain ⟨i₀, i₁, i_ne, deg_lt⟩ :=
     exists_approx_polynomial_aux le_rfl b (fun i => A i % b) fun i =>
       EuclideanDomain.mod_lt (A i) hb
-  simp only at deg_lt 
+  simp only at deg_lt
   use i₀, i₁, i_ne
   -- Again, if the remainders are equal we are done.
   by_cases h : A i₁ % b = A i₀ % b
@@ -176,7 +176,7 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
   · rwa [← hyz']
   by_cases hxz' : x = z
   · rwa [hxz', sub_self, AbsoluteValue.map_zero]
-  rw [← Ne.def, ← sub_ne_zero] at hxy' hyz' hxz' 
+  rw [← Ne.def, ← sub_ne_zero] at hxy' hyz' hxz'
   refine' lt_of_le_of_lt _ (max_lt hxy hyz)
   rw [card_pow_degree_nonzero _ hxz', card_pow_degree_nonzero _ hxy',
     card_pow_degree_nonzero _ hyz']
@@ -237,7 +237,7 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
       ∀ i : Fin n,
         t' i = j → (card_pow_degree (A 0 % b - A i.succ % b) : ℝ) < card_pow_degree b • ε :=
     by
-    by_contra this; push_neg at this 
+    by_contra this; push_neg at this
     obtain ⟨j₀, j₁, j_ne, approx⟩ :=
       exists_approx_polynomial hb hε
         (Fin.cons (A 0) fun j => A (Fin.succ (Classical.choose (this j))))
@@ -245,14 +245,14 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
     refine' Fin.cases _ (fun j₀ => _) j₀ <;>
       refine' Fin.cases (fun j_ne approx => _) (fun j₁ j_ne approx => _) j₁
     · exact absurd rfl j_ne
-    · rw [Fin.cons_succ, Fin.cons_zero, ← not_le, AbsoluteValue.map_sub] at approx 
+    · rw [Fin.cons_succ, Fin.cons_zero, ← not_le, AbsoluteValue.map_sub] at approx
       have := (Classical.choose_spec (this j₁)).2
       contradiction
-    · rw [Fin.cons_succ, Fin.cons_zero, ← not_le] at approx 
+    · rw [Fin.cons_succ, Fin.cons_zero, ← not_le] at approx
       have := (Classical.choose_spec (this j₀)).2
       contradiction
-    · rw [Fin.cons_succ, Fin.cons_succ] at approx 
-      rw [Ne.def, Fin.succ_inj] at j_ne 
+    · rw [Fin.cons_succ, Fin.cons_succ] at approx
+      rw [Ne.def, Fin.succ_inj] at j_ne
       have : j₀ = j₁ :=
         (Classical.choose_spec (this j₀)).1.symm.trans
           (((ht' (Classical.choose (this j₀)) (Classical.choose (this j₁))).mpr approx).trans

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

@@ -182,7 +182,7 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
     card_pow_degree_nonzero _ hyz']
   have : (1 : ℤ) ≤ Fintype.card Fq := by exact_mod_cast (@Fintype.one_lt_card Fq _ _).le
   simp only [Int.cast_pow, Int.cast_ofNat, le_max_iff]
-  refine' Or.imp (pow_le_pow this) (pow_le_pow this) _
+  refine' Or.imp (pow_le_pow_right this) (pow_le_pow_right this) _
   rw [nat_degree_le_iff_degree_le, nat_degree_le_iff_degree_le, ← le_max_iff, ←
     degree_eq_nat_degree hxy', ← degree_eq_nat_degree hyz']
   convert degree_add_le (x - y) (y - z) using 2

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

@@ -3,10 +3,10 @@ Copyright (c) 2021 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 -/
-import Mathbin.NumberTheory.ClassNumber.AdmissibleAbsoluteValue
-import Mathbin.Analysis.SpecialFunctions.Pow.Real
-import Mathbin.RingTheory.Ideal.LocalRing
-import Mathbin.Data.Polynomial.Degree.CardPowDegree
+import NumberTheory.ClassNumber.AdmissibleAbsoluteValue
+import Analysis.SpecialFunctions.Pow.Real
+import RingTheory.Ideal.LocalRing
+import Data.Polynomial.Degree.CardPowDegree
 
 #align_import number_theory.class_number.admissible_card_pow_degree from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module number_theory.class_number.admissible_card_pow_degree
-! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.NumberTheory.ClassNumber.AdmissibleAbsoluteValue
 import Mathbin.Analysis.SpecialFunctions.Pow.Real
 import Mathbin.RingTheory.Ideal.LocalRing
 import Mathbin.Data.Polynomial.Degree.CardPowDegree
 
+#align_import number_theory.class_number.admissible_card_pow_degree from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
+
 /-!
 # Admissible absolute values on polynomials
 

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

@@ -135,7 +135,7 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
       exists_eq_polynomial le_rfl b le_b (fun i => A i % b) fun i => EuclideanDomain.mod_lt (A i) hb
     refine' ⟨i₀, i₁, i_ne, _⟩
     simp only at mod_eq 
-    rwa [mod_eq, sub_self, map_zero, Int.cast_zero]
+    rwa [mod_eq, sub_self, AbsoluteValue.map_zero, Int.cast_zero]
   -- Otherwise, it suffices to choose two elements whose difference is of small enough degree.
   rw [not_le] at le_b 
   obtain ⟨i₀, i₁, i_ne, deg_lt⟩ :=
@@ -145,7 +145,7 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
   use i₀, i₁, i_ne
   -- Again, if the remainders are equal we are done.
   by_cases h : A i₁ % b = A i₀ % b
-  · rwa [h, sub_self, map_zero, Int.cast_zero]
+  · rwa [h, sub_self, AbsoluteValue.map_zero, Int.cast_zero]
   have h' : A i₁ % b - A i₀ % b ≠ 0 := mt sub_eq_zero.mp h
   -- If the remainders are not equal, we'll show their difference is of small degree.
   -- In particular, we'll show the degree is less than the following:
@@ -178,7 +178,7 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
   by_cases hyz' : y = z
   · rwa [← hyz']
   by_cases hxz' : x = z
-  · rwa [hxz', sub_self, map_zero]
+  · rwa [hxz', sub_self, AbsoluteValue.map_zero]
   rw [← Ne.def, ← sub_ne_zero] at hxy' hyz' hxz' 
   refine' lt_of_le_of_lt _ (max_lt hxy hyz)
   rw [card_pow_degree_nonzero _ hxz', card_pow_degree_nonzero _ hxy',

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

@@ -113,6 +113,7 @@ theorem exists_approx_polynomial_aux [Ring Fq] {d : ℕ} {m : ℕ} (hm : Fintype
 
 variable [Field Fq]
 
+#print Polynomial.exists_approx_polynomial /-
 /-- If `A` is a family of enough low-degree polynomials over a finite field,
 there is a pair of elements in `A` (with different indices but not necessarily
 distinct), such that the difference of their remainders is close together. -/
@@ -164,7 +165,9 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
   rw [← neg_div]
   exact le_of_eq (Nat.cast_sub le_b.le)
 #align polynomial.exists_approx_polynomial Polynomial.exists_approx_polynomial
+-/
 
+#print Polynomial.cardPowDegree_anti_archimedean /-
 /-- If `x` is close to `y` and `y` is close to `z`, then `x` and `z` are at least as close. -/
 theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowDegree (x - y) < a)
     (hyz : cardPowDegree (y - z) < a) : cardPowDegree (x - z) < a :=
@@ -188,7 +191,9 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
   convert degree_add_le (x - y) (y - z) using 2
   exact (sub_add_sub_cancel _ _ _).symm
 #align polynomial.card_pow_degree_anti_archimedean Polynomial.cardPowDegree_anti_archimedean
+-/
 
