PR contents

(last sync)

feat(data/{int,nat}/modeq): a/c ≡ b/c mod m/c → a ≡ b mod m (#18666)

Also prove -a ≡ -b [ZMOD n] ↔ a ≡ b [ZMOD n], a ≡ b [ZMOD -n] ↔ a ≡ b [ZMOD n], generalise int.modeq.mul_left'/int.modeq.mul_right', and rename

int.gcd_pos_of_non_zero_left → int.gcd_pos_of_ne_zero_left
int.gcd_pos_of_non_zero_right → int.gcd_pos_of_ne_zero_right
eq_iff_modeq_int, char_p.int_coe_eq_int_coe_iff → char_p.int_cast_eq_int_cast (they were duplicates)

Diff

@@ -121,10 +121,16 @@ begin
     rw [int.cast_coe_nat, char_p.cast_eq_zero_iff R p, int.coe_nat_dvd] }
 end
 
-lemma char_p.int_coe_eq_int_coe_iff [add_group_with_one R] (p : ℕ) [char_p R p] (a b : ℤ) :
-  (a : R) = (b : R) ↔ a ≡ b [ZMOD p] :=
-by rw [eq_comm, ←sub_eq_zero, ←int.cast_sub,
-       char_p.int_cast_eq_zero_iff R p, int.modeq_iff_dvd]
+lemma char_p.int_cast_eq_int_cast [add_group_with_one R] (p : ℕ) [char_p R p] {a b : ℤ} :
+  (a : R) = b ↔ a ≡ b [ZMOD p] :=
+by rw [eq_comm, ←sub_eq_zero, ←int.cast_sub, char_p.int_cast_eq_zero_iff R p, int.modeq_iff_dvd]
+
+lemma char_p.nat_cast_eq_nat_cast [add_group_with_one R] (p : ℕ) [char_p R p] {a b : ℕ} :
+  (a : R) = b ↔ a ≡ b [MOD p] :=
+begin
+  rw [←int.cast_coe_nat, ←int.cast_coe_nat b],
+  exact (char_p.int_cast_eq_int_cast _ _).trans int.coe_nat_modeq_iff,
+end
 
 theorem char_p.eq [add_monoid_with_one R] {p q : ℕ} (c1 : char_p R p) (c2 : char_p R q) :
   p = q :=
@@ -242,11 +248,6 @@ theorem sub_pow_char_pow [comm_ring R] {p : ℕ} [fact p.prime]
   (x - y) ^ (p ^ n) = x ^ (p ^ n) - y ^ (p ^ n) :=
 sub_pow_char_pow_of_commute _ _ _ (commute.all _ _)
 
-lemma eq_iff_modeq_int [ring R] (p : ℕ) [char_p R p] (a b : ℤ) :
-  (a : R) = b ↔ a ≡ b [ZMOD p] :=
-by rw [eq_comm, ←sub_eq_zero, ←int.cast_sub,
-       char_p.int_cast_eq_zero_iff R p, int.modeq_iff_dvd]
-
 lemma char_p.neg_one_ne_one [ring R] (p : ℕ) [char_p R p] [fact (2 < p)] :
   (-1 : R) ≠ (1 : R) :=
 begin

ceb887dd

feat(algebra/char_p/basic): refactor proof of add_pow_char_of_commute to extract a statement true in all rings (#11364)

If x and y commute, the pth power of their sum is the sum of the pth powers plus a multiple of p. This holds in any semiring and easily implies the additivity of frobenius in char p, but is occasionally useful in characteristic 0. Also make the fact that p is 0 in a char_p ring a simp lemma.

From flt-regular

Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

Diff

@@ -3,11 +3,8 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Joey van Langen, Casper Putz
 -/
-
-import algebra.hom.iterate
 import data.int.modeq
-import data.nat.choose.dvd
-import data.nat.choose.sum
+import data.nat.multiplicity
 import group_theory.order_of_element
 import ring_theory.nilpotent
 
@@ -17,7 +14,70 @@ import ring_theory.nilpotent
 
 universes u v
 
-variables (R : Type u)
+open finset
+open_locale big_operators
+
+variables {R : Type*}
+
+namespace commute
+variables [semiring R] {p : ℕ} {x y : R}
+
+protected lemma add_pow_prime_pow_eq (hp : p.prime) (h : commute x y) (n : ℕ) :
+  (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n +
+    p * ∑ k in Ioo 0 (p ^ n), x ^ k * y ^ (p ^ n - k) * ↑((p ^ n).choose k / p) :=
+begin
+  transitivity
+    x ^ p ^ n + y ^ p ^ n + ∑ k in Ioo 0 (p ^ n), x ^ k * y ^ (p ^ n - k) * (p ^ n).choose k,
+  { simp_rw [h.add_pow, ←nat.Ico_zero_eq_range, nat.Ico_succ_right, Icc_eq_cons_Ico (zero_le _),
+      finset.sum_cons, Ico_eq_cons_Ioo (pow_pos hp.pos _), finset.sum_cons, tsub_self, tsub_zero,
+      pow_zero, nat.choose_zero_right, nat.choose_self, nat.cast_one, mul_one, one_mul,
+      ←add_assoc] },
+  { congr' 1,
+    simp_rw [finset.mul_sum, nat.cast_comm, mul_assoc _ _ (p : R), ←nat.cast_mul],
+    refine finset.sum_congr rfl (λ i hi, _),
+    rw mem_Ioo at hi,
+    rw nat.div_mul_cancel (hp.dvd_choose_pow hi.1.ne' hi.2.ne) },
+end
+
+protected lemma add_pow_prime_eq (hp : p.prime) (h : commute x y) :
+  (x + y) ^ p = x ^ p + y ^ p +
+    p * ∑ k in finset.Ioo 0 p, x ^ k * y ^ (p - k) * ↑(p.choose k / p) :=
+by simpa using h.add_pow_prime_pow_eq hp 1
+
+protected lemma exists_add_pow_prime_pow_eq (hp : p.prime) (h : commute x y) (n : ℕ) :
+  ∃ r, (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n + p * r :=
+⟨_, h.add_pow_prime_pow_eq hp n⟩
+
+protected lemma exists_add_pow_prime_eq (hp : p.prime) (h : commute x y) :
+  ∃ r, (x + y) ^ p = x ^ p + y ^ p + p * r :=
+⟨_, h.add_pow_prime_eq hp⟩
+
+end commute
+
+section comm_semiring
+variables [comm_semiring R] {p : ℕ} {x y : R}
+
+lemma add_pow_prime_pow_eq (hp : p.prime) (x y : R) (n : ℕ) :
+  (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n +
+    p * ∑ k in finset.Ioo 0 (p ^ n), x ^ k * y ^ (p ^ n - k) * ↑((p ^ n).choose k / p) :=
+(commute.all x y).add_pow_prime_pow_eq hp n
+
+lemma add_pow_prime_eq (hp : p.prime) (x y : R) :
+  (x + y) ^ p = x ^ p + y ^ p +
+    p * ∑ k in finset.Ioo 0 p, x ^ k * y ^ (p - k) * ↑(p.choose k / p) :=
+(commute.all x y).add_pow_prime_eq hp
+
+lemma exists_add_pow_prime_pow_eq (hp : p.prime) (x y : R) (n : ℕ) :
+  ∃ r, (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n + p * r :=
+(commute.all x y).exists_add_pow_prime_pow_eq hp n
+
+lemma exists_add_pow_prime_eq (hp : p.prime) (x y : R) :
+  ∃ r, (x + y) ^ p = x ^ p + y ^ p + p * r :=
+(commute.all x y).exists_add_pow_prime_eq hp
+
+end comm_semiring
+
+variables (R)
 
 /-- The generator of the kernel of the unique homomorphism ℕ → R for a semiring R.
 
@@ -33,6 +93,7 @@ This example is formalized in `counterexamples/char_p_zero_ne_char_zero`.
 class char_p [add_monoid_with_one R] (p : ℕ) : Prop :=
 (cast_eq_zero_iff [] : ∀ x:ℕ, (x:R) = 0 ↔ p ∣ x)
 
+@[simp]
 theorem char_p.cast_eq_zero [add_monoid_with_one R] (p : ℕ) [char_p R p] :
   (p:R) = 0 :=
 (char_p.cast_eq_zero_iff R p p).2 (dvd_refl p)
@@ -133,32 +194,15 @@ by rw ring_char.spec
 
 end ring_char
 
-theorem add_pow_char_of_commute [semiring R] {p : ℕ} [fact p.prime]
+theorem add_pow_char_of_commute [semiring R] {p : ℕ} [hp : fact p.prime]
   [char_p R p] (x y : R) (h : commute x y) :
   (x + y)^p = x^p + y^p :=
-begin
-  rw [commute.add_pow h, finset.sum_range_succ_comm, tsub_self, pow_zero, nat.choose_self],
-  rw [nat.cast_one, mul_one, mul_one], congr' 1,
-  convert finset.sum_eq_single 0 _ _,
-  { simp only [mul_one, one_mul, nat.choose_zero_right, tsub_zero, nat.cast_one, pow_zero] },
-  { intros b h1 h2,
-    suffices : (p.choose b : R) = 0, { rw this, simp },
-    rw char_p.cast_eq_zero_iff R p,
-    exact nat.prime.dvd_choose_self (fact.out _) h2 (finset.mem_range.1 h1) },
-  { intro h1,
-    contrapose! h1,
-    rw finset.mem_range,
-    exact nat.prime.pos (fact.out _) }
-end
+let ⟨r, hr⟩ := h.exists_add_pow_prime_eq hp.out in by simp [hr]
 
-theorem add_pow_char_pow_of_commute [semiring R] {p : ℕ} [fact p.prime]
-  [char_p R p] {n : ℕ} (x y : R) (h : commute x y) :
+theorem add_pow_char_pow_of_commute [semiring R] {p n : ℕ} [hp : fact p.prime] [char_p R p]
+  (x y : R) (h : commute x y) :
   (x + y) ^ (p ^ n) = x ^ (p ^ n) + y ^ (p ^ n) :=
-begin
-  induction n, { simp, },
-  rw [pow_succ', pow_mul, pow_mul, pow_mul, n_ih],
-  apply add_pow_char_of_commute, apply commute.pow_pow h,
-end
+let ⟨r, hr⟩ := h.exists_add_pow_prime_pow_eq hp.out n in by simp [hr]
 
 theorem sub_pow_char_of_commute [ring R] {p : ℕ} [fact p.prime]
   [char_p R p] (x y : R) (h : commute x y) :

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-25-08

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

ad7a2212

Diff

@@ -6,7 +6,7 @@ Authors: Kenny Lau, Joey van Langen, Casper Putz
 import Data.Int.ModEq
 import Data.Nat.Multiplicity
 import GroupTheory.OrderOfElement
-import RingTheory.Nilpotent
+import RingTheory.Nilpotent.Defs
 
 #align_import algebra.char_p.basic from "leanprover-community/mathlib"@"47a1a73351de8dd6c8d3d32b569c8e434b03ca47"

bump to nightly-2024-04-19-08

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

a9e81450

Diff

@@ -150,8 +150,8 @@ theorem CharP.addOrderOf_one (R) [Semiring R] : CharP R (addOrderOf (1 : R)) :=
 #align char_p.add_order_of_one CharP.addOrderOf_one
 -/
 
-#print CharP.int_cast_eq_zero_iff /-
-theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a : ℤ) :
+#print CharP.intCast_eq_zero_iff /-
+theorem CharP.intCast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a : ℤ) :
     (a : R) = 0 ↔ (p : ℤ) ∣ a :=
   by
   rcases lt_trichotomy a 0 with (h | rfl | h)
@@ -161,13 +161,13 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
   · simp only [Int.cast_zero, eq_self_iff_true, dvd_zero]
   · lift a to ℕ using le_of_lt h with b
     rw [Int.cast_natCast, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
-#align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff
+#align char_p.int_cast_eq_zero_iff CharP.intCast_eq_zero_iff
 -/
 
 #print CharP.intCast_eq_intCast /-
 theorem CharP.intCast_eq_intCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℤ} :
     (a : R) = b ↔ a ≡ b [ZMOD p] := by
-  rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.int_cast_eq_zero_iff R p, Int.modEq_iff_dvd]
+  rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.intCast_eq_zero_iff R p, Int.modEq_iff_dvd]
 #align char_p.int_cast_eq_int_cast CharP.intCast_eq_intCast
 -/
 
@@ -503,10 +503,10 @@ theorem frobenius_add : frobenius R p (x + y) = frobenius R p x + frobenius R p
 #align frobenius_add frobenius_add
 -/
 
-#print frobenius_nat_cast /-
-theorem frobenius_nat_cast (n : ℕ) : frobenius R p n = n :=
+#print frobenius_natCast /-
+theorem frobenius_natCast (n : ℕ) : frobenius R p n = n :=
   map_natCast (frobenius R p) n
-#align frobenius_nat_cast frobenius_nat_cast
+#align frobenius_nat_cast frobenius_natCast
 -/
 
 open scoped BigOperators

bump to nightly-2024-04-08-08

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

e7589225

Diff

@@ -157,10 +157,10 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
   rcases lt_trichotomy a 0 with (h | rfl | h)
   · rw [← neg_eq_zero, ← Int.cast_neg, ← dvd_neg]
     lift -a to ℕ using neg_nonneg.mpr (le_of_lt h) with b
-    rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
+    rw [Int.cast_natCast, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
   · simp only [Int.cast_zero, eq_self_iff_true, dvd_zero]
   · lift a to ℕ using le_of_lt h with b
-    rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
+    rw [Int.cast_natCast, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
 #align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff
 -/
 
@@ -175,7 +175,7 @@ theorem CharP.intCast_eq_intCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b
 theorem CharP.natCast_eq_natCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℕ} :
     (a : R) = b ↔ a ≡ b [MOD p] :=
   by
-  rw [← Int.cast_ofNat, ← Int.cast_ofNat b]
+  rw [← Int.cast_natCast, ← Int.cast_natCast b]
   exact (CharP.intCast_eq_intCast _ _).trans Int.natCast_modEq_iff
 #align char_p.nat_cast_eq_nat_cast CharP.natCast_eq_natCast
 -/

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Joey van Langen, Casper Putz
 -/
-import Data.Int.Modeq
+import Data.Int.ModEq
 import Data.Nat.Multiplicity
 import GroupTheory.OrderOfElement
 import RingTheory.Nilpotent
@@ -157,10 +157,10 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
   rcases lt_trichotomy a 0 with (h | rfl | h)
   · rw [← neg_eq_zero, ← Int.cast_neg, ← dvd_neg]
     lift -a to ℕ using neg_nonneg.mpr (le_of_lt h) with b
-    rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
+    rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
   · simp only [Int.cast_zero, eq_self_iff_true, dvd_zero]
   · lift a to ℕ using le_of_lt h with b
-    rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
+    rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
 #align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff
 -/
 
@@ -176,7 +176,7 @@ theorem CharP.natCast_eq_natCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b
     (a : R) = b ↔ a ≡ b [MOD p] :=
   by
   rw [← Int.cast_ofNat, ← Int.cast_ofNat b]
-  exact (CharP.intCast_eq_intCast _ _).trans Int.coe_nat_modEq_iff
+  exact (CharP.intCast_eq_intCast _ _).trans Int.natCast_modEq_iff
 #align char_p.nat_cast_eq_nat_cast CharP.natCast_eq_natCast
 -/
 
@@ -333,7 +333,7 @@ theorem sub_pow_char_pow_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p
     (h : Commute x y) : (x - y) ^ p ^ n = x ^ p ^ n - y ^ p ^ n :=
   by
   induction n; · simp
-  rw [pow_succ', pow_mul, pow_mul, pow_mul, n_ih]
+  rw [pow_succ, pow_mul, pow_mul, pow_mul, n_ih]
   apply sub_pow_char_of_commute; apply Commute.pow_pow h
 #align sub_pow_char_pow_of_commute sub_pow_char_pow_of_commute
 -/
@@ -433,7 +433,7 @@ theorem frobenius_def : frobenius R p x = x ^ p :=
 theorem iterate_frobenius (n : ℕ) : (frobenius R p^[n]) x = x ^ p ^ n :=
   by
   induction n; · simp
-  rw [Function.iterate_succ', pow_succ', pow_mul, Function.comp_apply, frobenius_def, n_ih]
+  rw [Function.iterate_succ', pow_succ, pow_mul, Function.comp_apply, frobenius_def, n_ih]
 #align iterate_frobenius iterate_frobenius
 -/
 
@@ -624,7 +624,7 @@ theorem pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [Fact p.Prime] [CharP R p] (x
   induction' k with k hk
   · rw [pow_zero, one_mul]
   · refine' ⟨fun h => _, fun h => _⟩
-    · rw [pow_succ, mul_assoc, pow_mul', ← frobenius_def, ← frobenius_one p] at h
+    · rw [pow_succ', mul_assoc, pow_mul', ← frobenius_def, ← frobenius_one p] at h
       exact hk.1 (frobenius_inj R p h)
     · rw [pow_mul', h, one_pow]
 #align char_p.pow_prime_pow_mul_eq_one_iff ExpChar.pow_prime_pow_mul_eq_one_iff
@@ -649,7 +649,7 @@ section NoZeroDivisors
 
 variable [NoZeroDivisors R]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (d «expr ∣ » p) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (d «expr ∣ » p) -/
 #print CharP.char_is_prime_of_two_le /-
 theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.Prime p :=
   suffices ∀ (d) (_ : d ∣ p), d = 1 ∨ d = p from Nat.prime_def_lt''.mpr ⟨hp, this⟩

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -44,7 +44,7 @@ protected theorem add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ
   · congr 1
     simp_rw [Finset.mul_sum, Nat.cast_comm, mul_assoc _ _ (p : R), ← Nat.cast_mul]
     refine' Finset.sum_congr rfl fun i hi => _
-    rw [mem_Ioo] at hi 
+    rw [mem_Ioo] at hi
     rw [Nat.div_mul_cancel (hp.dvd_choose_pow hi.1.ne' hi.2.Ne)]
 #align commute.add_pow_prime_pow_eq Commute.add_pow_prime_pow_eq
 -/
@@ -213,7 +213,7 @@ theorem CharP.exists [NonAssocSemiring R] : ∃ p, CharP R p :=
                     rwa [← Nat.mod_add_div x (Nat.find (Classical.not_forall.1 H)), Nat.cast_add,
                       Nat.cast_mul,
                       of_not_not (not_not_of_not_imp <| Nat.find_spec (Classical.not_forall.1 H)),
-                      MulZeroClass.zero_mul, add_zero] at H1 ,
+                      MulZeroClass.zero_mul, add_zero] at H1,
                     H2⟩)),
           fun H1 => by
           rw [← Nat.mul_div_cancel' H1, Nat.cast_mul,
@@ -371,7 +371,7 @@ theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1
   by
   suffices (2 : R) ≠ 0 by symm; rw [Ne.def, ← sub_eq_zero, sub_neg_eq_add]; exact this
   intro h
-  rw [show (2 : R) = (2 : ℕ) by norm_cast] at h 
+  rw [show (2 : R) = (2 : ℕ) by norm_cast] at h
   have := (CharP.cast_eq_zero_iff R p 2).mp h
   have := Nat.le_of_dvd (by decide) this
   rw [fact_iff] at *; linarith
@@ -558,7 +558,7 @@ end frobenius
 #print frobenius_inj /-
 theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP R p] :
     Function.Injective (frobenius R p) := fun x h H => by rw [← sub_eq_zero] at H ⊢;
-  rw [← frobenius_sub] at H ; exact IsReduced.eq_zero _ ⟨_, H⟩
+  rw [← frobenius_sub] at H; exact IsReduced.eq_zero _ ⟨_, H⟩
 #align frobenius_inj frobenius_inj
 -/
 
@@ -624,7 +624,7 @@ theorem pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [Fact p.Prime] [CharP R p] (x
   induction' k with k hk
   · rw [pow_zero, one_mul]
   · refine' ⟨fun h => _, fun h => _⟩
-    · rw [pow_succ, mul_assoc, pow_mul', ← frobenius_def, ← frobenius_one p] at h 
+    · rw [pow_succ, mul_assoc, pow_mul', ← frobenius_def, ← frobenius_one p] at h
       exact hk.1 (frobenius_inj R p h)
     · rw [pow_mul', h, one_pow]
 #align char_p.pow_prime_pow_mul_eq_one_iff ExpChar.pow_prime_pow_mul_eq_one_iff
@@ -666,7 +666,7 @@ theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.
     have : e ∣ p := dvd_of_mul_left_eq d (Eq.symm hmul)
     have : e = p := dvd_antisymm ‹e ∣ p› ‹p ∣ e›
     have h₀ : 0 < p := two_pos.trans_le hp
-    have : d * p = 1 * p := by rw [‹e = p›] at hmul  <;> rw [one_mul] <;> exact Eq.symm hmul
+    have : d * p = 1 * p := by rw [‹e = p›] at hmul <;> rw [one_mul] <;> exact Eq.symm hmul
     show d = 1 ∨ d = p from Or.inl (mul_right_cancel₀ h₀.ne' this)
 #align char_p.char_is_prime_of_two_le CharP.char_is_prime_of_two_le
 -/
@@ -738,7 +738,7 @@ theorem ringChar_ne_one [Nontrivial R] : ringChar R ≠ 1 := by intro h; apply z
 #print CharP.nontrivial_of_char_ne_one /-
 theorem nontrivial_of_char_ne_one {v : ℕ} (hv : v ≠ 1) [hr : CharP R v] : Nontrivial R :=
   ⟨⟨(1 : ℕ), 0, fun h =>
-      hv <| by rwa [CharP.cast_eq_zero_iff _ v, Nat.dvd_one] at h  <;> assumption⟩⟩
+      hv <| by rwa [CharP.cast_eq_zero_iff _ v, Nat.dvd_one] at h <;> assumption⟩⟩
 #align char_p.nontrivial_of_char_ne_one CharP.nontrivial_of_char_ne_one
 -/
 
@@ -804,7 +804,7 @@ theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0
       constructor
       · intro h
         rw [← Nat.mod_add_div k n, Nat.cast_add, Nat.cast_mul, H, MulZeroClass.zero_mul,
-          add_zero] at h 
+          add_zero] at h
         rw [Nat.dvd_iff_mod_eq_zero]
         apply hR _ (Nat.mod_lt _ _) h
         rw [← hn, Fintype.card_pos_iff]
@@ -819,7 +819,7 @@ theorem charP_of_prime_pow_injective (R) [Ring R] [Fintype R] (p : ℕ) [hp : Fa
   by
   obtain ⟨c, hc⟩ := CharP.exists R; skip
   have hcpn : c ∣ p ^ n := by rw [← CharP.cast_eq_zero_iff R c, ← hn, CharP.cast_card_eq_zero]
-  obtain ⟨i, hi, hc⟩ : ∃ i ≤ n, c = p ^ i := by rwa [Nat.dvd_prime_pow hp.1] at hcpn 
+  obtain ⟨i, hi, hc⟩ : ∃ i ≤ n, c = p ^ i := by rwa [Nat.dvd_prime_pow hp.1] at hcpn
   obtain rfl : i = n := by apply hR i hi; rw [← Nat.cast_pow, ← hc, CharP.cast_eq_zero]
   rwa [← hc]
 #align char_p_of_prime_pow_injective charP_of_prime_pow_injective
@@ -869,23 +869,23 @@ theorem Int.cast_injOn_of_ringChar_ne_two {R : Type _} [NonAssocRing R] [Nontriv
   intro a ha b hb h
   apply eq_of_sub_eq_zero
   by_contra hf
-  change a = 0 ∨ a = 1 ∨ a = -1 at ha 
-  change b = 0 ∨ b = 1 ∨ b = -1 at hb 
+  change a = 0 ∨ a = 1 ∨ a = -1 at ha
+  change b = 0 ∨ b = 1 ∨ b = -1 at hb
   have hh : a - b = 1 ∨ b - a = 1 ∨ a - b = 2 ∨ b - a = 2 :=
     by
     rcases ha with (ha | ha | ha) <;> rcases hb with (hb | hb | hb)
     pick_goal 5; pick_goal 9
     -- move goals with `a = b` to the front
-    iterate 3 rw [ha, hb, sub_self] at hf ; tauto
+    iterate 3 rw [ha, hb, sub_self] at hf; tauto
     -- 6 goals remain
     all_goals rw [ha, hb]; norm_num
   have h' : ((a - b : ℤ) : R) = 0 := by exact_mod_cast sub_eq_zero_of_eq h
   have h'' : ((b - a : ℤ) : R) = 0 := by exact_mod_cast sub_eq_zero_of_eq h.symm
   rcases hh with (hh | hh | hh | hh)
-  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h' ; exact one_ne_zero h'
-  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h'' ; exact one_ne_zero h''
-  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h' ; exact Ring.two_ne_zero hR h'
-  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h'' ; exact Ring.two_ne_zero hR h''
+  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h'; exact one_ne_zero h'
+  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h''; exact one_ne_zero h''
+  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h'; exact Ring.two_ne_zero hR h'
+  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h''; exact Ring.two_ne_zero hR h''
 #align int.cast_inj_on_of_ring_char_ne_two Int.cast_injOn_of_ringChar_ne_two
 -/

bump to nightly-2024-02-05-08

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

516c6ec2

Diff

@@ -113,7 +113,7 @@ end CommSemiring
 variable (R)
 
 #print CharP /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
 /-- The generator of the kernel of the unique homomorphism ℕ → R for a semiring R.
 
 *Warning*: for a semiring `R`, `char_p R 0` and `char_zero R` need not coincide.
@@ -616,7 +616,7 @@ section CommRing
 
 variable [CommRing R] [IsReduced R] {R}
 
-#print CharP.pow_prime_pow_mul_eq_one_iff /-
+#print ExpChar.pow_prime_pow_mul_eq_one_iff /-
 @[simp]
 theorem pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [Fact p.Prime] [CharP R p] (x : R) :
     x ^ (p ^ k * m) = 1 ↔ x ^ m = 1 :=
@@ -627,7 +627,7 @@ theorem pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [Fact p.Prime] [CharP R p] (x
     · rw [pow_succ, mul_assoc, pow_mul', ← frobenius_def, ← frobenius_one p] at h 
       exact hk.1 (frobenius_inj R p h)
     · rw [pow_mul', h, one_pow]
-#align char_p.pow_prime_pow_mul_eq_one_iff CharP.pow_prime_pow_mul_eq_one_iff
+#align char_p.pow_prime_pow_mul_eq_one_iff ExpChar.pow_prime_pow_mul_eq_one_iff
 -/
 
 end CommRing

bump to nightly-2023-12-23-06

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

b8c74971

Diff

@@ -113,7 +113,7 @@ end CommSemiring
 variable (R)
 
 #print CharP /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
 /-- The generator of the kernel of the unique homomorphism ℕ → R for a semiring R.
 
 *Warning*: for a semiring `R`, `char_p R 0` and `char_zero R` need not coincide.

bump to nightly-2023-10-21-06

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

a2dc86f8

Diff

@@ -200,24 +200,24 @@ theorem CharP.exists [NonAssocSemiring R] : ∃ p, CharP R p :=
     (fun H : ∀ p : ℕ, (p : R) = 0 → p = 0 =>
       ⟨0, ⟨fun x => by rw [zero_dvd_iff] <;> exact ⟨H x, by rintro rfl <;> simp⟩⟩⟩)
     fun H =>
-    ⟨Nat.find (not_forall.1 H),
+    ⟨Nat.find (Classical.not_forall.1 H),
       ⟨fun x =>
         ⟨fun H1 =>
           Nat.dvd_of_mod_eq_zero
             (by_contradiction fun H2 =>
-              Nat.find_min (not_forall.1 H)
+              Nat.find_min (Classical.not_forall.1 H)
                 (Nat.mod_lt x <|
-                  Nat.pos_of_ne_zero <| not_of_not_imp <| Nat.find_spec (not_forall.1 H))
+                  Nat.pos_of_ne_zero <| not_of_not_imp <| Nat.find_spec (Classical.not_forall.1 H))
                 (not_imp_of_and_not
                   ⟨by
-                    rwa [← Nat.mod_add_div x (Nat.find (not_forall.1 H)), Nat.cast_add,
+                    rwa [← Nat.mod_add_div x (Nat.find (Classical.not_forall.1 H)), Nat.cast_add,
                       Nat.cast_mul,
-                      of_not_not (not_not_of_not_imp <| Nat.find_spec (not_forall.1 H)),
+                      of_not_not (not_not_of_not_imp <| Nat.find_spec (Classical.not_forall.1 H)),
                       MulZeroClass.zero_mul, add_zero] at H1 ,
                     H2⟩)),
           fun H1 => by
           rw [← Nat.mul_div_cancel' H1, Nat.cast_mul,
-            of_not_not (not_not_of_not_imp <| Nat.find_spec (not_forall.1 H)),
+            of_not_not (not_not_of_not_imp <| Nat.find_spec (Classical.not_forall.1 H)),
             MulZeroClass.zero_mul]⟩⟩⟩
 #align char_p.exists CharP.exists
 -/

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Joey van Langen, Casper Putz
 -/
-import Mathbin.Data.Int.Modeq
-import Mathbin.Data.Nat.Multiplicity
-import Mathbin.GroupTheory.OrderOfElement
-import Mathbin.RingTheory.Nilpotent
+import Data.Int.Modeq
+import Data.Nat.Multiplicity
+import GroupTheory.OrderOfElement
+import RingTheory.Nilpotent
 
 #align_import algebra.char_p.basic from "leanprover-community/mathlib"@"47a1a73351de8dd6c8d3d32b569c8e434b03ca47"
 
@@ -113,7 +113,7 @@ end CommSemiring
 variable (R)
 
 #print CharP /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
 /-- The generator of the kernel of the unique homomorphism ℕ → R for a semiring R.
 