+#print Polynomial.exists_partition_polynomial_aux /-
 /-- A slightly stronger version of `exists_partition` on which we perform induction on `n`:
 for all `ε > 0`, we can partition the remainders of any family of polynomials `A`
 into equivalence classes, where the equivalence(!) relation is "closer than `ε`". -/
@@ -271,7 +276,9 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
   have := exists_nonempty_j ⟨t' i, ⟨i, rfl⟩, fun i' hi' => anti_archim' hi ((ht' _ _).mp hi')⟩
   contradiction
 #align polynomial.exists_partition_polynomial_aux Polynomial.exists_partition_polynomial_aux
+-/
 
+#print Polynomial.exists_partition_polynomial /-
 /-- For all `ε > 0`, we can partition the remainders of any family of polynomials `A`
 into classes, where all remainders in a class are close together. -/
 theorem exists_partition_polynomial (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b : Fq[X]} (hb : b ≠ 0)
@@ -283,7 +290,9 @@ theorem exists_partition_polynomial (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b : Fq[
   obtain ⟨t, ht⟩ := exists_partition_polynomial_aux n hε hb A
   exact ⟨t, fun i₀ i₁ hi => (ht i₀ i₁).mp hi⟩
 #align polynomial.exists_partition_polynomial Polynomial.exists_partition_polynomial
+-/
 
+#print Polynomial.cardPowDegreeIsAdmissible /-
 /-- `λ p, fintype.card Fq ^ degree p` is an admissible absolute value.
 We set `q ^ degree 0 = 0`. -/
 noncomputable def cardPowDegreeIsAdmissible :
@@ -294,6 +303,7 @@ noncomputable def cardPowDegreeIsAdmissible :
     card := fun ε => Fintype.card Fq ^ ⌈-log ε / log (Fintype.card Fq)⌉₊
     exists_partition' := fun n ε hε b hb => exists_partition_polynomial n hε hb }
 #align polynomial.card_pow_degree_is_admissible Polynomial.cardPowDegreeIsAdmissible
+-/
 
 end Polynomial
 

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

@@ -235,7 +235,7 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
       ∀ i : Fin n,
         t' i = j → (card_pow_degree (A 0 % b - A i.succ % b) : ℝ) < card_pow_degree b • ε :=
     by
-    by_contra this; push_neg  at this 
+    by_contra this; push_neg at this 
     obtain ⟨j₀, j₁, j_ne, approx⟩ :=
       exists_approx_polynomial hb hε
         (Fin.cons (A 0) fun j => A (Fin.succ (Classical.choose (this j))))

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

@@ -61,7 +61,7 @@ theorem exists_eq_polynomial [Semiring Fq] {d : ℕ} {m : ℕ} (hm : Fintype.car
     rw [coeff_eq_zero_of_degree_lt (lt_of_lt_of_le (hA _) hbj),
       coeff_eq_zero_of_degree_lt (lt_of_lt_of_le (hA _) hbj)]
   -- So we only need to look for the coefficients between `0` and `deg b`.
-  rw [not_le] at hbj
+  rw [not_le] at hbj 
   apply congr_fun i_eq.symm ⟨j, _⟩
   exact lt_of_lt_of_le (coe_lt_degree.mp hbj) hb
 #align polynomial.exists_eq_polynomial Polynomial.exists_eq_polynomial
@@ -78,7 +78,7 @@ theorem exists_approx_polynomial_aux [Ring Fq] {d : ℕ} {m : ℕ} (hm : Fintype
   have hb : b ≠ 0 := by
     rintro rfl
     specialize hA 0
-    rw [degree_zero] at hA
+    rw [degree_zero] at hA 
     exact not_lt_of_le bot_le hA
   -- Since there are > q^d elements of A, and only q^d choices for the highest `d` coefficients,
   -- there must be two elements of A with the same coefficients at
@@ -97,14 +97,14 @@ theorem exists_approx_polynomial_aux [Ring Fq] {d : ℕ} {m : ℕ} (hm : Fintype
     exact lt_of_le_of_lt (degree_sub_le _ _) (max_lt (hA _) (hA _))
   -- So we only need to look for the coefficients between `deg b - d` and `deg b`.
   rw [coeff_sub, sub_eq_zero]
-  rw [not_le, degree_eq_nat_degree hb, WithBot.coe_lt_coe] at hbj
+  rw [not_le, degree_eq_nat_degree hb, WithBot.coe_lt_coe] at hbj 
   have hj : nat_degree b - j.succ < d :=
     by
     by_cases hd : nat_degree b < d
     · exact lt_of_le_of_lt tsub_le_self hd
-    · rw [not_lt] at hd
+    · rw [not_lt] at hd 
       have := lt_of_le_of_lt hj (Nat.lt_succ_self j)
-      rwa [tsub_lt_iff_tsub_lt hd hbj] at this
+      rwa [tsub_lt_iff_tsub_lt hd hbj] at this 
   have : j = b.nat_degree - (nat_degree b - j.succ).succ := by
     rw [← Nat.succ_sub hbj, Nat.succ_sub_succ, tsub_tsub_cancel_of_le hbj.le]
   convert congr_fun i_eq.symm ⟨nat_degree b - j.succ, hj⟩
@@ -133,14 +133,14 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
   · obtain ⟨i₀, i₁, i_ne, mod_eq⟩ :=
       exists_eq_polynomial le_rfl b le_b (fun i => A i % b) fun i => EuclideanDomain.mod_lt (A i) hb
     refine' ⟨i₀, i₁, i_ne, _⟩
-    simp only at mod_eq
+    simp only at mod_eq 
     rwa [mod_eq, sub_self, map_zero, Int.cast_zero]
   -- Otherwise, it suffices to choose two elements whose difference is of small enough degree.
-  rw [not_le] at le_b
+  rw [not_le] at le_b 
   obtain ⟨i₀, i₁, i_ne, deg_lt⟩ :=
     exists_approx_polynomial_aux le_rfl b (fun i => A i % b) fun i =>
       EuclideanDomain.mod_lt (A i) hb
-  simp only at deg_lt
+  simp only at deg_lt 
   use i₀, i₁, i_ne
   -- Again, if the remainders are equal we are done.
   by_cases h : A i₁ % b = A i₀ % b
@@ -176,7 +176,7 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
   · rwa [← hyz']
   by_cases hxz' : x = z
   · rwa [hxz', sub_self, map_zero]
-  rw [← Ne.def, ← sub_ne_zero] at hxy' hyz' hxz'
+  rw [← Ne.def, ← sub_ne_zero] at hxy' hyz' hxz' 
   refine' lt_of_le_of_lt _ (max_lt hxy hyz)
   rw [card_pow_degree_nonzero _ hxz', card_pow_degree_nonzero _ hxy',
     card_pow_degree_nonzero _ hyz']
@@ -235,7 +235,7 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
       ∀ i : Fin n,
         t' i = j → (card_pow_degree (A 0 % b - A i.succ % b) : ℝ) < card_pow_degree b • ε :=
     by
-    by_contra this; push_neg  at this
+    by_contra this; push_neg  at this 
     obtain ⟨j₀, j₁, j_ne, approx⟩ :=
       exists_approx_polynomial hb hε
         (Fin.cons (A 0) fun j => A (Fin.succ (Classical.choose (this j))))
@@ -243,14 +243,14 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
     refine' Fin.cases _ (fun j₀ => _) j₀ <;>
       refine' Fin.cases (fun j_ne approx => _) (fun j₁ j_ne approx => _) j₁
     · exact absurd rfl j_ne
-    · rw [Fin.cons_succ, Fin.cons_zero, ← not_le, AbsoluteValue.map_sub] at approx
+    · rw [Fin.cons_succ, Fin.cons_zero, ← not_le, AbsoluteValue.map_sub] at approx 
       have := (Classical.choose_spec (this j₁)).2
       contradiction
-    · rw [Fin.cons_succ, Fin.cons_zero, ← not_le] at approx
+    · rw [Fin.cons_succ, Fin.cons_zero, ← not_le] at approx 
       have := (Classical.choose_spec (this j₀)).2
       contradiction
-    · rw [Fin.cons_succ, Fin.cons_succ] at approx
-      rw [Ne.def, Fin.succ_inj] at j_ne
+    · rw [Fin.cons_succ, Fin.cons_succ] at approx 
+      rw [Ne.def, Fin.succ_inj] at j_ne 
       have : j₀ = j₁ :=
         (Classical.choose_spec (this j₀)).1.symm.trans
           (((ht' (Classical.choose (this j₀)) (Classical.choose (this j₁))).mpr approx).trans