 *Warning*: for a semiring `R`, `char_p R 0` and `char_zero R` need not coincide.
@@ -649,7 +649,7 @@ section NoZeroDivisors
 
 variable [NoZeroDivisors R]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (d «expr ∣ » p) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (d «expr ∣ » p) -/
 #print CharP.char_is_prime_of_two_le /-
 theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.Prime p :=
   suffices ∀ (d) (_ : d ∣ p), d = 1 ∨ d = p from Nat.prime_def_lt''.mpr ⟨hp, this⟩

bump to nightly-2023-08-17-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

60285dcc

Diff

@@ -439,7 +439,7 @@ theorem iterate_frobenius (n : ℕ) : (frobenius R p^[n]) x = x ^ p ^ n :=
 
 #print frobenius_mul /-
 theorem frobenius_mul : frobenius R p (x * y) = frobenius R p x * frobenius R p y :=
-  (frobenius R p).map_mul x y
+  (frobenius R p).map_hMul x y
 #align frobenius_mul frobenius_mul
 -/
 
@@ -657,7 +657,7 @@ theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.
   let ⟨e, hmul⟩ := hdvd
   have : (p : R) = 0 := (cast_eq_zero_iff R p p).mpr (dvd_refl p)
   have : (d : R) * e = 0 := @cast_mul R _ d e ▸ hmul ▸ this
-  Or.elim (eq_zero_or_eq_zero_of_mul_eq_zero this)
+  Or.elim (eq_zero_or_eq_zero_of_hMul_eq_zero this)
     (fun hd : (d : R) = 0 =>
       have : p ∣ d := (cast_eq_zero_iff R p d).mp hd
       show d = 1 ∨ d = p from Or.inr (dvd_antisymm ⟨e, hmul⟩ this))

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Joey van Langen, Casper Putz
-
-! This file was ported from Lean 3 source module algebra.char_p.basic
-! leanprover-community/mathlib commit 47a1a73351de8dd6c8d3d32b569c8e434b03ca47
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Int.Modeq
 import Mathbin.Data.Nat.Multiplicity
 import Mathbin.GroupTheory.OrderOfElement
 import Mathbin.RingTheory.Nilpotent
 
+#align_import algebra.char_p.basic from "leanprover-community/mathlib"@"47a1a73351de8dd6c8d3d32b569c8e434b03ca47"
+
 /-!
 # Characteristic of semirings
 
@@ -652,7 +649,7 @@ section NoZeroDivisors
 
 variable [NoZeroDivisors R]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (d «expr ∣ » p) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (d «expr ∣ » p) -/
 #print CharP.char_is_prime_of_two_le /-
 theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.Prime p :=
   suffices ∀ (d) (_ : d ∣ p), d = 1 ∨ d = p from Nat.prime_def_lt''.mpr ⟨hp, this⟩

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -33,6 +33,7 @@ namespace Commute
 
 variable [Semiring R] {p : ℕ} {x y : R}
 
+#print Commute.add_pow_prime_pow_eq /-
 protected theorem add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ) :
     (x + y) ^ p ^ n =
       x ^ p ^ n + y ^ p ^ n +
@@ -49,22 +50,29 @@ protected theorem add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ
     rw [mem_Ioo] at hi 
     rw [Nat.div_mul_cancel (hp.dvd_choose_pow hi.1.ne' hi.2.Ne)]
 #align commute.add_pow_prime_pow_eq Commute.add_pow_prime_pow_eq
+-/
 
+#print Commute.add_pow_prime_eq /-
 protected theorem add_pow_prime_eq (hp : p.Prime) (h : Commute x y) :
     (x + y) ^ p =
       x ^ p + y ^ p + p * ∑ k in Finset.Ioo 0 p, x ^ k * y ^ (p - k) * ↑(p.choose k / p) :=
   by simpa using h.add_pow_prime_pow_eq hp 1
 #align commute.add_pow_prime_eq Commute.add_pow_prime_eq
+-/
 
+#print Commute.exists_add_pow_prime_pow_eq /-
 protected theorem exists_add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ) :
     ∃ r, (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n + p * r :=
   ⟨_, h.add_pow_prime_pow_eq hp n⟩
 #align commute.exists_add_pow_prime_pow_eq Commute.exists_add_pow_prime_pow_eq
+-/
 
+#print Commute.exists_add_pow_prime_eq /-
 protected theorem exists_add_pow_prime_eq (hp : p.Prime) (h : Commute x y) :
     ∃ r, (x + y) ^ p = x ^ p + y ^ p + p * r :=
   ⟨_, h.add_pow_prime_eq hp⟩
 #align commute.exists_add_pow_prime_eq Commute.exists_add_pow_prime_eq
+-/
 
 end Commute
 
@@ -72,35 +80,43 @@ section CommSemiring
 
 variable [CommSemiring R] {p : ℕ} {x y : R}
 
+#print add_pow_prime_pow_eq /-
 theorem add_pow_prime_pow_eq (hp : p.Prime) (x y : R) (n : ℕ) :
     (x + y) ^ p ^ n =
       x ^ p ^ n + y ^ p ^ n +
         p * ∑ k in Finset.Ioo 0 (p ^ n), x ^ k * y ^ (p ^ n - k) * ↑((p ^ n).choose k / p) :=
   (Commute.all x y).add_pow_prime_pow_eq hp n
 #align add_pow_prime_pow_eq add_pow_prime_pow_eq
+-/
 
+#print add_pow_prime_eq /-
 theorem add_pow_prime_eq (hp : p.Prime) (x y : R) :
     (x + y) ^ p =
       x ^ p + y ^ p + p * ∑ k in Finset.Ioo 0 p, x ^ k * y ^ (p - k) * ↑(p.choose k / p) :=
   (Commute.all x y).add_pow_prime_eq hp
 #align add_pow_prime_eq add_pow_prime_eq
+-/
 
+#print exists_add_pow_prime_pow_eq /-
 theorem exists_add_pow_prime_pow_eq (hp : p.Prime) (x y : R) (n : ℕ) :
     ∃ r, (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n + p * r :=
   (Commute.all x y).exists_add_pow_prime_pow_eq hp n
 #align exists_add_pow_prime_pow_eq exists_add_pow_prime_pow_eq
+-/
 
+#print exists_add_pow_prime_eq /-
 theorem exists_add_pow_prime_eq (hp : p.Prime) (x y : R) :
     ∃ r, (x + y) ^ p = x ^ p + y ^ p + p * r :=
   (Commute.all x y).exists_add_pow_prime_eq hp
 #align exists_add_pow_prime_eq exists_add_pow_prime_eq
+-/
 
 end CommSemiring
 
 variable (R)
 
 #print CharP /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
 /-- The generator of the kernel of the unique homomorphism ℕ → R for a semiring R.
 
 *Warning*: for a semiring `R`, `char_p R 0` and `char_zero R` need not coincide.
@@ -117,15 +133,19 @@ class CharP [AddMonoidWithOne R] (p : ℕ) : Prop where
 #align char_p CharP
 -/
 
+#print CharP.cast_eq_zero /-
 @[simp]
 theorem CharP.cast_eq_zero [AddMonoidWithOne R] (p : ℕ) [CharP R p] : (p : R) = 0 :=
   (CharP.cast_eq_zero_iff R p p).2 (dvd_refl p)
 #align char_p.cast_eq_zero CharP.cast_eq_zero
+-/
 
+#print CharP.cast_card_eq_zero /-
 @[simp]
 theorem CharP.cast_card_eq_zero [AddGroupWithOne R] [Fintype R] : (Fintype.card R : R) = 0 := by
   rw [← nsmul_one, card_nsmul_eq_zero]
 #align char_p.cast_card_eq_zero CharP.cast_card_eq_zero
+-/
 
 #print CharP.addOrderOf_one /-
 theorem CharP.addOrderOf_one (R) [Semiring R] : CharP R (addOrderOf (1 : R)) :=
@@ -133,6 +153,7 @@ theorem CharP.addOrderOf_one (R) [Semiring R] : CharP R (addOrderOf (1 : R)) :=
 #align char_p.add_order_of_one CharP.addOrderOf_one
 -/
 
+#print CharP.int_cast_eq_zero_iff /-
 theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a : ℤ) :
     (a : R) = 0 ↔ (p : ℤ) ∣ a :=
   by
@@ -144,11 +165,14 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
   · lift a to ℕ using le_of_lt h with b
     rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
 #align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff
+-/
 
+#print CharP.intCast_eq_intCast /-
 theorem CharP.intCast_eq_intCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℤ} :
     (a : R) = b ↔ a ≡ b [ZMOD p] := by
   rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.int_cast_eq_zero_iff R p, Int.modEq_iff_dvd]
 #align char_p.int_cast_eq_int_cast CharP.intCast_eq_intCast
+-/
 
 #print CharP.natCast_eq_natCast /-
 theorem CharP.natCast_eq_natCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℕ} :
@@ -226,10 +250,12 @@ namespace ringChar
 
 variable [NonAssocSemiring R]
 
+#print ringChar.spec /-
 theorem spec : ∀ x : ℕ, (x : R) = 0 ↔ ringChar R ∣ x := by
   letI := (Classical.choose_spec (CharP.exists_unique R)).1 <;> unfold ringChar <;>
     exact CharP.cast_eq_zero_iff R (ringChar R)
 #align ring_char.spec ringChar.spec
+-/
 
 #print ringChar.eq /-
 theorem eq (p : ℕ) [C : CharP R p] : ringChar R = p :=
@@ -257,9 +283,11 @@ theorem eq_iff {p : ℕ} : ringChar R = p ↔ CharP R p :=
 #align ring_char.eq_iff ringChar.eq_iff
 -/
 
+#print ringChar.dvd /-
 theorem dvd {x : ℕ} (hx : (x : R) = 0) : ringChar R ∣ x :=
   (spec R x).1 hx
 #align ring_char.dvd ringChar.dvd
+-/
 
 #print ringChar.eq_zero /-
 @[simp]
@@ -268,33 +296,42 @@ theorem eq_zero [CharZero R] : ringChar R = 0 :=
 #align ring_char.eq_zero ringChar.eq_zero
 -/
 
+#print ringChar.Nat.cast_ringChar /-
 @[simp]
 theorem Nat.cast_ringChar : (ringChar R : R) = 0 := by rw [ringChar.spec]
 #align ring_char.nat.cast_ring_char ringChar.Nat.cast_ringChar
+-/
 
 end ringChar
 
+#print add_pow_char_of_commute /-
 theorem add_pow_char_of_commute [Semiring R] {p : ℕ} [hp : Fact p.Prime] [CharP R p] (x y : R)
     (h : Commute x y) : (x + y) ^ p = x ^ p + y ^ p :=
   by
   let ⟨r, hr⟩ := h.exists_add_pow_prime_eq hp.out
   simp [hr]
 #align add_pow_char_of_commute add_pow_char_of_commute
+-/
 
+#print add_pow_char_pow_of_commute /-
 theorem add_pow_char_pow_of_commute [Semiring R] {p n : ℕ} [hp : Fact p.Prime] [CharP R p] (x y : R)
     (h : Commute x y) : (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n :=
   by
   let ⟨r, hr⟩ := h.exists_add_pow_prime_pow_eq hp.out n
   simp [hr]
 #align add_pow_char_pow_of_commute add_pow_char_pow_of_commute
+-/
 
+#print sub_pow_char_of_commute /-
 theorem sub_pow_char_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R)
     (h : Commute x y) : (x - y) ^ p = x ^ p - y ^ p :=
   by
   rw [eq_sub_iff_add_eq, ← add_pow_char_of_commute _ _ _ (Commute.sub_left h rfl)]
   simp; repeat' infer_instance
 #align sub_pow_char_of_commute sub_pow_char_of_commute
+-/
 
+#print sub_pow_char_pow_of_commute /-
 theorem sub_pow_char_pow_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p] {n : ℕ} (x y : R)
     (h : Commute x y) : (x - y) ^ p ^ n = x ^ p ^ n - y ^ p ^ n :=
   by
@@ -302,27 +339,37 @@ theorem sub_pow_char_pow_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p
   rw [pow_succ', pow_mul, pow_mul, pow_mul, n_ih]
   apply sub_pow_char_of_commute; apply Commute.pow_pow h
 #align sub_pow_char_pow_of_commute sub_pow_char_pow_of_commute
+-/
 
+#print add_pow_char /-
 theorem add_pow_char [CommSemiring R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R) :
     (x + y) ^ p = x ^ p + y ^ p :=
   add_pow_char_of_commute _ _ _ (Commute.all _ _)
 #align add_pow_char add_pow_char
+-/
 
+#print add_pow_char_pow /-
 theorem add_pow_char_pow [CommSemiring R] {p : ℕ} [Fact p.Prime] [CharP R p] {n : ℕ} (x y : R) :
     (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n :=
   add_pow_char_pow_of_commute _ _ _ (Commute.all _ _)
 #align add_pow_char_pow add_pow_char_pow
+-/
 
+#print sub_pow_char /-
 theorem sub_pow_char [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R) :
     (x - y) ^ p = x ^ p - y ^ p :=
   sub_pow_char_of_commute _ _ _ (Commute.all _ _)
 #align sub_pow_char sub_pow_char
+-/
 
+#print sub_pow_char_pow /-
 theorem sub_pow_char_pow [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] {n : ℕ} (x y : R) :
     (x - y) ^ p ^ n = x ^ p ^ n - y ^ p ^ n :=
   sub_pow_char_pow_of_commute _ _ _ (Commute.all _ _)
 #align sub_pow_char_pow sub_pow_char_pow
+-/
 
+#print CharP.neg_one_ne_one /-
 theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1 : R) ≠ (1 : R) :=
   by
   suffices (2 : R) ≠ 0 by symm; rw [Ne.def, ← sub_eq_zero, sub_neg_eq_add]; exact this
@@ -332,25 +379,32 @@ theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1
   have := Nat.le_of_dvd (by decide) this
   rw [fact_iff] at *; linarith
 #align char_p.neg_one_ne_one CharP.neg_one_ne_one
+-/
 
+#print CharP.neg_one_pow_char /-
 theorem CharP.neg_one_pow_char [CommRing R] (p : ℕ) [CharP R p] [Fact p.Prime] :
     (-1 : R) ^ p = -1 := by
   rw [eq_neg_iff_add_eq_zero]
   nth_rw 2 [← one_pow p]
   rw [← add_pow_char, add_left_neg, zero_pow (Fact.out (Nat.Prime p)).Pos]
 #align char_p.neg_one_pow_char CharP.neg_one_pow_char
+-/
 
+#print CharP.neg_one_pow_char_pow /-
 theorem CharP.neg_one_pow_char_pow [CommRing R] (p n : ℕ) [CharP R p] [Fact p.Prime] :
     (-1 : R) ^ p ^ n = -1 := by
   rw [eq_neg_iff_add_eq_zero]
   nth_rw 2 [← one_pow (p ^ n)]
   rw [← add_pow_char_pow, add_left_neg, zero_pow (pow_pos (Fact.out (Nat.Prime p)).Pos _)]
 #align char_p.neg_one_pow_char_pow CharP.neg_one_pow_char_pow
+-/
 
+#print RingHom.charP_iff_charP /-
 theorem RingHom.charP_iff_charP {K L : Type _} [DivisionRing K] [Semiring L] [Nontrivial L]
     (f : K →+* L) (p : ℕ) : CharP K p ↔ CharP L p := by
   simp only [charP_iff, ← f.injective.eq_iff, map_natCast f, f.map_zero]
 #align ring_hom.char_p_iff_char_p RingHom.charP_iff_charP
+-/
 
 section frobenius
 
@@ -372,73 +426,101 @@ def frobenius : R →+* R where
 
 variable {R}
 
+#print frobenius_def /-
 theorem frobenius_def : frobenius R p x = x ^ p :=
   rfl
 #align frobenius_def frobenius_def
+-/
 
+#print iterate_frobenius /-
 theorem iterate_frobenius (n : ℕ) : (frobenius R p^[n]) x = x ^ p ^ n :=
   by
   induction n; · simp
   rw [Function.iterate_succ', pow_succ', pow_mul, Function.comp_apply, frobenius_def, n_ih]
 #align iterate_frobenius iterate_frobenius
+-/
 
+#print frobenius_mul /-
 theorem frobenius_mul : frobenius R p (x * y) = frobenius R p x * frobenius R p y :=
   (frobenius R p).map_mul x y
 #align frobenius_mul frobenius_mul
+-/
 
+#print frobenius_one /-
 theorem frobenius_one : frobenius R p 1 = 1 :=
   one_pow _
 #align frobenius_one frobenius_one
+-/
 
+#print MonoidHom.map_frobenius /-
 theorem MonoidHom.map_frobenius : f (frobenius R p x) = frobenius S p (f x) :=
   f.map_pow x p
 #align monoid_hom.map_frobenius MonoidHom.map_frobenius
+-/
 
+#print RingHom.map_frobenius /-
 theorem RingHom.map_frobenius : g (frobenius R p x) = frobenius S p (g x) :=
   g.map_pow x p
 #align ring_hom.map_frobenius RingHom.map_frobenius
+-/
 
+#print MonoidHom.map_iterate_frobenius /-
 theorem MonoidHom.map_iterate_frobenius (n : ℕ) :
     f ((frobenius R p^[n]) x) = (frobenius S p^[n]) (f x) :=
   Function.Semiconj.iterate_right (f.map_frobenius p) n x
 #align monoid_hom.map_iterate_frobenius MonoidHom.map_iterate_frobenius
+-/
 
+#print RingHom.map_iterate_frobenius /-
 theorem RingHom.map_iterate_frobenius (n : ℕ) :
     g ((frobenius R p^[n]) x) = (frobenius S p^[n]) (g x) :=
   g.toMonoidHom.map_iterate_frobenius p x n
 #align ring_hom.map_iterate_frobenius RingHom.map_iterate_frobenius
+-/
 
+#print MonoidHom.iterate_map_frobenius /-
 theorem MonoidHom.iterate_map_frobenius (f : R →* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
     (f^[n]) (frobenius R p x) = frobenius R p ((f^[n]) x) :=
   f.iterate_map_pow _ _ _
 #align monoid_hom.iterate_map_frobenius MonoidHom.iterate_map_frobenius
+-/
 
+#print RingHom.iterate_map_frobenius /-
 theorem RingHom.iterate_map_frobenius (f : R →+* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
     (f^[n]) (frobenius R p x) = frobenius R p ((f^[n]) x) :=
   f.iterate_map_pow _ _ _
 #align ring_hom.iterate_map_frobenius RingHom.iterate_map_frobenius
+-/
 
 variable (R)
 
+#print frobenius_zero /-
 theorem frobenius_zero : frobenius R p 0 = 0 :=
   (frobenius R p).map_zero
 #align frobenius_zero frobenius_zero
+-/
 
+#print frobenius_add /-
 theorem frobenius_add : frobenius R p (x + y) = frobenius R p x + frobenius R p y :=
   (frobenius R p).map_add x y
 #align frobenius_add frobenius_add
+-/
 
+#print frobenius_nat_cast /-
 theorem frobenius_nat_cast (n : ℕ) : frobenius R p n = n :=
   map_natCast (frobenius R p) n
 #align frobenius_nat_cast frobenius_nat_cast
+-/
 
 open scoped BigOperators
 
 variable {R}
 
+#print list_sum_pow_char /-
 theorem list_sum_pow_char (l : List R) : l.Sum ^ p = (l.map (· ^ p)).Sum :=
   (frobenius R p).map_list_sum _
 #align list_sum_pow_char list_sum_pow_char
+-/
 
 #print multiset_sum_pow_char /-
 theorem multiset_sum_pow_char (s : Multiset R) : s.Sum ^ p = (s.map (· ^ p)).Sum :=
@@ -460,23 +542,30 @@ section CommRing
 variable [CommRing R] {S : Type v} [CommRing S] (f : R →* S) (g : R →+* S) (p : ℕ) [Fact p.Prime]
   [CharP R p] [CharP S p] (x y : R)
 
+#print frobenius_neg /-
 theorem frobenius_neg : frobenius R p (-x) = -frobenius R p x :=
   (frobenius R p).map_neg x
 #align frobenius_neg frobenius_neg
+-/
 
+#print frobenius_sub /-
 theorem frobenius_sub : frobenius R p (x - y) = frobenius R p x - frobenius R p y :=
   (frobenius R p).map_sub x y
 #align frobenius_sub frobenius_sub
+-/
 
 end CommRing
 
 end frobenius
 
+#print frobenius_inj /-
 theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP R p] :
     Function.Injective (frobenius R p) := fun x h H => by rw [← sub_eq_zero] at H ⊢;
   rw [← frobenius_sub] at H ; exact IsReduced.eq_zero _ ⟨_, H⟩
 #align frobenius_inj frobenius_inj
+-/
 
+#print isSquare_of_charTwo' /-
 /-- If `ring_char R = 2`, where `R` is a finite reduced commutative ring,
 then every `a : R` is a square. -/
 theorem isSquare_of_charTwo' {R : Type _} [Finite R] [CommRing R] [IsReduced R] [CharP R 2]
@@ -485,6 +574,7 @@ theorem isSquare_of_charTwo' {R : Type _} [Finite R] [CommRing R] [IsReduced R]
     Exists.imp (fun b h => pow_two b ▸ Eq.symm h)
       (((Fintype.bijective_iff_injective_and_card _).mpr ⟨frobenius_inj R 2, rfl⟩).Surjective a)
 #align is_square_of_char_two' isSquare_of_charTwo'
+-/
 
 namespace CharP
 
@@ -529,6 +619,7 @@ section CommRing
 
 variable [CommRing R] [IsReduced R] {R}
 
+#print CharP.pow_prime_pow_mul_eq_one_iff /-
 @[simp]
 theorem pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [Fact p.Prime] [CharP R p] (x : R) :
     x ^ (p ^ k * m) = 1 ↔ x ^ m = 1 :=
@@ -540,6 +631,7 @@ theorem pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [Fact p.Prime] [CharP R p] (x
       exact hk.1 (frobenius_inj R p h)
     · rw [pow_mul', h, one_pow]
 #align char_p.pow_prime_pow_mul_eq_one_iff CharP.pow_prime_pow_mul_eq_one_iff
+-/
 
 end CommRing
 
@@ -561,6 +653,7 @@ section NoZeroDivisors
 variable [NoZeroDivisors R]
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (d «expr ∣ » p) -/
+#print CharP.char_is_prime_of_two_le /-
 theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.Prime p :=
   suffices ∀ (d) (_ : d ∣ p), d = 1 ∨ d = p from Nat.prime_def_lt''.mpr ⟨hp, this⟩
   fun (d : ℕ) (hdvd : ∃ e, p = d * e) =>
@@ -579,21 +672,26 @@ theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.
     have : d * p = 1 * p := by rw [‹e = p›] at hmul  <;> rw [one_mul] <;> exact Eq.symm hmul
     show d = 1 ∨ d = p from Or.inl (mul_right_cancel₀ h₀.ne' this)
 #align char_p.char_is_prime_of_two_le CharP.char_is_prime_of_two_le
+-/
 
 section Nontrivial
 
 variable [Nontrivial R]
 
+#print CharP.char_is_prime_or_zero /-
 theorem char_is_prime_or_zero (p : ℕ) [hc : CharP R p] : Nat.Prime p ∨ p = 0 :=
   match p, hc with
   | 0, _ => Or.inr rfl
   | 1, hc => absurd (Eq.refl (1 : ℕ)) (@char_ne_one R _ _ (1 : ℕ) hc)
   | m + 2, hc => Or.inl (@char_is_prime_of_two_le R _ _ (m + 2) hc (Nat.le_add_left 2 m))
 #align char_p.char_is_prime_or_zero CharP.char_is_prime_or_zero
+-/
 
+#print CharP.char_is_prime_of_pos /-
 theorem char_is_prime_of_pos (p : ℕ) [NeZero p] [CharP R p] : Fact p.Prime :=
   ⟨(CharP.char_is_prime_or_zero R _).resolve_right <| NeZero.ne p⟩
 #align char_p.char_is_prime_of_pos CharP.char_is_prime_of_pos
+-/
 
 end Nontrivial
 
@@ -605,9 +703,11 @@ section Ring
 
 variable (R) [Ring R] [NoZeroDivisors R] [Nontrivial R] [Finite R]
 
+#print CharP.char_is_prime /-
 theorem char_is_prime (p : ℕ) [CharP R p] : p.Prime :=
   Or.resolve_right (char_is_prime_or_zero R p) (char_ne_zero_of_finite R p)
 #align char_p.char_is_prime CharP.char_is_prime
+-/
 
 end Ring
 
@@ -645,10 +745,12 @@ theorem nontrivial_of_char_ne_one {v : ℕ} (hv : v ≠ 1) [hr : CharP R v] : No
 #align char_p.nontrivial_of_char_ne_one CharP.nontrivial_of_char_ne_one
 -/
 
+#print CharP.ringChar_of_prime_eq_zero /-
 theorem ringChar_of_prime_eq_zero [Nontrivial R] {p : ℕ} (hprime : Nat.Prime p)
     (hp0 : (p : R) = 0) : ringChar R = p :=
   Or.resolve_left ((Nat.dvd_prime hprime).1 (ringChar.dvd hp0)) ringChar_ne_one
 #align char_p.ring_char_of_prime_eq_zero CharP.ringChar_of_prime_eq_zero
+-/
 
 end CharOne
 
@@ -656,6 +758,7 @@ end CharP
 
 section
 
+#print Ring.two_ne_zero /-
 /-- We have `2 ≠ 0` in a nontrivial ring whose characteristic is not `2`. -/
 @[protected]
 theorem Ring.two_ne_zero {R : Type _} [NonAssocSemiring R] [Nontrivial R] (hR : ringChar R ≠ 2) :
@@ -664,7 +767,9 @@ theorem Ring.two_ne_zero {R : Type _} [NonAssocSemiring R] [Nontrivial R] (hR :
   rw [Ne.def, (by norm_cast : (2 : R) = (2 : ℕ)), ringChar.spec, Nat.dvd_prime Nat.prime_two]
   exact mt (or_iff_left hR).mp CharP.ringChar_ne_one
 #align ring.two_ne_zero Ring.two_ne_zero
+-/
 
+#print Ring.neg_one_ne_one_of_char_ne_two /-
 -- We have `char_p.neg_one_ne_one`, which assumes `[ring R] (p : ℕ) [char_p R p] [fact (2 < p)]`.
 -- This is a version using `ring_char` instead.
 /-- Characteristic `≠ 2` and nontrivial implies that `-1 ≠ 1`. -/
@@ -672,7 +777,9 @@ theorem Ring.neg_one_ne_one_of_char_ne_two {R : Type _} [NonAssocRing R] [Nontri
     (hR : ringChar R ≠ 2) : (-1 : R) ≠ 1 := fun h =>
   Ring.two_ne_zero hR (neg_eq_iff_add_eq_zero.mp h)
 #align ring.neg_one_ne_one_of_char_ne_two Ring.neg_one_ne_one_of_char_ne_two
+-/
 
+#print Ring.eq_self_iff_eq_zero_of_char_ne_two /-
 /-- Characteristic `≠ 2` in a domain implies that `-a = a` iff `a = 0`. -/
 theorem Ring.eq_self_iff_eq_zero_of_char_ne_two {R : Type _} [NonAssocRing R] [Nontrivial R]
     [NoZeroDivisors R] (hR : ringChar R ≠ 2) {a : R} : -a = a ↔ a = 0 :=
@@ -681,6 +788,7 @@ theorem Ring.eq_self_iff_eq_zero_of_char_ne_two {R : Type _} [NonAssocRing R] [N
       (Ring.two_ne_zero hR),
     fun h => ((congr_arg (fun x => -x) h).trans neg_zero).trans h.symm⟩
 #align ring.eq_self_iff_eq_zero_of_char_ne_two Ring.eq_self_iff_eq_zero_of_char_ne_two
+-/
 
 end
 
@@ -688,6 +796,7 @@ section
 
 variable (R) [NonAssocRing R] [Fintype R] (n : ℕ)
 