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

@@ -31,12 +31,13 @@ use to show the class number of the ring of integers of a function field is fini
 
 namespace Polynomial
 
-open Polynomial
+open scoped Polynomial
 
 open AbsoluteValue Real
 
 variable {Fq : Type _} [Fintype Fq]
 
+#print Polynomial.exists_eq_polynomial /-
 /-- If `A` is a family of enough low-degree polynomials over a finite semiring, there is a
 pair of equal elements in `A`. -/
 theorem exists_eq_polynomial [Semiring Fq] {d : ℕ} {m : ℕ} (hm : Fintype.card Fq ^ d ≤ m)
@@ -64,7 +65,9 @@ theorem exists_eq_polynomial [Semiring Fq] {d : ℕ} {m : ℕ} (hm : Fintype.car
   apply congr_fun i_eq.symm ⟨j, _⟩
   exact lt_of_lt_of_le (coe_lt_degree.mp hbj) hb
 #align polynomial.exists_eq_polynomial Polynomial.exists_eq_polynomial
+-/
 
+#print Polynomial.exists_approx_polynomial_aux /-
 /-- If `A` is a family of enough low-degree polynomials over a finite ring,
 there is a pair of elements in `A` (with different indices but not necessarily
 distinct), such that their difference has small degree. -/
@@ -106,6 +109,7 @@ theorem exists_approx_polynomial_aux [Ring Fq] {d : ℕ} {m : ℕ} (hm : Fintype
     rw [← Nat.succ_sub hbj, Nat.succ_sub_succ, tsub_tsub_cancel_of_le hbj.le]
   convert congr_fun i_eq.symm ⟨nat_degree b - j.succ, hj⟩
 #align polynomial.exists_approx_polynomial_aux Polynomial.exists_approx_polynomial_aux
+-/
 
 variable [Field Fq]
 

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

@@ -37,12 +37,6 @@ open AbsoluteValue Real
 
 variable {Fq : Type _} [Fintype Fq]
 
-/- warning: polynomial.exists_eq_polynomial -> Polynomial.exists_eq_polynomial is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align polynomial.exists_eq_polynomial Polynomial.exists_eq_polynomialₓ'. -/
 /-- If `A` is a family of enough low-degree polynomials over a finite semiring, there is a
 pair of equal elements in `A`. -/
 theorem exists_eq_polynomial [Semiring Fq] {d : ℕ} {m : ℕ} (hm : Fintype.card Fq ^ d ≤ m)
@@ -71,12 +65,6 @@ theorem exists_eq_polynomial [Semiring Fq] {d : ℕ} {m : ℕ} (hm : Fintype.car
   exact lt_of_lt_of_le (coe_lt_degree.mp hbj) hb
 #align polynomial.exists_eq_polynomial Polynomial.exists_eq_polynomial
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.exists_approx_polynomial_aux Polynomial.exists_approx_polynomial_auxₓ'. -/
 /-- If `A` is a family of enough low-degree polynomials over a finite ring,
 there is a pair of elements in `A` (with different indices but not necessarily
 distinct), such that their difference has small degree. -/
@@ -121,9 +109,6 @@ theorem exists_approx_polynomial_aux [Ring Fq] {d : ℕ} {m : ℕ} (hm : Fintype
 
 variable [Field Fq]
 
-/- warning: polynomial.exists_approx_polynomial -> Polynomial.exists_approx_polynomial is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.exists_approx_polynomial Polynomial.exists_approx_polynomialₓ'. -/
 /-- If `A` is a family of enough low-degree polynomials over a finite field,
 there is a pair of elements in `A` (with different indices but not necessarily
 distinct), such that the difference of their remainders is close together. -/
@@ -176,9 +161,6 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
   exact le_of_eq (Nat.cast_sub le_b.le)
 #align polynomial.exists_approx_polynomial Polynomial.exists_approx_polynomial
 
-/- warning: polynomial.card_pow_degree_anti_archimedean -> Polynomial.cardPowDegree_anti_archimedean is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.card_pow_degree_anti_archimedean Polynomial.cardPowDegree_anti_archimedeanₓ'. -/
 /-- If `x` is close to `y` and `y` is close to `z`, then `x` and `z` are at least as close. -/
 theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowDegree (x - y) < a)
     (hyz : cardPowDegree (y - z) < a) : cardPowDegree (x - z) < a :=
@@ -203,9 +185,6 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
   exact (sub_add_sub_cancel _ _ _).symm
 #align polynomial.card_pow_degree_anti_archimedean Polynomial.cardPowDegree_anti_archimedean
 
-/- warning: polynomial.exists_partition_polynomial_aux -> Polynomial.exists_partition_polynomial_aux is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.exists_partition_polynomial_aux Polynomial.exists_partition_polynomial_auxₓ'. -/
 /-- A slightly stronger version of `exists_partition` on which we perform induction on `n`:
 for all `ε > 0`, we can partition the remainders of any family of polynomials `A`
 into equivalence classes, where the equivalence(!) relation is "closer than `ε`". -/
@@ -289,9 +268,6 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
   contradiction
 #align polynomial.exists_partition_polynomial_aux Polynomial.exists_partition_polynomial_aux
 
-/- warning: polynomial.exists_partition_polynomial -> Polynomial.exists_partition_polynomial is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.exists_partition_polynomial Polynomial.exists_partition_polynomialₓ'. -/
 /-- For all `ε > 0`, we can partition the remainders of any family of polynomials `A`
 into classes, where all remainders in a class are close together. -/
 theorem exists_partition_polynomial (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b : Fq[X]} (hb : b ≠ 0)
@@ -304,12 +280,6 @@ theorem exists_partition_polynomial (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b : Fq[
   exact ⟨t, fun i₀ i₁ hi => (ht i₀ i₁).mp hi⟩
 #align polynomial.exists_partition_polynomial Polynomial.exists_partition_polynomial
 
-/- warning: polynomial.card_pow_degree_is_admissible -> Polynomial.cardPowDegreeIsAdmissible is a dubious translation:
-lean 3 declaration is
-  forall {Fq : Type.{u1}} [_inst_1 : Fintype.{u1} Fq] [_inst_2 : Field.{u1} Fq], AbsoluteValue.IsAdmissible.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.euclideanDomain.{u1} Fq _inst_2) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1)
-but is expected to have type
-  forall {Fq : Type.{u1}} [_inst_1 : Fintype.{u1} Fq] [_inst_2 : Field.{u1} Fq], AbsoluteValue.IsAdmissible.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} Fq _inst_2) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1)
-Case conversion may be inaccurate. Consider using '#align polynomial.card_pow_degree_is_admissible Polynomial.cardPowDegreeIsAdmissibleₓ'. -/
 /-- `λ p, fintype.card Fq ^ degree p` is an admissible absolute value.
 We set `q ^ degree 0 = 0`. -/
 noncomputable def cardPowDegreeIsAdmissible :

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

@@ -169,9 +169,7 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
   -- And that result follows from manipulating the result from `exists_approx_polynomial_aux`
   -- to turn the `-⌈-stuff⌉₊` into `+ stuff`.
   refine' lt_of_lt_of_le (nat.cast_lt.mpr (with_bot.coe_lt_coe.mp _)) _
-  swap
-  · convert deg_lt
-    rw [degree_eq_nat_degree h']
+  swap; · convert deg_lt; rw [degree_eq_nat_degree h']
   rw [← sub_neg_eq_add, neg_div]
   refine' le_trans _ (sub_le_sub_left (Nat.le_ceil _) (b.nat_degree : ℝ))
   rw [← neg_div]
@@ -254,8 +252,7 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
       ∀ i : Fin n,
         t' i = j → (card_pow_degree (A 0 % b - A i.succ % b) : ℝ) < card_pow_degree b • ε :=
     by
-    by_contra this
-    push_neg  at this
+    by_contra this; push_neg  at this
     obtain ⟨j₀, j₁, j_ne, approx⟩ :=
       exists_approx_polynomial hb hε
         (Fin.cons (A 0) fun j => A (Fin.succ (Classical.choose (this j))))