+#print charP_of_ne_zero /-
 theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0 → i = 0) :
     CharP R n :=
   {
@@ -705,7 +814,9 @@ theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0
         exact ⟨0⟩
       · rintro ⟨k, rfl⟩; rw [Nat.cast_mul, H, MulZeroClass.zero_mul] }
 #align char_p_of_ne_zero charP_of_ne_zero
+-/
 
+#print charP_of_prime_pow_injective /-
 theorem charP_of_prime_pow_injective (R) [Ring R] [Fintype R] (p : ℕ) [hp : Fact p.Prime] (n : ℕ)
     (hn : Fintype.card R = p ^ n) (hR : ∀ i ≤ n, (p ^ i : R) = 0 → i = n) : CharP R (p ^ n) :=
   by
@@ -715,6 +826,7 @@ theorem charP_of_prime_pow_injective (R) [Ring R] [Fintype R] (p : ℕ) [hp : Fa
   obtain rfl : i = n := by apply hR i hi; rw [← Nat.cast_pow, ← hc, CharP.cast_eq_zero]
   rwa [← hc]
 #align char_p_of_prime_pow_injective charP_of_prime_pow_injective
+-/
 
 end
 
@@ -728,10 +840,12 @@ instance [CharP S q] : CharP (R × S) (Nat.lcm p q)
     where cast_eq_zero_iff := by
     simp [Prod.ext_iff, CharP.cast_eq_zero_iff R p, CharP.cast_eq_zero_iff S q, Nat.lcm_dvd_iff]
 
+#print Prod.charP /-
 /-- The characteristic of the product of two rings of the same characteristic
   is the same as the characteristic of the rings -/
 instance Prod.charP [CharP S p] : CharP (R × S) p := by convert Nat.lcm.charP R S p p <;> simp
 #align prod.char_p Prod.charP
+-/
 
 end Prod
 
@@ -749,6 +863,7 @@ instance MulOpposite.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP R
 
 section
 
+#print Int.cast_injOn_of_ringChar_ne_two /-
 /-- If two integers from `{0, 1, -1}` result in equal elements in a ring `R`
 that is nontrivial and of characteristic not `2`, then they are equal. -/
 theorem Int.cast_injOn_of_ringChar_ne_two {R : Type _} [NonAssocRing R] [Nontrivial R]
@@ -775,6 +890,7 @@ theorem Int.cast_injOn_of_ringChar_ne_two {R : Type _} [NonAssocRing R] [Nontriv
   · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h' ; exact Ring.two_ne_zero hR h'
   · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h'' ; exact Ring.two_ne_zero hR h''
 #align int.cast_inj_on_of_ring_char_ne_two Int.cast_injOn_of_ringChar_ne_two
+-/
 
 end
 
@@ -782,13 +898,17 @@ namespace NeZero
 
 variable (R) [AddMonoidWithOne R] {r : R} {n p : ℕ} {a : ℕ+}
 
+#print NeZero.of_not_dvd /-
 theorem of_not_dvd [CharP R p] (h : ¬p ∣ n) : NeZero (n : R) :=
   ⟨(CharP.cast_eq_zero_iff R p n).Not.mpr h⟩
 #align ne_zero.of_not_dvd NeZero.of_not_dvd
+-/
 
+#print NeZero.not_char_dvd /-
 theorem not_char_dvd (p : ℕ) [CharP R p] (k : ℕ) [h : NeZero (k : R)] : ¬p ∣ k := by
   rwa [← CharP.cast_eq_zero_iff R p k, ← Ne.def, ← neZero_iff]
 #align ne_zero.not_char_dvd NeZero.not_char_dvd
+-/
 
 end NeZero

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -503,7 +503,6 @@ theorem cast_eq_mod (p : ℕ) [CharP R p] (k : ℕ) : (k : R) = (k % p : ℕ) :=
   calc
     (k : R) = ↑(k % p + p * (k / p)) := by rw [Nat.mod_add_div]
     _ = ↑(k % p) := by simp [cast_eq_zero]
-    
 #align char_p.cast_eq_mod CharP.cast_eq_mod
 -/
 
@@ -626,7 +625,6 @@ instance (priority := 100) [CharP R 1] : Subsingleton R :=
       _ = (1 : ℕ) * r := by rw [Nat.cast_one]
       _ = 0 * r := by rw [CharP.cast_eq_zero]
       _ = 0 := by rw [MulZeroClass.zero_mul]
-      
 
 #print CharP.false_of_nontrivial_of_char_one /-
 theorem false_of_nontrivial_of_char_one [Nontrivial R] [CharP R 1] : False :=

bump to nightly-2023-06-08-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

d3cfe2e3

Diff

@@ -561,7 +561,7 @@ section NoZeroDivisors
 
 variable [NoZeroDivisors R]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (d «expr ∣ » p) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (d «expr ∣ » p) -/
 theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.Prime p :=
   suffices ∀ (d) (_ : d ∣ p), d = 1 ∨ d = p from Nat.prime_def_lt''.mpr ⟨hp, this⟩
   fun (d : ℕ) (hdvd : ∃ e, p = d * e) =>

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -100,7 +100,7 @@ end CommSemiring
 variable (R)
 
 #print CharP /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
 /-- The generator of the kernel of the unique homomorphism ℕ → R for a semiring R.
 
 *Warning*: for a semiring `R`, `char_p R 0` and `char_zero R` need not coincide.

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -46,7 +46,7 @@ protected theorem add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ
   · congr 1
     simp_rw [Finset.mul_sum, Nat.cast_comm, mul_assoc _ _ (p : R), ← Nat.cast_mul]
     refine' Finset.sum_congr rfl fun i hi => _
-    rw [mem_Ioo] at hi
+    rw [mem_Ioo] at hi 
     rw [Nat.div_mul_cancel (hp.dvd_choose_pow hi.1.ne' hi.2.Ne)]
 #align commute.add_pow_prime_pow_eq Commute.add_pow_prime_pow_eq
 
@@ -192,7 +192,7 @@ theorem CharP.exists [NonAssocSemiring R] : ∃ p, CharP R p :=
                     rwa [← Nat.mod_add_div x (Nat.find (not_forall.1 H)), Nat.cast_add,
                       Nat.cast_mul,
                       of_not_not (not_not_of_not_imp <| Nat.find_spec (not_forall.1 H)),
-                      MulZeroClass.zero_mul, add_zero] at H1,
+                      MulZeroClass.zero_mul, add_zero] at H1 ,
                     H2⟩)),
           fun H1 => by
           rw [← Nat.mul_div_cancel' H1, Nat.cast_mul,
@@ -327,7 +327,7 @@ theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1
   by
   suffices (2 : R) ≠ 0 by symm; rw [Ne.def, ← sub_eq_zero, sub_neg_eq_add]; exact this
   intro h
-  rw [show (2 : R) = (2 : ℕ) by norm_cast] at h
+  rw [show (2 : R) = (2 : ℕ) by norm_cast] at h 
   have := (CharP.cast_eq_zero_iff R p 2).mp h
   have := Nat.le_of_dvd (by decide) this
   rw [fact_iff] at *; linarith
@@ -473,8 +473,8 @@ end CommRing
 end frobenius
 
 theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP R p] :
-    Function.Injective (frobenius R p) := fun x h H => by rw [← sub_eq_zero] at H⊢;
-  rw [← frobenius_sub] at H; exact IsReduced.eq_zero _ ⟨_, H⟩
+    Function.Injective (frobenius R p) := fun x h H => by rw [← sub_eq_zero] at H ⊢;
+  rw [← frobenius_sub] at H ; exact IsReduced.eq_zero _ ⟨_, H⟩
 #align frobenius_inj frobenius_inj
 
 /-- If `ring_char R = 2`, where `R` is a finite reduced commutative ring,
@@ -537,7 +537,7 @@ theorem pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [Fact p.Prime] [CharP R p] (x
   induction' k with k hk
   · rw [pow_zero, one_mul]
   · refine' ⟨fun h => _, fun h => _⟩
-    · rw [pow_succ, mul_assoc, pow_mul', ← frobenius_def, ← frobenius_one p] at h
+    · rw [pow_succ, mul_assoc, pow_mul', ← frobenius_def, ← frobenius_one p] at h 
       exact hk.1 (frobenius_inj R p h)
     · rw [pow_mul', h, one_pow]
 #align char_p.pow_prime_pow_mul_eq_one_iff CharP.pow_prime_pow_mul_eq_one_iff
@@ -577,7 +577,7 @@ theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.
     have : e ∣ p := dvd_of_mul_left_eq d (Eq.symm hmul)
     have : e = p := dvd_antisymm ‹e ∣ p› ‹p ∣ e›
     have h₀ : 0 < p := two_pos.trans_le hp
-    have : d * p = 1 * p := by rw [‹e = p›] at hmul <;> rw [one_mul] <;> exact Eq.symm hmul
+    have : d * p = 1 * p := by rw [‹e = p›] at hmul  <;> rw [one_mul] <;> exact Eq.symm hmul
     show d = 1 ∨ d = p from Or.inl (mul_right_cancel₀ h₀.ne' this)
 #align char_p.char_is_prime_of_two_le CharP.char_is_prime_of_two_le
 
@@ -643,7 +643,7 @@ theorem ringChar_ne_one [Nontrivial R] : ringChar R ≠ 1 := by intro h; apply z
 #print CharP.nontrivial_of_char_ne_one /-
 theorem nontrivial_of_char_ne_one {v : ℕ} (hv : v ≠ 1) [hr : CharP R v] : Nontrivial R :=
   ⟨⟨(1 : ℕ), 0, fun h =>
-      hv <| by rwa [CharP.cast_eq_zero_iff _ v, Nat.dvd_one] at h <;> assumption⟩⟩
+      hv <| by rwa [CharP.cast_eq_zero_iff _ v, Nat.dvd_one] at h  <;> assumption⟩⟩
 #align char_p.nontrivial_of_char_ne_one CharP.nontrivial_of_char_ne_one
 -/
 
@@ -700,7 +700,7 @@ theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0
       constructor
       · intro h
         rw [← Nat.mod_add_div k n, Nat.cast_add, Nat.cast_mul, H, MulZeroClass.zero_mul,
-          add_zero] at h
+          add_zero] at h 
         rw [Nat.dvd_iff_mod_eq_zero]
         apply hR _ (Nat.mod_lt _ _) h
         rw [← hn, Fintype.card_pos_iff]
@@ -713,7 +713,7 @@ theorem charP_of_prime_pow_injective (R) [Ring R] [Fintype R] (p : ℕ) [hp : Fa
   by
   obtain ⟨c, hc⟩ := CharP.exists R; skip
   have hcpn : c ∣ p ^ n := by rw [← CharP.cast_eq_zero_iff R c, ← hn, CharP.cast_card_eq_zero]
-  obtain ⟨i, hi, hc⟩ : ∃ i ≤ n, c = p ^ i := by rwa [Nat.dvd_prime_pow hp.1] at hcpn
+  obtain ⟨i, hi, hc⟩ : ∃ i ≤ n, c = p ^ i := by rwa [Nat.dvd_prime_pow hp.1] at hcpn 
   obtain rfl : i = n := by apply hR i hi; rw [← Nat.cast_pow, ← hc, CharP.cast_eq_zero]
   rwa [← hc]
 #align char_p_of_prime_pow_injective charP_of_prime_pow_injective
@@ -759,23 +759,23 @@ theorem Int.cast_injOn_of_ringChar_ne_two {R : Type _} [NonAssocRing R] [Nontriv
   intro a ha b hb h
   apply eq_of_sub_eq_zero
   by_contra hf
-  change a = 0 ∨ a = 1 ∨ a = -1 at ha
-  change b = 0 ∨ b = 1 ∨ b = -1 at hb
+  change a = 0 ∨ a = 1 ∨ a = -1 at ha 
+  change b = 0 ∨ b = 1 ∨ b = -1 at hb 
   have hh : a - b = 1 ∨ b - a = 1 ∨ a - b = 2 ∨ b - a = 2 :=
     by
     rcases ha with (ha | ha | ha) <;> rcases hb with (hb | hb | hb)
     pick_goal 5; pick_goal 9
     -- move goals with `a = b` to the front
-    iterate 3 rw [ha, hb, sub_self] at hf; tauto
+    iterate 3 rw [ha, hb, sub_self] at hf ; tauto
     -- 6 goals remain
     all_goals rw [ha, hb]; norm_num
   have h' : ((a - b : ℤ) : R) = 0 := by exact_mod_cast sub_eq_zero_of_eq h
   have h'' : ((b - a : ℤ) : R) = 0 := by exact_mod_cast sub_eq_zero_of_eq h.symm
   rcases hh with (hh | hh | hh | hh)
-  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h'; exact one_ne_zero h'
-  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h''; exact one_ne_zero h''
-  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h'; exact Ring.two_ne_zero hR h'
-  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h''; exact Ring.two_ne_zero hR h''
+  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h' ; exact one_ne_zero h'
+  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h'' ; exact one_ne_zero h''
+  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h' ; exact Ring.two_ne_zero hR h'
+  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h'' ; exact Ring.two_ne_zero hR h''
 #align int.cast_inj_on_of_ring_char_ne_two Int.cast_injOn_of_ringChar_ne_two
 
 end

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -25,7 +25,7 @@ universe u v
 
 open Finset
 
-open BigOperators
+open scoped BigOperators
 
 variable {R : Type _}
 
@@ -432,7 +432,7 @@ theorem frobenius_nat_cast (n : ℕ) : frobenius R p n = n :=
   map_natCast (frobenius R p) n
 #align frobenius_nat_cast frobenius_nat_cast
 
-open BigOperators
+open scoped BigOperators
 
 variable {R}

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -33,12 +33,6 @@ namespace Commute
 
 variable [Semiring R] {p : ℕ} {x y : R}
 
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-Case conversion may be inaccurate. Consider using '#align commute.add_pow_prime_pow_eq Commute.add_pow_prime_pow_eqₓ'. -/
 protected theorem add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ) :
     (x + y) ^ p ^ n =
       x ^ p ^ n + y ^ p ^ n +
@@ -56,35 +50,17 @@ protected theorem add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ
     rw [Nat.div_mul_cancel (hp.dvd_choose_pow hi.1.ne' hi.2.Ne)]
 #align commute.add_pow_prime_pow_eq Commute.add_pow_prime_pow_eq
 
-/- warning: commute.add_pow_prime_eq -> Commute.add_pow_prime_eq is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align commute.add_pow_prime_eq Commute.add_pow_prime_eqₓ'. -/
 protected theorem add_pow_prime_eq (hp : p.Prime) (h : Commute x y) :
     (x + y) ^ p =
       x ^ p + y ^ p + p * ∑ k in Finset.Ioo 0 p, x ^ k * y ^ (p - k) * ↑(p.choose k / p) :=
   by simpa using h.add_pow_prime_pow_eq hp 1
 #align commute.add_pow_prime_eq Commute.add_pow_prime_eq
 
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 protected theorem exists_add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ) :
     ∃ r, (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n + p * r :=
   ⟨_, h.add_pow_prime_pow_eq hp n⟩
 #align commute.exists_add_pow_prime_pow_eq Commute.exists_add_pow_prime_pow_eq
 
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-Case conversion may be inaccurate. Consider using '#align commute.exists_add_pow_prime_eq Commute.exists_add_pow_prime_eqₓ'. -/
 protected theorem exists_add_pow_prime_eq (hp : p.Prime) (h : Commute x y) :
     ∃ r, (x + y) ^ p = x ^ p + y ^ p + p * r :=
   ⟨_, h.add_pow_prime_eq hp⟩
@@ -96,12 +72,6 @@ section CommSemiring
 
 variable [CommSemiring R] {p : ℕ} {x y : R}
 
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-Case conversion may be inaccurate. Consider using '#align add_pow_prime_pow_eq add_pow_prime_pow_eqₓ'. -/
 theorem add_pow_prime_pow_eq (hp : p.Prime) (x y : R) (n : ℕ) :
     (x + y) ^ p ^ n =
       x ^ p ^ n + y ^ p ^ n +
@@ -109,35 +79,17 @@ theorem add_pow_prime_pow_eq (hp : p.Prime) (x y : R) (n : ℕ) :
   (Commute.all x y).add_pow_prime_pow_eq hp n
 #align add_pow_prime_pow_eq add_pow_prime_pow_eq
 
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-Case conversion may be inaccurate. Consider using '#align add_pow_prime_eq add_pow_prime_eqₓ'. -/
 theorem add_pow_prime_eq (hp : p.Prime) (x y : R) :
     (x + y) ^ p =
       x ^ p + y ^ p + p * ∑ k in Finset.Ioo 0 p, x ^ k * y ^ (p - k) * ↑(p.choose k / p) :=
   (Commute.all x y).add_pow_prime_eq hp
 #align add_pow_prime_eq add_pow_prime_eq
 
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 theorem exists_add_pow_prime_pow_eq (hp : p.Prime) (x y : R) (n : ℕ) :
     ∃ r, (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n + p * r :=
   (Commute.all x y).exists_add_pow_prime_pow_eq hp n
 #align exists_add_pow_prime_pow_eq exists_add_pow_prime_pow_eq
 
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 theorem exists_add_pow_prime_eq (hp : p.Prime) (x y : R) :
     ∃ r, (x + y) ^ p = x ^ p + y ^ p + p * r :=
   (Commute.all x y).exists_add_pow_prime_eq hp
@@ -165,23 +117,11 @@ class CharP [AddMonoidWithOne R] (p : ℕ) : Prop where
 #align char_p CharP
 -/
 
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 @[simp]
 theorem CharP.cast_eq_zero [AddMonoidWithOne R] (p : ℕ) [CharP R p] : (p : R) = 0 :=
   (CharP.cast_eq_zero_iff R p p).2 (dvd_refl p)
 #align char_p.cast_eq_zero CharP.cast_eq_zero
 
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 @[simp]
 theorem CharP.cast_card_eq_zero [AddGroupWithOne R] [Fintype R] : (Fintype.card R : R) = 0 := by
   rw [← nsmul_one, card_nsmul_eq_zero]
@@ -193,12 +133,6 @@ theorem CharP.addOrderOf_one (R) [Semiring R] : CharP R (addOrderOf (1 : R)) :=
 #align char_p.add_order_of_one CharP.addOrderOf_one
 -/
 
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 theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a : ℤ) :
     (a : R) = 0 ↔ (p : ℤ) ∣ a :=
   by
@@ -211,12 +145,6 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
     rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
 #align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff
 
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 theorem CharP.intCast_eq_intCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℤ} :
     (a : R) = b ↔ a ≡ b [ZMOD p] := by
   rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.int_cast_eq_zero_iff R p, Int.modEq_iff_dvd]
@@ -298,12 +226,6 @@ namespace ringChar
 
 variable [NonAssocSemiring R]
 
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 theorem spec : ∀ x : ℕ, (x : R) = 0 ↔ ringChar R ∣ x := by
   letI := (Classical.choose_spec (CharP.exists_unique R)).1 <;> unfold ringChar <;>
     exact CharP.cast_eq_zero_iff R (ringChar R)
@@ -335,12 +257,6 @@ theorem eq_iff {p : ℕ} : ringChar R = p ↔ CharP R p :=
 #align ring_char.eq_iff ringChar.eq_iff
 -/
 
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 theorem dvd {x : ℕ} (hx : (x : R) = 0) : ringChar R ∣ x :=
   (spec R x).1 hx
 #align ring_char.dvd ringChar.dvd
@@ -352,24 +268,12 @@ theorem eq_zero [CharZero R] : ringChar R = 0 :=
 #align ring_char.eq_zero ringChar.eq_zero
 -/
 
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 @[simp]
 theorem Nat.cast_ringChar : (ringChar R : R) = 0 := by rw [ringChar.spec]
 #align ring_char.nat.cast_ring_char ringChar.Nat.cast_ringChar
 
 end ringChar
 
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 theorem add_pow_char_of_commute [Semiring R] {p : ℕ} [hp : Fact p.Prime] [CharP R p] (x y : R)
     (h : Commute x y) : (x + y) ^ p = x ^ p + y ^ p :=
   by
@@ -377,12 +281,6 @@ theorem add_pow_char_of_commute [Semiring R] {p : ℕ} [hp : Fact p.Prime] [Char
   simp [hr]
 #align add_pow_char_of_commute add_pow_char_of_commute
 
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 theorem add_pow_char_pow_of_commute [Semiring R] {p n : ℕ} [hp : Fact p.Prime] [CharP R p] (x y : R)
     (h : Commute x y) : (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n :=
   by
@@ -390,12 +288,6 @@ theorem add_pow_char_pow_of_commute [Semiring R] {p n : ℕ} [hp : Fact p.Prime]
   simp [hr]
 #align add_pow_char_pow_of_commute add_pow_char_pow_of_commute
 
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 theorem sub_pow_char_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R)
     (h : Commute x y) : (x - y) ^ p = x ^ p - y ^ p :=
   by
@@ -403,12 +295,6 @@ theorem sub_pow_char_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p] (x
   simp; repeat' infer_instance
 #align sub_pow_char_of_commute sub_pow_char_of_commute
 
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-Case conversion may be inaccurate. Consider using '#align sub_pow_char_pow_of_commute sub_pow_char_pow_of_commuteₓ'. -/
 theorem sub_pow_char_pow_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p] {n : ℕ} (x y : R)
     (h : Commute x y) : (x - y) ^ p ^ n = x ^ p ^ n - y ^ p ^ n :=
   by
@@ -417,56 +303,26 @@ theorem sub_pow_char_pow_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p
   apply sub_pow_char_of_commute; apply Commute.pow_pow h
 #align sub_pow_char_pow_of_commute sub_pow_char_pow_of_commute
 
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 theorem add_pow_char [CommSemiring R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R) :
     (x + y) ^ p = x ^ p + y ^ p :=
   add_pow_char_of_commute _ _ _ (Commute.all _ _)
 #align add_pow_char add_pow_char
 
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 theorem add_pow_char_pow [CommSemiring R] {p : ℕ} [Fact p.Prime] [CharP R p] {n : ℕ} (x y : R) :
     (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n :=
   add_pow_char_pow_of_commute _ _ _ (Commute.all _ _)
 #align add_pow_char_pow add_pow_char_pow
 
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 theorem sub_pow_char [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R) :
     (x - y) ^ p = x ^ p - y ^ p :=
   sub_pow_char_of_commute _ _ _ (Commute.all _ _)
 #align sub_pow_char sub_pow_char
 
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 theorem sub_pow_char_pow [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] {n : ℕ} (x y : R) :
     (x - y) ^ p ^ n = x ^ p ^ n - y ^ p ^ n :=
   sub_pow_char_pow_of_commute _ _ _ (Commute.all _ _)
 #align sub_pow_char_pow sub_pow_char_pow
 
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 theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1 : R) ≠ (1 : R) :=
   by
   suffices (2 : R) ≠ 0 by symm; rw [Ne.def, ← sub_eq_zero, sub_neg_eq_add]; exact this
@@ -477,12 +333,6 @@ theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1
   rw [fact_iff] at *; linarith
 #align char_p.neg_one_ne_one CharP.neg_one_ne_one
 
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 theorem CharP.neg_one_pow_char [CommRing R] (p : ℕ) [CharP R p] [Fact p.Prime] :
     (-1 : R) ^ p = -1 := by
   rw [eq_neg_iff_add_eq_zero]
@@ -490,12 +340,6 @@ theorem CharP.neg_one_pow_char [CommRing R] (p : ℕ) [CharP R p] [Fact p.Prime]
   rw [← add_pow_char, add_left_neg, zero_pow (Fact.out (Nat.Prime p)).Pos]
 #align char_p.neg_one_pow_char CharP.neg_one_pow_char
 
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 theorem CharP.neg_one_pow_char_pow [CommRing R] (p n : ℕ) [CharP R p] [Fact p.Prime] :
     (-1 : R) ^ p ^ n = -1 := by
   rw [eq_neg_iff_add_eq_zero]
@@ -503,12 +347,6 @@ theorem CharP.neg_one_pow_char_pow [CommRing R] (p n : ℕ) [CharP R p] [Fact p.
   rw [← add_pow_char_pow, add_left_neg, zero_pow (pow_pos (Fact.out (Nat.Prime p)).Pos _)]
 #align char_p.neg_one_pow_char_pow CharP.neg_one_pow_char_pow
 
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 theorem RingHom.charP_iff_charP {K L : Type _} [DivisionRing K] [Semiring L] [Nontrivial L]
     (f : K →+* L) (p : ℕ) : CharP K p ↔ CharP L p := by
   simp only [charP_iff, ← f.injective.eq_iff, map_natCast f, f.map_zero]
@@ -534,86 +372,47 @@ def frobenius : R →+* R where
 
 variable {R}
 
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 theorem frobenius_def : frobenius R p x = x ^ p :=
   rfl
 #align frobenius_def frobenius_def
 
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 theorem iterate_frobenius (n : ℕ) : (frobenius R p^[n]) x = x ^ p ^ n :=
   by
   induction n; · simp
   rw [Function.iterate_succ', pow_succ', pow_mul, Function.comp_apply, frobenius_def, n_ih]
 #align iterate_frobenius iterate_frobenius
 
-/- warning: frobenius_mul -> frobenius_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align frobenius_mul frobenius_mulₓ'. -/
 theorem frobenius_mul : frobenius R p (x * y) = frobenius R p x * frobenius R p y :=
   (frobenius R p).map_mul x y
 #align frobenius_mul frobenius_mul
 
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-Case conversion may be inaccurate. Consider using '#align frobenius_one frobenius_oneₓ'. -/
 theorem frobenius_one : frobenius R p 1 = 1 :=
   one_pow _
 #align frobenius_one frobenius_one
 
-/- warning: monoid_hom.map_frobenius -> MonoidHom.map_frobenius is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monoid_hom.map_frobenius MonoidHom.map_frobeniusₓ'. -/
 theorem MonoidHom.map_frobenius : f (frobenius R p x) = frobenius S p (f x) :=
   f.map_pow x p
 #align monoid_hom.map_frobenius MonoidHom.map_frobenius
 
-/- warning: ring_hom.map_frobenius -> RingHom.map_frobenius is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ring_hom.map_frobenius RingHom.map_frobeniusₓ'. -/
 theorem RingHom.map_frobenius : g (frobenius R p x) = frobenius S p (g x) :=
   g.map_pow x p
 #align ring_hom.map_frobenius RingHom.map_frobenius
 
-/- warning: monoid_hom.map_iterate_frobenius -> MonoidHom.map_iterate_frobenius is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monoid_hom.map_iterate_frobenius MonoidHom.map_iterate_frobeniusₓ'. -/
 theorem MonoidHom.map_iterate_frobenius (n : ℕ) :
     f ((frobenius R p^[n]) x) = (frobenius S p^[n]) (f x) :=
   Function.Semiconj.iterate_right (f.map_frobenius p) n x
 #align monoid_hom.map_iterate_frobenius MonoidHom.map_iterate_frobenius
 
-/- warning: ring_hom.map_iterate_frobenius -> RingHom.map_iterate_frobenius is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ring_hom.map_iterate_frobenius RingHom.map_iterate_frobeniusₓ'. -/
 theorem RingHom.map_iterate_frobenius (n : ℕ) :
     g ((frobenius R p^[n]) x) = (frobenius S p^[n]) (g x) :=
   g.toMonoidHom.map_iterate_frobenius p x n
 #align ring_hom.map_iterate_frobenius RingHom.map_iterate_frobenius
 
-/- warning: monoid_hom.iterate_map_frobenius -> MonoidHom.iterate_map_frobenius is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monoid_hom.iterate_map_frobenius MonoidHom.iterate_map_frobeniusₓ'. -/
 theorem MonoidHom.iterate_map_frobenius (f : R →* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
     (f^[n]) (frobenius R p x) = frobenius R p ((f^[n]) x) :=
   f.iterate_map_pow _ _ _
 #align monoid_hom.iterate_map_frobenius MonoidHom.iterate_map_frobenius
 
-/- warning: ring_hom.iterate_map_frobenius -> RingHom.iterate_map_frobenius is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ring_hom.iterate_map_frobenius RingHom.iterate_map_frobeniusₓ'. -/
 theorem RingHom.iterate_map_frobenius (f : R →+* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
     (f^[n]) (frobenius R p x) = frobenius R p ((f^[n]) x) :=
   f.iterate_map_pow _ _ _
@@ -621,29 +420,14 @@ theorem RingHom.iterate_map_frobenius (f : R →+* R) (p : ℕ) [Fact p.Prime] [
 
 variable (R)
 
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-Case conversion may be inaccurate. Consider using '#align frobenius_zero frobenius_zeroₓ'. -/
 theorem frobenius_zero : frobenius R p 0 = 0 :=
   (frobenius R p).map_zero
 #align frobenius_zero frobenius_zero
 