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

@@ -122,10 +122,7 @@ theorem exists_approx_polynomial_aux [Ring Fq] {d : ℕ} {m : ℕ} (hm : Fintype
 variable [Field Fq]
 
 /- warning: polynomial.exists_approx_polynomial -> Polynomial.exists_approx_polynomial is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_approx_polynomial Polynomial.exists_approx_polynomialₓ'. -/
 /-- If `A` is a family of enough low-degree polynomials over a finite field,
 there is a pair of elements in `A` (with different indices but not necessarily
@@ -182,10 +179,7 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
 #align polynomial.exists_approx_polynomial Polynomial.exists_approx_polynomial
 
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Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (fun (f : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) f) (SubadditiveHomClass.toFunLike.{u1, u1, 0} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) x y)) a) -> (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) y z)) Int.instLTInt (FunLike.coe.{succ u1, succ u1, 1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (fun (f : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) f) (SubadditiveHomClass.toFunLike.{u1, u1, 0} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) y z)) a) -> (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) x z)) Int.instLTInt (FunLike.coe.{succ u1, succ u1, 1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (fun (f : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) f) (SubadditiveHomClass.toFunLike.{u1, u1, 0} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) x z)) a)
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.card_pow_degree_anti_archimedean Polynomial.cardPowDegree_anti_archimedeanₓ'. -/
 /-- If `x` is close to `y` and `y` is close to `z`, then `x` and `z` are at least as close. -/
 theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowDegree (x - y) < a)
@@ -212,10 +206,7 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
 #align polynomial.card_pow_degree_anti_archimedean Polynomial.cardPowDegree_anti_archimedean
 
 /- warning: polynomial.exists_partition_polynomial_aux -> Polynomial.exists_partition_polynomial_aux is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_partition_polynomial_aux Polynomial.exists_partition_polynomial_auxₓ'. -/
 /-- A slightly stronger version of `exists_partition` on which we perform induction on `n`:
 for all `ε > 0`, we can partition the remainders of any family of polynomials `A`
@@ -302,10 +293,7 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
 #align polynomial.exists_partition_polynomial_aux Polynomial.exists_partition_polynomial_aux
 
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(LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Real.log ε)) (Real.log (Nat.cast.{0} Real Real.natCast (Fintype.card.{u1} Fq _inst_1)))))))) => forall (i₀ : Fin n) (i₁ : Fin n), (Eq.{1} (Fin (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (Fintype.card.{u1} Fq _inst_1) (Nat.ceil.{0} Real Real.orderedSemiring (FloorRing.toFloorSemiring.{0} Real Real.instLinearOrderedRingReal Real.instFloorRingRealInstLinearOrderedRingReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Real.log ε)) (Real.log (Nat.cast.{0} Real Real.natCast (Fintype.card.{u1} Fq _inst_1))))))) (t i₀) (t i₁)) -> (LT.lt.{0} Real Real.instLTReal (Int.cast.{0} Real Real.intCast (FunLike.coe.{succ u1, succ u1, 1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (fun (f : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) f) (SubadditiveHomClass.toFunLike.{u1, u1, 0} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHMod.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.instModPolynomialToSemiringToDivisionSemiringToSemifield.{u1} Fq _inst_2)) (A i₁) b) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHMod.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.instModPolynomialToSemiringToDivisionSemiringToSemifield.{u1} Fq _inst_2)) (A i₀) b)))) (HSMul.hSMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) b) Real Real (instHSMul.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) b) Real (SubNegMonoid.SMulInt.{0} Real (AddGroup.toSubNegMonoid.{0} Real Real.instAddGroupReal))) (FunLike.coe.{succ u1, succ u1, 1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (fun (f : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) f) (SubadditiveHomClass.toFunLike.{u1, u1, 0} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) b) ε)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_partition_polynomial Polynomial.exists_partition_polynomialₓ'. -/
 /-- For all `ε > 0`, we can partition the remainders of any family of polynomials `A`
 into classes, where all remainders in a class are close together. -/

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module number_theory.class_number.admissible_card_pow_degree
-! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
+! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Data.Polynomial.Degree.CardPowDegree
 /-!
 # Admissible absolute values on polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines an admissible absolute value `polynomial.card_pow_degree_is_admissible` which we
 use to show the class number of the ring of integers of a function field is finite.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -34,6 +34,12 @@ open AbsoluteValue Real
 
 variable {Fq : Type _} [Fintype Fq]
 
+/- warning: polynomial.exists_eq_polynomial -> Polynomial.exists_eq_polynomial is a dubious translation:
+lean 3 declaration is
+  forall {Fq : Type.{u1}} [_inst_1 : Fintype.{u1} Fq] [_inst_2 : Semiring.{u1} Fq] {d : Nat} {m : Nat}, (LE.le.{0} Nat Nat.hasLe (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (Fintype.card.{u1} Fq _inst_1) d) m) -> (forall (b : Polynomial.{u1} Fq _inst_2), (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} Fq _inst_2 b) d) -> (forall (A : (Fin (Nat.succ m)) -> (Polynomial.{u1} Fq _inst_2)), (forall (i : Fin (Nat.succ m)), 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))))) (Polynomial.degree.{u1} Fq _inst_2 (A i)) (Polynomial.degree.{u1} Fq _inst_2 b)) -> (Exists.{1} (Fin (Nat.succ m)) (fun (i₀ : Fin (Nat.succ m)) => Exists.{1} (Fin (Nat.succ m)) (fun (i₁ : Fin (Nat.succ m)) => And (Ne.{1} (Fin (Nat.succ m)) i₀ i₁) (Eq.{succ u1} (Polynomial.{u1} Fq _inst_2) (A i₁) (A i₀)))))))
+but is expected to have type
+  forall {Fq : Type.{u1}} [_inst_1 : Fintype.{u1} Fq] [_inst_2 : Semiring.{u1} Fq] {d : Nat} {m : Nat}, (LE.le.{0} Nat instLENat (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (Fintype.card.{u1} Fq _inst_1) d) m) -> (forall (b : Polynomial.{u1} Fq _inst_2), (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} Fq _inst_2 b) d) -> (forall (A : (Fin (Nat.succ m)) -> (Polynomial.{u1} Fq _inst_2)), (forall (i : Fin (Nat.succ m)), 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)))) (Polynomial.degree.{u1} Fq _inst_2 (A i)) (Polynomial.degree.{u1} Fq _inst_2 b)) -> (Exists.{1} (Fin (Nat.succ m)) (fun (i₀ : Fin (Nat.succ m)) => Exists.{1} (Fin (Nat.succ m)) (fun (i₁ : Fin (Nat.succ m)) => And (Ne.{1} (Fin (Nat.succ m)) i₀ i₁) (Eq.{succ u1} (Polynomial.{u1} Fq _inst_2) (A i₁) (A i₀)))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_eq_polynomial Polynomial.exists_eq_polynomialₓ'. -/
 /-- If `A` is a family of enough low-degree polynomials over a finite semiring, there is a
 pair of equal elements in `A`. -/
 theorem exists_eq_polynomial [Semiring Fq] {d : ℕ} {m : ℕ} (hm : Fintype.card Fq ^ d ≤ m)
@@ -62,6 +68,12 @@ theorem exists_eq_polynomial [Semiring Fq] {d : ℕ} {m : ℕ} (hm : Fintype.car
   exact lt_of_lt_of_le (coe_lt_degree.mp hbj) hb
 #align polynomial.exists_eq_polynomial Polynomial.exists_eq_polynomial
 
+/- warning: polynomial.exists_approx_polynomial_aux -> Polynomial.exists_approx_polynomial_aux is a dubious translation:
+lean 3 declaration is
+  forall {Fq : Type.{u1}} [_inst_1 : Fintype.{u1} Fq] [_inst_2 : Ring.{u1} Fq] {d : Nat} {m : Nat}, (LE.le.{0} Nat Nat.hasLe (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (Fintype.card.{u1} Fq _inst_1) d) m) -> (forall (b : Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq _inst_2)) (A : (Fin (Nat.succ m)) -> (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq _inst_2))), (forall (i : Fin (Nat.succ m)), 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))))) (Polynomial.degree.{u1} Fq (Ring.toSemiring.{u1} Fq _inst_2) (A i)) (Polynomial.degree.{u1} Fq (Ring.toSemiring.{u1} Fq _inst_2) b)) -> (Exists.{1} (Fin (Nat.succ m)) (fun (i₀ : Fin (Nat.succ m)) => Exists.{1} (Fin (Nat.succ m)) (fun (i₁ : Fin (Nat.succ m)) => And (Ne.{1} (Fin (Nat.succ m)) i₀ i₁) (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))))) (Polynomial.degree.{u1} Fq (Ring.toSemiring.{u1} Fq _inst_2) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq _inst_2)) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq _inst_2)) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq _inst_2)) (instHSub.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq _inst_2)) (Polynomial.sub.{u1} Fq _inst_2)) (A i₁) (A i₀))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} Fq (Ring.toSemiring.{u1} Fq _inst_2) b) d)))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.exists_approx_polynomial_aux Polynomial.exists_approx_polynomial_auxₓ'. -/
 /-- If `A` is a family of enough low-degree polynomials over a finite ring,
 there is a pair of elements in `A` (with different indices but not necessarily
 distinct), such that their difference has small degree. -/
@@ -106,6 +118,12 @@ theorem exists_approx_polynomial_aux [Ring Fq] {d : ℕ} {m : ℕ} (hm : Fintype
 
 variable [Field Fq]
 
+/- warning: polynomial.exists_approx_polynomial -> Polynomial.exists_approx_polynomial is a dubious translation:
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0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Real.log ε)) (Real.log (Nat.cast.{0} Real Real.natCast (Fintype.card.{u1} Fq _inst_1)))))))) (fun (i₁ : Fin (Nat.succ (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (Fintype.card.{u1} Fq _inst_1) (Nat.ceil.{0} Real Real.orderedSemiring (FloorRing.toFloorSemiring.{0} Real Real.instLinearOrderedRingReal Real.instFloorRingRealInstLinearOrderedRingReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Real.log ε)) (Real.log (Nat.cast.{0} Real Real.natCast (Fintype.card.{u1} Fq _inst_1)))))))) => And (Ne.{1} (Fin (Nat.succ (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (Fintype.card.{u1} Fq _inst_1) (Nat.ceil.{0} Real Real.orderedSemiring (FloorRing.toFloorSemiring.{0} Real 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(Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (fun (f : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) f) (SubadditiveHomClass.toFunLike.{u1, u1, 0} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHMod.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.instModPolynomialToSemiringToDivisionSemiringToSemifield.{u1} Fq _inst_2)) (A i₁) b) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHMod.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.instModPolynomialToSemiringToDivisionSemiringToSemifield.{u1} Fq _inst_2)) (A i₀) b)))) (HSMul.hSMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) b) Real Real (instHSMul.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) b) Real (SubNegMonoid.SMulInt.{0} Real (AddGroup.toSubNegMonoid.{0} Real Real.instAddGroupReal))) (FunLike.coe.{succ u1, succ u1, 1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (fun (f : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) f) (SubadditiveHomClass.toFunLike.{u1, u1, 0} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) b) ε))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_approx_polynomial Polynomial.exists_approx_polynomialₓ'. -/
 /-- If `A` is a family of enough low-degree polynomials over a finite field,
 there is a pair of elements in `A` (with different indices but not necessarily
 distinct), such that the difference of their remainders is close together. -/
@@ -160,6 +178,12 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
   exact le_of_eq (Nat.cast_sub le_b.le)
 #align polynomial.exists_approx_polynomial Polynomial.exists_approx_polynomial
 
+/- warning: polynomial.card_pow_degree_anti_archimedean -> Polynomial.cardPowDegree_anti_archimedean is a dubious translation:
+lean 3 declaration is
+  forall {Fq : Type.{u1}} [_inst_1 : Fintype.{u1} Fq] [_inst_2 : Field.{u1} Fq] {x : Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))} {y : Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))} {z : Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))} {a : Int}, (LT.lt.{0} Int Int.hasLt (coeFn.{succ u1, succ u1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (StrictOrderedSemiring.toOrderedSemiring.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) 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(StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) x y)) a) -> (LT.lt.{0} Int Int.hasLt (coeFn.{succ u1, succ u1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (StrictOrderedSemiring.toOrderedSemiring.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (fun (f : AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (StrictOrderedSemiring.toOrderedSemiring.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) => (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) -> Int) (AbsoluteValue.hasCoeToFun.{u1, 0} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (StrictOrderedSemiring.toOrderedSemiring.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) y z)) a) -> (LT.lt.{0} Int Int.hasLt (coeFn.{succ u1, succ u1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (StrictOrderedSemiring.toOrderedSemiring.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (fun (f : AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (StrictOrderedSemiring.toOrderedSemiring.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) => (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) -> Int) (AbsoluteValue.hasCoeToFun.{u1, 0} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (StrictOrderedSemiring.toOrderedSemiring.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) x z)) a)
+but is expected to have type
+  forall {Fq : Type.{u1}} [_inst_1 : Fintype.{u1} Fq] [_inst_2 : Field.{u1} Fq] {x : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))} {y : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))} {z : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))} {a : Int}, (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) x y)) Int.instLTInt (FunLike.coe.{succ u1, succ u1, 1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (fun (f : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) f) (SubadditiveHomClass.toFunLike.{u1, u1, 0} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) x y)) a) -> (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) y z)) Int.instLTInt (FunLike.coe.{succ u1, succ u1, 1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (fun (f : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) f) (SubadditiveHomClass.toFunLike.{u1, u1, 0} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) y z)) a) -> (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) x z)) Int.instLTInt (FunLike.coe.{succ u1, succ u1, 1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (fun (f : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) f) (SubadditiveHomClass.toFunLike.{u1, u1, 0} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) x z)) a)
+Case conversion may be inaccurate. Consider using '#align polynomial.card_pow_degree_anti_archimedean Polynomial.cardPowDegree_anti_archimedeanₓ'. -/
 /-- If `x` is close to `y` and `y` is close to `z`, then `x` and `z` are at least as close. -/
 theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowDegree (x - y) < a)
     (hyz : cardPowDegree (y - z) < a) : cardPowDegree (x - z) < a :=
@@ -184,6 +208,12 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
   exact (sub_add_sub_cancel _ _ _).symm
 #align polynomial.card_pow_degree_anti_archimedean Polynomial.cardPowDegree_anti_archimedean
 
+/- warning: polynomial.exists_partition_polynomial_aux -> Polynomial.exists_partition_polynomial_aux is a dubious translation:
+lean 3 declaration is
+  forall {Fq : Type.{u1}} [_inst_1 : Fintype.{u1} Fq] [_inst_2 : Field.{u1} Fq] (n : Nat) {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (forall {b : Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) b (OfNat.ofNat.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) 0 (Zero.zero.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.zero.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq 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+but is expected to have type
+  forall {Fq : Type.{u1}} [_inst_1 : Fintype.{u1} Fq] [_inst_2 : Field.{u1} Fq] (n : Nat) {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (forall {b : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) b (OfNat.ofNat.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.zero.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2))))))) -> (forall (A : (Fin n) -> (Polynomial.{u1} 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(Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq 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(HSMul.hSMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) b) Real Real (instHSMul.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) b) Real (SubNegMonoid.SMulInt.{0} Real (AddGroup.toSubNegMonoid.{0} Real Real.instAddGroupReal))) (FunLike.coe.{succ u1, succ u1, 1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (fun (f : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) f) (SubadditiveHomClass.toFunLike.{u1, u1, 0} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) b) ε)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_partition_polynomial_aux Polynomial.exists_partition_polynomial_auxₓ'. -/
 /-- A slightly stronger version of `exists_partition` on which we perform induction on `n`:
 for all `ε > 0`, we can partition the remainders of any family of polynomials `A`
 into equivalence classes, where the equivalence(!) relation is "closer than `ε`". -/
@@ -268,6 +298,12 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
   contradiction
 #align polynomial.exists_partition_polynomial_aux Polynomial.exists_partition_polynomial_aux
 