-/- warning: frobenius_add -> frobenius_add is a dubious translation:
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 theorem frobenius_add : frobenius R p (x + y) = frobenius R p x + frobenius R p y :=
   (frobenius R p).map_add x y
 #align frobenius_add frobenius_add
 
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-Case conversion may be inaccurate. Consider using '#align frobenius_nat_cast frobenius_nat_castₓ'. -/
 theorem frobenius_nat_cast (n : ℕ) : frobenius R p n = n :=
   map_natCast (frobenius R p) n
 #align frobenius_nat_cast frobenius_nat_cast
@@ -652,12 +436,6 @@ open BigOperators
 
 variable {R}
 
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-Case conversion may be inaccurate. Consider using '#align list_sum_pow_char list_sum_pow_charₓ'. -/
 theorem list_sum_pow_char (l : List R) : l.Sum ^ p = (l.map (· ^ p)).Sum :=
   (frobenius R p).map_list_sum _
 #align list_sum_pow_char list_sum_pow_char
@@ -682,19 +460,10 @@ section CommRing
 variable [CommRing R] {S : Type v} [CommRing S] (f : R →* S) (g : R →+* S) (p : ℕ) [Fact p.Prime]
   [CharP R p] [CharP S p] (x y : R)
 
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-Case conversion may be inaccurate. Consider using '#align frobenius_neg frobenius_negₓ'. -/
 theorem frobenius_neg : frobenius R p (-x) = -frobenius R p x :=
   (frobenius R p).map_neg x
 #align frobenius_neg frobenius_neg
 
-/- warning: frobenius_sub -> frobenius_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align frobenius_sub frobenius_subₓ'. -/
 theorem frobenius_sub : frobenius R p (x - y) = frobenius R p x - frobenius R p y :=
   (frobenius R p).map_sub x y
 #align frobenius_sub frobenius_sub
@@ -703,23 +472,11 @@ end CommRing
 
 end frobenius
 
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 theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP R p] :
     Function.Injective (frobenius R p) := fun x h H => by rw [← sub_eq_zero] at H⊢;
   rw [← frobenius_sub] at H; exact IsReduced.eq_zero _ ⟨_, H⟩
 #align frobenius_inj frobenius_inj
 
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 /-- If `ring_char R = 2`, where `R` is a finite reduced commutative ring,
 then every `a : R` is a square. -/
 theorem isSquare_of_charTwo' {R : Type _} [Finite R] [CommRing R] [IsReduced R] [CharP R 2]
@@ -773,12 +530,6 @@ section CommRing
 
 variable [CommRing R] [IsReduced R] {R}
 
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 @[simp]
 theorem pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [Fact p.Prime] [CharP R p] (x : R) :
     x ^ (p ^ k * m) = 1 ↔ x ^ m = 1 :=
@@ -810,12 +561,6 @@ section NoZeroDivisors
 
 variable [NoZeroDivisors R]
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (d «expr ∣ » p) -/
 theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.Prime p :=
   suffices ∀ (d) (_ : d ∣ p), d = 1 ∨ d = p from Nat.prime_def_lt''.mpr ⟨hp, this⟩
@@ -840,12 +585,6 @@ section Nontrivial
 
 variable [Nontrivial R]
 
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-Case conversion may be inaccurate. Consider using '#align char_p.char_is_prime_or_zero CharP.char_is_prime_or_zeroₓ'. -/
 theorem char_is_prime_or_zero (p : ℕ) [hc : CharP R p] : Nat.Prime p ∨ p = 0 :=
   match p, hc with
   | 0, _ => Or.inr rfl
@@ -853,12 +592,6 @@ theorem char_is_prime_or_zero (p : ℕ) [hc : CharP R p] : Nat.Prime p ∨ p = 0
   | m + 2, hc => Or.inl (@char_is_prime_of_two_le R _ _ (m + 2) hc (Nat.le_add_left 2 m))
 #align char_p.char_is_prime_or_zero CharP.char_is_prime_or_zero
 
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 theorem char_is_prime_of_pos (p : ℕ) [NeZero p] [CharP R p] : Fact p.Prime :=
   ⟨(CharP.char_is_prime_or_zero R _).resolve_right <| NeZero.ne p⟩
 #align char_p.char_is_prime_of_pos CharP.char_is_prime_of_pos
@@ -873,12 +606,6 @@ section Ring
 
 variable (R) [Ring R] [NoZeroDivisors R] [Nontrivial R] [Finite R]
 
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-Case conversion may be inaccurate. Consider using '#align char_p.char_is_prime CharP.char_is_primeₓ'. -/
 theorem char_is_prime (p : ℕ) [CharP R p] : p.Prime :=
   Or.resolve_right (char_is_prime_or_zero R p) (char_ne_zero_of_finite R p)
 #align char_p.char_is_prime CharP.char_is_prime
@@ -920,12 +647,6 @@ theorem nontrivial_of_char_ne_one {v : ℕ} (hv : v ≠ 1) [hr : CharP R v] : No
 #align char_p.nontrivial_of_char_ne_one CharP.nontrivial_of_char_ne_one
 -/
 
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 theorem ringChar_of_prime_eq_zero [Nontrivial R] {p : ℕ} (hprime : Nat.Prime p)
     (hp0 : (p : R) = 0) : ringChar R = p :=
   Or.resolve_left ((Nat.dvd_prime hprime).1 (ringChar.dvd hp0)) ringChar_ne_one
@@ -937,12 +658,6 @@ end CharP
 
 section
 
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 /-- We have `2 ≠ 0` in a nontrivial ring whose characteristic is not `2`. -/
 @[protected]
 theorem Ring.two_ne_zero {R : Type _} [NonAssocSemiring R] [Nontrivial R] (hR : ringChar R ≠ 2) :
@@ -952,12 +667,6 @@ theorem Ring.two_ne_zero {R : Type _} [NonAssocSemiring R] [Nontrivial R] (hR :
   exact mt (or_iff_left hR).mp CharP.ringChar_ne_one
 #align ring.two_ne_zero Ring.two_ne_zero
 
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 -- We have `char_p.neg_one_ne_one`, which assumes `[ring R] (p : ℕ) [char_p R p] [fact (2 < p)]`.
 -- This is a version using `ring_char` instead.
 /-- Characteristic `≠ 2` and nontrivial implies that `-1 ≠ 1`. -/
@@ -966,12 +675,6 @@ theorem Ring.neg_one_ne_one_of_char_ne_two {R : Type _} [NonAssocRing R] [Nontri
   Ring.two_ne_zero hR (neg_eq_iff_add_eq_zero.mp h)
 #align ring.neg_one_ne_one_of_char_ne_two Ring.neg_one_ne_one_of_char_ne_two
 
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 /-- Characteristic `≠ 2` in a domain implies that `-a = a` iff `a = 0`. -/
 theorem Ring.eq_self_iff_eq_zero_of_char_ne_two {R : Type _} [NonAssocRing R] [Nontrivial R]
     [NoZeroDivisors R] (hR : ringChar R ≠ 2) {a : R} : -a = a ↔ a = 0 :=
@@ -987,12 +690,6 @@ section
 
 variable (R) [NonAssocRing R] [Fintype R] (n : ℕ)
 
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 theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0 → i = 0) :
     CharP R n :=
   {
@@ -1011,12 +708,6 @@ theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0
       · rintro ⟨k, rfl⟩; rw [Nat.cast_mul, H, MulZeroClass.zero_mul] }
 #align char_p_of_ne_zero charP_of_ne_zero
 
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 theorem charP_of_prime_pow_injective (R) [Ring R] [Fintype R] (p : ℕ) [hp : Fact p.Prime] (n : ℕ)
     (hn : Fintype.card R = p ^ n) (hR : ∀ i ≤ n, (p ^ i : R) = 0 → i = n) : CharP R (p ^ n) :=
   by
@@ -1039,12 +730,6 @@ instance [CharP S q] : CharP (R × S) (Nat.lcm p q)
     where cast_eq_zero_iff := by
     simp [Prod.ext_iff, CharP.cast_eq_zero_iff R p, CharP.cast_eq_zero_iff S q, Nat.lcm_dvd_iff]
 
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 /-- The characteristic of the product of two rings of the same characteristic
   is the same as the characteristic of the rings -/
 instance Prod.charP [CharP S p] : CharP (R × S) p := by convert Nat.lcm.charP R S p p <;> simp
@@ -1066,12 +751,6 @@ instance MulOpposite.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP R
 
 section
 
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 /-- If two integers from `{0, 1, -1}` result in equal elements in a ring `R`
 that is nontrivial and of characteristic not `2`, then they are equal. -/
 theorem Int.cast_injOn_of_ringChar_ne_two {R : Type _} [NonAssocRing R] [Nontrivial R]
@@ -1105,22 +784,10 @@ namespace NeZero
 
 variable (R) [AddMonoidWithOne R] {r : R} {n p : ℕ} {a : ℕ+}
 
-/- warning: ne_zero.of_not_dvd -> NeZero.of_not_dvd is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] {n : Nat} {p : Nat} [_inst_2 : CharP.{u1} R _inst_1 p], (Not (Dvd.Dvd.{0} Nat Nat.hasDvd p n)) -> (NeZero.{u1} R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R _inst_1)))) n))
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] {n : Nat} {p : Nat} [_inst_2 : CharP.{u1} R _inst_1 p], (Not (Dvd.dvd.{0} Nat Nat.instDvdNat p n)) -> (NeZero.{u1} R (AddMonoid.toZero.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R _inst_1)) (Nat.cast.{u1} R (AddMonoidWithOne.toNatCast.{u1} R _inst_1) n))
-Case conversion may be inaccurate. Consider using '#align ne_zero.of_not_dvd NeZero.of_not_dvdₓ'. -/
 theorem of_not_dvd [CharP R p] (h : ¬p ∣ n) : NeZero (n : R) :=
   ⟨(CharP.cast_eq_zero_iff R p n).Not.mpr h⟩
 #align ne_zero.of_not_dvd NeZero.of_not_dvd
 
-/- warning: ne_zero.not_char_dvd -> NeZero.not_char_dvd is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R _inst_1 p] (k : Nat) [h : NeZero.{u1} R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R _inst_1)))) k)], Not (Dvd.Dvd.{0} Nat Nat.hasDvd p k)
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R _inst_1 p] (k : Nat) [h : NeZero.{u1} R (AddMonoid.toZero.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R _inst_1)) (Nat.cast.{u1} R (AddMonoidWithOne.toNatCast.{u1} R _inst_1) k)], Not (Dvd.dvd.{0} Nat Nat.instDvdNat p k)
-Case conversion may be inaccurate. Consider using '#align ne_zero.not_char_dvd NeZero.not_char_dvdₓ'. -/
 theorem not_char_dvd (p : ℕ) [CharP R p] (k : ℕ) [h : NeZero (k : R)] : ¬p ∣ k := by
   rwa [← CharP.cast_eq_zero_iff R p k, ← Ne.def, ← neZero_iff]
 #align ne_zero.not_char_dvd NeZero.not_char_dvd

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -469,16 +469,12 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align char_p.neg_one_ne_one CharP.neg_one_ne_oneₓ'. -/
 theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1 : R) ≠ (1 : R) :=
   by
-  suffices (2 : R) ≠ 0 by
-    symm
-    rw [Ne.def, ← sub_eq_zero, sub_neg_eq_add]
-    exact this
+  suffices (2 : R) ≠ 0 by symm; rw [Ne.def, ← sub_eq_zero, sub_neg_eq_add]; exact this
   intro h
   rw [show (2 : R) = (2 : ℕ) by norm_cast] at h
   have := (CharP.cast_eq_zero_iff R p 2).mp h
   have := Nat.le_of_dvd (by decide) this
-  rw [fact_iff] at *
-  linarith
+  rw [fact_iff] at *; linarith
 #align char_p.neg_one_ne_one CharP.neg_one_ne_one
 
 /- warning: char_p.neg_one_pow_char -> CharP.neg_one_pow_char is a dubious translation:
@@ -714,11 +710,8 @@ but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p], Function.Injective.{succ u1, succ u1} R R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4))
 Case conversion may be inaccurate. Consider using '#align frobenius_inj frobenius_injₓ'. -/
 theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP R p] :
-    Function.Injective (frobenius R p) := fun x h H =>
-  by
-  rw [← sub_eq_zero] at H⊢
-  rw [← frobenius_sub] at H
-  exact IsReduced.eq_zero _ ⟨_, H⟩
+    Function.Injective (frobenius R p) := fun x h H => by rw [← sub_eq_zero] at H⊢;
+  rw [← frobenius_sub] at H; exact IsReduced.eq_zero _ ⟨_, H⟩
 #align frobenius_inj frobenius_inj
 
 /- warning: is_square_of_char_two' -> isSquare_of_charTwo' is a dubious translation:
@@ -730,8 +723,7 @@ Case conversion may be inaccurate. Consider using '#align is_square_of_char_two'
 /-- If `ring_char R = 2`, where `R` is a finite reduced commutative ring,
 then every `a : R` is a square. -/
 theorem isSquare_of_charTwo' {R : Type _} [Finite R] [CommRing R] [IsReduced R] [CharP R 2]
-    (a : R) : IsSquare a := by
-  cases nonempty_fintype R
+    (a : R) : IsSquare a := by cases nonempty_fintype R;
   exact
     Exists.imp (fun b h => pow_two b ▸ Eq.symm h)
       (((Fintype.bijective_iff_injective_and_card _).mpr ⟨frobenius_inj R 2, rfl⟩).Surjective a)
@@ -916,11 +908,7 @@ theorem false_of_nontrivial_of_char_one [Nontrivial R] [CharP R 1] : False :=
 -/
 
 #print CharP.ringChar_ne_one /-
-theorem ringChar_ne_one [Nontrivial R] : ringChar R ≠ 1 :=
-  by
-  intro h
-  apply zero_ne_one' R
-  symm
+theorem ringChar_ne_one [Nontrivial R] : ringChar R ≠ 1 := by intro h; apply zero_ne_one' R; symm;
   rw [← Nat.cast_one, ringChar.spec, h]
 #align char_p.ring_char_ne_one CharP.ringChar_ne_one
 -/
@@ -1020,8 +1008,7 @@ theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0
         apply hR _ (Nat.mod_lt _ _) h
         rw [← hn, Fintype.card_pos_iff]
         exact ⟨0⟩
-      · rintro ⟨k, rfl⟩
-        rw [Nat.cast_mul, H, MulZeroClass.zero_mul] }
+      · rintro ⟨k, rfl⟩; rw [Nat.cast_mul, H, MulZeroClass.zero_mul] }
 #align char_p_of_ne_zero charP_of_ne_zero
 