+/- warning: polynomial.exists_partition_polynomial -> Polynomial.exists_partition_polynomial is a dubious translation:
+lean 3 declaration is
+  forall {Fq : Type.{u1}} [_inst_1 : Fintype.{u1} Fq] [_inst_2 : Field.{u1} Fq] (n : Nat) {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (forall {b : Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) b (OfNat.ofNat.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) 0 (Zero.zero.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.zero.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq 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Real Real.orderedSemiring (FloorRing.toFloorSemiring.{0} Real Real.linearOrderedRing Real.floorRing) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Neg.neg.{0} Real Real.hasNeg (Real.log ε)) (Real.log ((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))) (Fintype.card.{u1} Fq _inst_1)))))))) => forall (i₀ : Fin n) (i₁ : Fin n), (Eq.{1} (Fin (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (Fintype.card.{u1} Fq _inst_1) (Nat.ceil.{0} Real Real.orderedSemiring (FloorRing.toFloorSemiring.{0} Real Real.linearOrderedRing Real.floorRing) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Neg.neg.{0} Real Real.hasNeg (Real.log ε)) (Real.log 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(Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (StrictOrderedSemiring.toOrderedSemiring.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) => (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) -> Int) (AbsoluteValue.hasCoeToFun.{u1, 0} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (StrictOrderedSemiring.toOrderedSemiring.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (instHMod.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.hasMod.{u1} Fq _inst_2)) (A i₁) b) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (instHMod.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.hasMod.{u1} Fq _inst_2)) (A i₀) b)))) (SMul.smul.{0, 0} Int Real (SubNegMonoid.SMulInt.{0} Real (AddGroup.toSubNegMonoid.{0} Real Real.addGroup)) (coeFn.{succ u1, succ u1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (StrictOrderedSemiring.toOrderedSemiring.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (fun (f : AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (StrictOrderedSemiring.toOrderedSemiring.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) => (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) -> Int) (AbsoluteValue.hasCoeToFun.{u1, 0} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (StrictOrderedSemiring.toOrderedSemiring.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) b) ε)))))
+but is expected to have type
+  forall {Fq : Type.{u1}} [_inst_1 : Fintype.{u1} Fq] [_inst_2 : Field.{u1} Fq] (n : Nat) {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (forall {b : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) b (OfNat.ofNat.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.zero.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2))))))) -> (forall (A : (Fin n) -> (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2))))), Exists.{1} ((Fin n) -> (Fin (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (Fintype.card.{u1} Fq _inst_1) (Nat.ceil.{0} Real Real.orderedSemiring (FloorRing.toFloorSemiring.{0} Real Real.instLinearOrderedRingReal Real.instFloorRingRealInstLinearOrderedRingReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Real.log ε)) (Real.log (Nat.cast.{0} Real Real.natCast (Fintype.card.{u1} Fq _inst_1)))))))) (fun (t : (Fin n) -> (Fin (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (Fintype.card.{u1} Fq _inst_1) (Nat.ceil.{0} Real Real.orderedSemiring (FloorRing.toFloorSemiring.{0} Real Real.instLinearOrderedRingReal Real.instFloorRingRealInstLinearOrderedRingReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Real.log ε)) (Real.log (Nat.cast.{0} Real Real.natCast (Fintype.card.{u1} Fq _inst_1)))))))) => forall (i₀ : Fin n) (i₁ : Fin n), (Eq.{1} (Fin (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (Fintype.card.{u1} Fq _inst_1) (Nat.ceil.{0} Real Real.orderedSemiring (FloorRing.toFloorSemiring.{0} Real Real.instLinearOrderedRingReal Real.instFloorRingRealInstLinearOrderedRingReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Real.log ε)) (Real.log (Nat.cast.{0} Real Real.natCast (Fintype.card.{u1} Fq _inst_1))))))) (t i₀) (t i₁)) -> (LT.lt.{0} Real Real.instLTReal (Int.cast.{0} Real Real.intCast (FunLike.coe.{succ u1, succ u1, 1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (fun (f : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) f) (SubadditiveHomClass.toFunLike.{u1, u1, 0} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHSub.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.sub.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHMod.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.instModPolynomialToSemiringToDivisionSemiringToSemifield.{u1} Fq _inst_2)) (A i₁) b) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (instHMod.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.instModPolynomialToSemiringToDivisionSemiringToSemifield.{u1} Fq _inst_2)) (A i₀) b)))) (HSMul.hSMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) b) Real Real (instHSMul.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) b) Real (SubNegMonoid.SMulInt.{0} Real (AddGroup.toSubNegMonoid.{0} Real Real.instAddGroupReal))) (FunLike.coe.{succ u1, succ u1, 1} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (fun (f : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) => Int) f) (SubadditiveHomClass.toFunLike.{u1, u1, 0} (AbsoluteValue.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Distrib.toAdd.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))))))) (Distrib.toAdd.{0} Int (NonUnitalNonAssocSemiring.toDistrib.{0} Int (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Int (Semiring.toNonAssocSemiring.{0} Int (OrderedSemiring.toSemiring.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))))) (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedSemiring.toPartialOrder.{0} Int (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))))) (AbsoluteValue.subadditiveHomClass.{u1, 0} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) Int (Polynomial.semiring.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (OrderedCommSemiring.toOrderedSemiring.{0} Int (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Int (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing)))))) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1) b) ε)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_partition_polynomial Polynomial.exists_partition_polynomialₓ'. -/
 /-- For all `ε > 0`, we can partition the remainders of any family of polynomials `A`
 into classes, where all remainders in a class are close together. -/
 theorem exists_partition_polynomial (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b : Fq[X]} (hb : b ≠ 0)
@@ -280,6 +316,12 @@ theorem exists_partition_polynomial (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b : Fq[
   exact ⟨t, fun i₀ i₁ hi => (ht i₀ i₁).mp hi⟩
 #align polynomial.exists_partition_polynomial Polynomial.exists_partition_polynomial
 
+/- warning: polynomial.card_pow_degree_is_admissible -> Polynomial.cardPowDegreeIsAdmissible is a dubious translation:
+lean 3 declaration is
+  forall {Fq : Type.{u1}} [_inst_1 : Fintype.{u1} Fq] [_inst_2 : Field.{u1} Fq], AbsoluteValue.IsAdmissible.{u1} (Polynomial.{u1} Fq (Ring.toSemiring.{u1} Fq (DivisionRing.toRing.{u1} Fq (Field.toDivisionRing.{u1} Fq _inst_2)))) (Polynomial.euclideanDomain.{u1} Fq _inst_2) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1)
+but is expected to have type
+  forall {Fq : Type.{u1}} [_inst_1 : Fintype.{u1} Fq] [_inst_2 : Field.{u1} Fq], AbsoluteValue.IsAdmissible.{u1} (Polynomial.{u1} Fq (DivisionSemiring.toSemiring.{u1} Fq (Semifield.toDivisionSemiring.{u1} Fq (Field.toSemifield.{u1} Fq _inst_2)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} Fq _inst_2) (Polynomial.cardPowDegree.{u1} Fq _inst_2 _inst_1)
+Case conversion may be inaccurate. Consider using '#align polynomial.card_pow_degree_is_admissible Polynomial.cardPowDegreeIsAdmissibleₓ'. -/
 /-- `λ p, fintype.card Fq ^ degree p` is an admissible absolute value.
 We set `q ^ degree 0 = 0`. -/
 noncomputable def cardPowDegreeIsAdmissible :

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

@@ -4,20 +4,20 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module number_theory.class_number.admissible_card_pow_degree
-! leanprover-community/mathlib commit 6155d4351090a6fad236e3d2e4e0e4e7342668e8
+! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.NumberTheory.ClassNumber.AdmissibleAbsoluteValue
-import Mathbin.Analysis.SpecialFunctions.Pow
+import Mathbin.Analysis.SpecialFunctions.Pow.Real
 import Mathbin.RingTheory.Ideal.LocalRing
 import Mathbin.Data.Polynomial.Degree.CardPowDegree
 
 /-!
 # Admissible absolute values on polynomials
-This file defines an admissible absolute value
-`polynomial.card_pow_degree_is_admissible` which we use to show the class number
-of the ring of integers of a function field is finite.
+
+This file defines an admissible absolute value `polynomial.card_pow_degree_is_admissible` which we
+use to show the class number of the ring of integers of a function field is finite.
 
 ## Main results
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af

@@ -44,7 +44,7 @@ theorem exists_eq_polynomial [Semiring Fq] {d : ℕ} {m : ℕ} (hm : Fintype.car
   -- there must be two elements of A with the same coefficients at
   -- `0`, ... `degree b - 1` ≤ `d - 1`.
   -- In other words, the following map is not injective:
-  set f : Fin m.succ → Fin d → Fq := fun i j => (A i).coeff j
+  set f : Fin m.succ → Fin d → Fq := fun i j => (A i).Coeff j
   have : Fintype.card (Fin d → Fq) < Fintype.card (Fin m.succ) := by
     simpa using lt_of_le_of_lt hm (Nat.lt_succ_self m)
   -- Therefore, the differences have all coefficients higher than `deg b - d` equal.
@@ -78,7 +78,7 @@ theorem exists_approx_polynomial_aux [Ring Fq] {d : ℕ} {m : ℕ} (hm : Fintype
   -- there must be two elements of A with the same coefficients at
   -- `degree b - 1`, ... `degree b - d`.
   -- In other words, the following map is not injective:
-  set f : Fin m.succ → Fin d → Fq := fun i j => (A i).coeff (nat_degree b - j.succ)
+  set f : Fin m.succ → Fin d → Fq := fun i j => (A i).Coeff (nat_degree b - j.succ)
   have : Fintype.card (Fin d → Fq) < Fintype.card (Fin m.succ) := by
     simpa using lt_of_le_of_lt hm (Nat.lt_succ_self m)
   -- Therefore, the differences have all coefficients higher than `deg b - d` equal.

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

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

@@ -134,7 +134,7 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
     rwa [← Real.log_lt_log_iff (Int.cast_pos.mpr (cardPowDegree.pos h')) hbε,
       cardPowDegree_nonzero _ h', cardPowDegree_nonzero _ hb, Algebra.smul_def, eq_intCast,
       Int.cast_pow, Int.cast_natCast, Int.cast_pow, Int.cast_natCast,
-      log_mul (pow_ne_zero _ q_pos'.ne') hε.ne', ← rpow_nat_cast, ← rpow_nat_cast, log_rpow q_pos',
+      log_mul (pow_ne_zero _ q_pos'.ne') hε.ne', ← rpow_natCast, ← rpow_natCast, log_rpow q_pos',
       log_rpow q_pos', ← lt_div_iff (log_pos one_lt_q'), add_div,
       mul_div_cancel_right₀ _ (log_pos one_lt_q').ne']
   -- And that result follows from manipulating the result from `exists_approx_polynomial_aux`

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -159,7 +159,7 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
   · rwa [← hyz']
   by_cases hxz' : x = z
   · rwa [hxz', sub_self, map_zero]
-  rw [← Ne.def, ← sub_ne_zero] at hxy' hyz' hxz'
+  rw [← Ne, ← sub_ne_zero] at hxy' hyz' hxz'
   refine' lt_of_le_of_lt _ (max_lt hxy hyz)
   rw [cardPowDegree_nonzero _ hxz', cardPowDegree_nonzero _ hxy',
     cardPowDegree_nonzero _ hyz']

This renames

• Int.cast_ofNat to Int.cast_natCast
• Int.int_cast_ofNat to Int.cast_ofNat

I think the history here is that this lemma was previously about Int.ofNat, before we globally fixed the simp-normal form to be Nat.cast.

Since the Int.cast_ofNat name is repurposed, it can't be deprecated. Int.int_cast_ofNat is such a wonky name that it was probably never used.

@@ -133,7 +133,7 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
   suffices (natDegree (A i₁ % b - A i₀ % b) : ℝ) < b.natDegree + log ε / log (Fintype.card Fq) by
     rwa [← Real.log_lt_log_iff (Int.cast_pos.mpr (cardPowDegree.pos h')) hbε,
       cardPowDegree_nonzero _ h', cardPowDegree_nonzero _ hb, Algebra.smul_def, eq_intCast,
-      Int.cast_pow, Int.cast_ofNat, Int.cast_pow, Int.cast_ofNat,
+      Int.cast_pow, Int.cast_natCast, Int.cast_pow, Int.cast_natCast,
       log_mul (pow_ne_zero _ q_pos'.ne') hε.ne', ← rpow_nat_cast, ← rpow_nat_cast, log_rpow q_pos',
       log_rpow q_pos', ← lt_div_iff (log_pos one_lt_q'), add_div,
       mul_div_cancel_right₀ _ (log_pos one_lt_q').ne']
@@ -164,7 +164,7 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
   rw [cardPowDegree_nonzero _ hxz', cardPowDegree_nonzero _ hxy',
     cardPowDegree_nonzero _ hyz']
   have : (1 : ℤ) ≤ Fintype.card Fq := mod_cast (@Fintype.one_lt_card Fq _ _).le
-  simp only [Int.cast_pow, Int.cast_ofNat, le_max_iff]
+  simp only [Int.cast_pow, Int.cast_natCast, le_max_iff]
   refine' Or.imp (pow_le_pow_right this) (pow_le_pow_right this) _
   rw [natDegree_le_iff_degree_le, natDegree_le_iff_degree_le, ← le_max_iff, ←
     degree_eq_natDegree hxy', ← degree_eq_natDegree hyz']

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

@@ -3,10 +3,10 @@ Copyright (c) 2021 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 -/
-import Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue
+import Mathlib.Algebra.Polynomial.Degree.CardPowDegree
 import Mathlib.Analysis.SpecialFunctions.Pow.Real
+import Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue
 import Mathlib.RingTheory.Ideal.LocalRing
-import Mathlib.Data.Polynomial.Degree.CardPowDegree
 
 #align_import number_theory.class_number.admissible_card_pow_degree from "leanprover-community/mathlib"@"0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8"
 

@@ -224,7 +224,7 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
       have := (Classical.choose_spec (hg j₀)).2
       contradiction
     · rw [Fin.cons_succ, Fin.cons_succ] at approx
-      rw [Ne.def, Fin.succ_inj] at j_ne
+      rw [Ne, Fin.succ_inj] at j_ne
       have : j₀ = j₁ := (Classical.choose_spec (hg j₀)).1.symm.trans
         (((ht' (Classical.choose (hg j₀)) (Classical.choose (hg j₁))).mpr approx).trans
           (Classical.choose_spec (hg j₁)).1)

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -136,7 +136,7 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
       Int.cast_pow, Int.cast_ofNat, Int.cast_pow, Int.cast_ofNat,
       log_mul (pow_ne_zero _ q_pos'.ne') hε.ne', ← rpow_nat_cast, ← rpow_nat_cast, log_rpow q_pos',
       log_rpow q_pos', ← lt_div_iff (log_pos one_lt_q'), add_div,
-      mul_div_cancel _ (log_pos one_lt_q').ne']
+      mul_div_cancel_right₀ _ (log_pos one_lt_q').ne']
   -- And that result follows from manipulating the result from `exists_approx_polynomial_aux`
   -- to turn the `-⌈-stuff⌉₊` into `+ stuff`.
   refine' lt_of_lt_of_le (Nat.cast_lt.mpr (WithBot.coe_lt_coe.mp _)) _

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

@@ -111,7 +111,7 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
     exact mul_pos (Int.cast_pos.mpr (AbsoluteValue.pos _ hb)) hε
   have one_lt_q : 1 < Fintype.card Fq := Fintype.one_lt_card
   have one_lt_q' : (1 : ℝ) < Fintype.card Fq := by assumption_mod_cast
-  have q_pos : 0 < Fintype.card Fq := by linarith
+  have q_pos : 0 < Fintype.card Fq := by omega
   have q_pos' : (0 : ℝ) < Fintype.card Fq := by assumption_mod_cast
   -- If `b` is already small enough, then the remainders are equal and we are done.
   by_cases le_b : b.natDegree ≤ ⌈-log ε / log (Fintype.card Fq)⌉₊

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -215,7 +215,7 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
       (Fin.cons (A 0) fun j => A (Fin.succ (Classical.choose (hg j))))
     revert j_ne approx
     refine' Fin.cases _ (fun j₀ => _) j₀ <;>
-      refine' Fin.cases (fun j_ne approx => _) (fun j₁ j_ne approx => _) j₁
+      refine Fin.cases (fun j_ne approx => ?_) (fun j₁ j_ne approx => ?_) j₁
     · exact absurd rfl j_ne
     · rw [Fin.cons_succ, Fin.cons_zero, ← not_le, AbsoluteValue.map_sub] at approx
       have := (Classical.choose_spec (hg j₁)).2

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

Algebra.GroupPower.Order

• pow_mono → pow_right_mono
• pow_le_pow → pow_le_pow_right
• pow_le_pow_of_le_left → pow_le_pow_left
• pow_lt_pow_of_lt_left → pow_lt_pow_left
• strictMonoOn_pow → pow_left_strictMonoOn
• pow_strictMono_right → pow_right_strictMono
• pow_lt_pow → pow_lt_pow_right
• pow_lt_pow_iff → pow_lt_pow_iff_right
• pow_le_pow_iff → pow_le_pow_iff_right
• self_lt_pow → lt_self_pow
• strictAnti_pow → pow_right_strictAnti
• pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
• pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
• lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
• le_of_pow_le_pow → le_of_pow_le_pow_left
• pow_lt_pow₀ → pow_lt_pow_right₀

Algebra.GroupPower.CovariantClass

• pow_le_pow_of_le_left' → pow_le_pow_left'
• nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
• pow_lt_pow' → pow_lt_pow_right'
• nsmul_lt_nsmul → nsmul_lt_nsmul_left
• pow_strictMono_left → pow_right_strictMono'
• nsmul_strictMono_right → nsmul_left_strictMono
• StrictMono.pow_right' → StrictMono.pow_const
• StrictMono.nsmul_left → StrictMono.const_nsmul
• pow_strictMono_right' → pow_left_strictMono
• nsmul_strictMono_left → nsmul_right_strictMono
• Monotone.pow_right → Monotone.pow_const
• Monotone.nsmul_left → Monotone.const_nsmul
• lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
• lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
• pow_le_pow' → pow_le_pow_right'
• nsmul_le_nsmul → nsmul_le_nsmul_left
• pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
• nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
• le_of_pow_le_pow' → le_of_pow_le_pow_left'
• le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
• pow_le_pow_iff' → pow_le_pow_iff_right'
• nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
• pow_lt_pow_iff' → pow_lt_pow_iff_right'
• nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

Data.Nat.Pow

• Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
• Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
• Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

• pow_le_pow_iff_left
• pow_lt_pow_iff_left
• pow_right_injective
• pow_right_inj
• Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
• Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

• self_le_pow was a duplicate of le_self_pow.
• Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
• Nat.pow_right_strictMono is defeq to pow_right_strictMono.
• Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
• Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

• A bunch of proofs have been golfed.
• Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
• A few Nat lemmas have been protected.
• One docstring has been fixed.

@@ -165,7 +165,7 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
     cardPowDegree_nonzero _ hyz']
   have : (1 : ℤ) ≤ Fintype.card Fq := mod_cast (@Fintype.one_lt_card Fq _ _).le
   simp only [Int.cast_pow, Int.cast_ofNat, le_max_iff]
-  refine' Or.imp (pow_le_pow this) (pow_le_pow this) _
+  refine' Or.imp (pow_le_pow_right this) (pow_le_pow_right this) _
   rw [natDegree_le_iff_degree_le, natDegree_le_iff_degree_le, ← le_max_iff, ←
     degree_eq_natDegree hxy', ← degree_eq_natDegree hyz']
   convert degree_add_le (x - y) (y - z) using 2

To fit with the "please try harder" convention of ! tactics.

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

@@ -210,7 +210,7 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
   -- but not that `j` is uniquely defined (which is needed to keep the induction going).
   obtain ⟨j, hj⟩ : ∃ j, ∀ i : Fin n,
       t' i = j → (cardPowDegree (A 0 % b - A i.succ % b) : ℝ) < cardPowDegree b • ε := by
-    by_contra' hg
+    by_contra! hg
     obtain ⟨j₀, j₁, j_ne, approx⟩ := exists_approx_polynomial hb hε
       (Fin.cons (A 0) fun j => A (Fin.succ (Classical.choose (hg j))))
     revert j_ne approx

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

@@ -210,8 +210,7 @@ theorem exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε) {b :
   -- but not that `j` is uniquely defined (which is needed to keep the induction going).
   obtain ⟨j, hj⟩ : ∃ j, ∀ i : Fin n,
       t' i = j → (cardPowDegree (A 0 % b - A i.succ % b) : ℝ) < cardPowDegree b • ε := by
-    by_contra hg
-    push_neg at hg
+    by_contra' hg
     obtain ⟨j₀, j₁, j_ne, approx⟩ := exists_approx_polynomial hb hε
       (Fin.cons (A 0) fun j => A (Fin.succ (Classical.choose (hg j))))
     revert j_ne approx

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>

@@ -163,7 +163,7 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
   refine' lt_of_le_of_lt _ (max_lt hxy hyz)
   rw [cardPowDegree_nonzero _ hxz', cardPowDegree_nonzero _ hxy',
     cardPowDegree_nonzero _ hyz']
-  have : (1 : ℤ) ≤ Fintype.card Fq := by exact_mod_cast (@Fintype.one_lt_card Fq _ _).le
+  have : (1 : ℤ) ≤ Fintype.card Fq := mod_cast (@Fintype.one_lt_card Fq _ _).le
   simp only [Int.cast_pow, Int.cast_ofNat, le_max_iff]
   refine' Or.imp (pow_le_pow this) (pow_le_pow this) _
   rw [natDegree_le_iff_degree_le, natDegree_le_iff_degree_le, ← le_max_iff, ←

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

@@ -118,13 +118,11 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
   · obtain ⟨i₀, i₁, i_ne, mod_eq⟩ :=
       exists_eq_polynomial le_rfl b le_b (fun i => A i % b) fun i => EuclideanDomain.mod_lt (A i) hb
     refine' ⟨i₀, i₁, i_ne, _⟩
-    simp only at mod_eq
     rwa [mod_eq, sub_self, map_zero, Int.cast_zero]
   -- Otherwise, it suffices to choose two elements whose difference is of small enough degree.
   rw [not_le] at le_b
   obtain ⟨i₀, i₁, i_ne, deg_lt⟩ := exists_approx_polynomial_aux le_rfl b (fun i => A i % b) fun i =>
     EuclideanDomain.mod_lt (A i) hb
-  simp only at deg_lt
   use i₀, i₁, i_ne
   -- Again, if the remainders are equal we are done.
   by_cases h : A i₁ % b = A i₀ % b

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

This has nice performance benefits.

@@ -29,7 +29,7 @@ open Polynomial
 
 open AbsoluteValue Real
 
-variable {Fq : Type _} [Fintype Fq]
+variable {Fq : Type*} [Fintype Fq]
 
 /-- If `A` is a family of enough low-degree polynomials over a finite semiring, there is a
 pair of equal elements in `A`. -/

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module number_theory.class_number.admissible_card_pow_degree
-! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue
 import Mathlib.Analysis.SpecialFunctions.Pow.Real
 import Mathlib.RingTheory.Ideal.LocalRing
 import Mathlib.Data.Polynomial.Degree.CardPowDegree
 
+#align_import number_theory.class_number.admissible_card_pow_degree from "leanprover-community/mathlib"@"0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8"
+
 /-!
 # Admissible absolute values on polynomials