 /- warning: char_p_of_prime_pow_injective -> charP_of_prime_pow_injective is a dubious translation:
@@ -1033,13 +1020,10 @@ Case conversion may be inaccurate. Consider using '#align char_p_of_prime_pow_in
 theorem charP_of_prime_pow_injective (R) [Ring R] [Fintype R] (p : ℕ) [hp : Fact p.Prime] (n : ℕ)
     (hn : Fintype.card R = p ^ n) (hR : ∀ i ≤ n, (p ^ i : R) = 0 → i = n) : CharP R (p ^ n) :=
   by
-  obtain ⟨c, hc⟩ := CharP.exists R
-  skip
+  obtain ⟨c, hc⟩ := CharP.exists R; skip
   have hcpn : c ∣ p ^ n := by rw [← CharP.cast_eq_zero_iff R c, ← hn, CharP.cast_card_eq_zero]
   obtain ⟨i, hi, hc⟩ : ∃ i ≤ n, c = p ^ i := by rwa [Nat.dvd_prime_pow hp.1] at hcpn
-  obtain rfl : i = n := by
-    apply hR i hi
-    rw [← Nat.cast_pow, ← hc, CharP.cast_eq_zero]
+  obtain rfl : i = n := by apply hR i hi; rw [← Nat.cast_pow, ← hc, CharP.cast_eq_zero]
   rwa [← hc]
 #align char_p_of_prime_pow_injective charP_of_prime_pow_injective
 
@@ -1101,8 +1085,7 @@ theorem Int.cast_injOn_of_ringChar_ne_two {R : Type _} [NonAssocRing R] [Nontriv
   have hh : a - b = 1 ∨ b - a = 1 ∨ a - b = 2 ∨ b - a = 2 :=
     by
     rcases ha with (ha | ha | ha) <;> rcases hb with (hb | hb | hb)
-    pick_goal 5
-    pick_goal 9
+    pick_goal 5; pick_goal 9
     -- move goals with `a = b` to the front
     iterate 3 rw [ha, hb, sub_self] at hf; tauto
     -- 6 goals remain
@@ -1110,14 +1093,10 @@ theorem Int.cast_injOn_of_ringChar_ne_two {R : Type _} [NonAssocRing R] [Nontriv
   have h' : ((a - b : ℤ) : R) = 0 := by exact_mod_cast sub_eq_zero_of_eq h
   have h'' : ((b - a : ℤ) : R) = 0 := by exact_mod_cast sub_eq_zero_of_eq h.symm
   rcases hh with (hh | hh | hh | hh)
-  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h'
-    exact one_ne_zero h'
-  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h''
-    exact one_ne_zero h''
-  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h'
-    exact Ring.two_ne_zero hR h'
-  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h''
-    exact Ring.two_ne_zero hR h''
+  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h'; exact one_ne_zero h'
+  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h''; exact one_ne_zero h''
+  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h'; exact Ring.two_ne_zero hR h'
+  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h''; exact Ring.two_ne_zero hR h''
 #align int.cast_inj_on_of_ring_char_ne_two Int.cast_injOn_of_ringChar_ne_two
 
 end

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -561,10 +561,7 @@ theorem iterate_frobenius (n : ℕ) : (frobenius R p^[n]) x = x ^ p ^ n :=
 #align iterate_frobenius iterate_frobenius
 
 /- warning: frobenius_mul -> frobenius_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) y))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x y)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align frobenius_mul frobenius_mulₓ'. -/
 theorem frobenius_mul : frobenius R p (x * y) = frobenius R p x * frobenius R p y :=
   (frobenius R p).map_mul x y
@@ -581,30 +578,21 @@ theorem frobenius_one : frobenius R p 1 = 1 :=
 #align frobenius_one frobenius_one
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align monoid_hom.map_frobenius MonoidHom.map_frobeniusₓ'. -/
 theorem MonoidHom.map_frobenius : f (frobenius R p x) = frobenius S p (f x) :=
   f.map_pow x p
 #align monoid_hom.map_frobenius MonoidHom.map_frobenius
 
 /- warning: ring_hom.map_frobenius -> RingHom.map_frobenius is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_hom.map_frobenius RingHom.map_frobeniusₓ'. -/
 theorem RingHom.map_frobenius : g (frobenius R p x) = frobenius S p (g x) :=
   g.map_pow x p
 #align ring_hom.map_frobenius RingHom.map_frobenius
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align monoid_hom.map_iterate_frobenius MonoidHom.map_iterate_frobeniusₓ'. -/
 theorem MonoidHom.map_iterate_frobenius (n : ℕ) :
     f ((frobenius R p^[n]) x) = (frobenius S p^[n]) (f x) :=
@@ -612,10 +600,7 @@ theorem MonoidHom.map_iterate_frobenius (n : ℕ) :
 #align monoid_hom.map_iterate_frobenius MonoidHom.map_iterate_frobenius
 
 /- warning: ring_hom.map_iterate_frobenius -> RingHom.map_iterate_frobenius is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_hom.map_iterate_frobenius RingHom.map_iterate_frobeniusₓ'. -/
 theorem RingHom.map_iterate_frobenius (n : ℕ) :
     g ((frobenius R p^[n]) x) = (frobenius S p^[n]) (g x) :=
@@ -623,10 +608,7 @@ theorem RingHom.map_iterate_frobenius (n : ℕ) :
 #align ring_hom.map_iterate_frobenius RingHom.map_iterate_frobenius
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align monoid_hom.iterate_map_frobenius MonoidHom.iterate_map_frobeniusₓ'. -/
 theorem MonoidHom.iterate_map_frobenius (f : R →* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
     (f^[n]) (frobenius R p x) = frobenius R p ((f^[n]) x) :=
@@ -634,10 +616,7 @@ theorem MonoidHom.iterate_map_frobenius (f : R →* R) (p : ℕ) [Fact p.Prime]
 #align monoid_hom.iterate_map_frobenius MonoidHom.iterate_map_frobenius
 
 /- warning: ring_hom.iterate_map_frobenius -> RingHom.iterate_map_frobenius is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_hom.iterate_map_frobenius RingHom.iterate_map_frobeniusₓ'. -/
 theorem RingHom.iterate_map_frobenius (f : R →+* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
     (f^[n]) (frobenius R p x) = frobenius R p ((f^[n]) x) :=
@@ -657,10 +636,7 @@ theorem frobenius_zero : frobenius R p 0 = 0 :=
 #align frobenius_zero frobenius_zero
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align frobenius_add frobenius_addₓ'. -/
 theorem frobenius_add : frobenius R p (x + y) = frobenius R p x + frobenius R p y :=
   (frobenius R p).map_add x y
@@ -721,10 +697,7 @@ theorem frobenius_neg : frobenius R p (-x) = -frobenius R p x :=
 #align frobenius_neg frobenius_neg
 
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-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R) (y : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) y) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (Ring.toSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align frobenius_sub frobenius_subₓ'. -/
 theorem frobenius_sub : frobenius R p (x - y) = frobenius R p x - frobenius R p y :=
   (frobenius R p).map_sub x y

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -204,10 +204,10 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
   by
   rcases lt_trichotomy a 0 with (h | rfl | h)
   · rw [← neg_eq_zero, ← Int.cast_neg, ← dvd_neg]
-    lift -a to ℕ using neg_nonneg.mpr (le_of_lt h)
+    lift -a to ℕ using neg_nonneg.mpr (le_of_lt h) with b
     rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
   · simp only [Int.cast_zero, eq_self_iff_true, dvd_zero]
-  · lift a to ℕ using le_of_lt h
+  · lift a to ℕ using le_of_lt h with b
     rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
 #align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -204,10 +204,10 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
   by
   rcases lt_trichotomy a 0 with (h | rfl | h)
   · rw [← neg_eq_zero, ← Int.cast_neg, ← dvd_neg]
-    lift -a to ℕ using neg_nonneg.mpr (le_of_lt h) with b
+    lift -a to ℕ using neg_nonneg.mpr (le_of_lt h)
     rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
   · simp only [Int.cast_zero, eq_self_iff_true, dvd_zero]
-  · lift a to ℕ using le_of_lt h with b
+  · lift a to ℕ using le_of_lt h
     rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
 #align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -542,7 +542,7 @@ variable {R}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x p)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x p)
 Case conversion may be inaccurate. Consider using '#align frobenius_def frobenius_defₓ'. -/
 theorem frobenius_def : frobenius R p x = x ^ p :=
   rfl
@@ -552,7 +552,7 @@ theorem frobenius_def : frobenius R p x = x ^ p :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (n : Nat), Eq.{succ u1} R (Nat.iterate.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (n : Nat), Eq.{succ u1} R (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (n : Nat), Eq.{succ u1} R (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n))
 Case conversion may be inaccurate. Consider using '#align iterate_frobenius iterate_frobeniusₓ'. -/
 theorem iterate_frobenius (n : ℕ) : (frobenius R p^[n]) x = x ^ p ^ n :=
   by
@@ -564,7 +564,7 @@ theorem iterate_frobenius (n : ℕ) : (frobenius R p^[n]) x = x ^ p ^ n :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) y))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x y)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x y)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) y) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) y))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x y)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x y)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) y) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) y))
 Case conversion may be inaccurate. Consider using '#align frobenius_mul frobenius_mulₓ'. -/
 theorem frobenius_mul : frobenius R p (x * y) = frobenius R p x * frobenius R p y :=
   (frobenius R p).map_mul x y
@@ -574,7 +574,7 @@ theorem frobenius_mul : frobenius R p (x * y) = frobenius R p x * frobenius R p
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p], Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align frobenius_one frobenius_oneₓ'. -/
 theorem frobenius_one : frobenius R p 1 = 1 :=
   one_pow _
@@ -584,7 +584,7 @@ theorem frobenius_one : frobenius R p 1 = 1 :=
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] (f : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] [_inst_5 : CharP.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) p] (x : R), Eq.{succ u1} S (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (fun (_x : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) f (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (frobenius.{u2} R _inst_1 p _inst_3 _inst_4) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (frobenius.{u1} S _inst_2 p _inst_3 _inst_5) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (fun (_x : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) f x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) 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(NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f x))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.map_frobenius MonoidHom.map_frobeniusₓ'. -/
 theorem MonoidHom.map_frobenius : f (frobenius R p x) = frobenius S p (f x) :=
   f.map_pow x p
@@ -594,7 +594,7 @@ theorem MonoidHom.map_frobenius : f (frobenius R p x) = frobenius S p (f x) :=
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] (g : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] [_inst_5 : CharP.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) p] (x : R), Eq.{succ u1} S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) g (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (frobenius.{u2} R _inst_1 p _inst_3 _inst_4) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (frobenius.{u1} S _inst_2 p _inst_3 _inst_5) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) g x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g x))
 Case conversion may be inaccurate. Consider using '#align ring_hom.map_frobenius RingHom.map_frobeniusₓ'. -/
 theorem RingHom.map_frobenius : g (frobenius R p x) = frobenius S p (g x) :=
   g.map_pow x p
@@ -604,7 +604,7 @@ theorem RingHom.map_frobenius : g (frobenius R p x) = frobenius S p (g x) :=
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] (f : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] [_inst_5 : CharP.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u1} S (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (fun (_x : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) f (Nat.iterate.{succ u2} R (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (frobenius.{u2} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u1} S (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (frobenius.{u1} S _inst_2 p _inst_3 _inst_5)) n (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (fun (_x : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) f x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f x))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.map_iterate_frobenius MonoidHom.map_iterate_frobeniusₓ'. -/
 theorem MonoidHom.map_iterate_frobenius (n : ℕ) :
     f ((frobenius R p^[n]) x) = (frobenius S p^[n]) (f x) :=
@@ -615,7 +615,7 @@ theorem MonoidHom.map_iterate_frobenius (n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] (g : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] [_inst_5 : CharP.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u1} S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) g (Nat.iterate.{succ u2} R (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (frobenius.{u2} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u1} S (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (frobenius.{u1} S _inst_2 p _inst_3 _inst_5)) n (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) g x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g x))
 Case conversion may be inaccurate. Consider using '#align ring_hom.map_iterate_frobenius RingHom.map_iterate_frobeniusₓ'. -/
 theorem RingHom.map_iterate_frobenius (n : ℕ) :
     g ((frobenius R p^[n]) x) = (frobenius S p^[n]) (g x) :=
@@ -626,7 +626,7 @@ theorem RingHom.map_iterate_frobenius (n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (x : R) (f : MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (p : Nat) [_inst_6 : Fact (Nat.Prime p)] [_inst_7 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} R (Nat.iterate.{succ u1} R (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (fun (_x : MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) => R -> R) (MonoidHom.hasCoeToFun.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) f) n (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) (Nat.iterate.{succ u1} R (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (fun (_x : MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) => R -> R) (MonoidHom.hasCoeToFun.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) f) n x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (x : R) (f : MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (p : Nat) [_inst_6 : Fact (Nat.Prime p)] [_inst_7 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} R (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R R (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidHom.monoidHomClass.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f) n (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R R (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidHom.monoidHomClass.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f) n x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (x : R) (f : MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (p : Nat) [_inst_6 : Fact (Nat.Prime p)] [_inst_7 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} R (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R R (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidHom.monoidHomClass.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f) n (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R R (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidHom.monoidHomClass.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f) n x))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.iterate_map_frobenius MonoidHom.iterate_map_frobeniusₓ'. -/
 theorem MonoidHom.iterate_map_frobenius (f : R →* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
     (f^[n]) (frobenius R p x) = frobenius R p ((f^[n]) x) :=
@@ -637,7 +637,7 @@ theorem MonoidHom.iterate_map_frobenius (f : R →* R) (p : ℕ) [Fact p.Prime]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (x : R) (f : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (p : Nat) [_inst_6 : Fact (Nat.Prime p)] [_inst_7 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} R (Nat.iterate.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f) n (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) (Nat.iterate.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f) n x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (x : R) (f : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (p : Nat) [_inst_6 : Fact (Nat.Prime p)] [_inst_7 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} R (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) f) n (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) f) n x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (x : R) (f : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (p : Nat) [_inst_6 : Fact (Nat.Prime p)] [_inst_7 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} R (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) f) n (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) f) n x))
 Case conversion may be inaccurate. Consider using '#align ring_hom.iterate_map_frobenius RingHom.iterate_map_frobeniusₓ'. -/
 theorem RingHom.iterate_map_frobenius (f : R →+* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
     (f^[n]) (frobenius R p x) = frobenius R p ((f^[n]) x) :=
@@ -650,7 +650,7 @@ variable (R)
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p], Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) _inst_1))))
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align frobenius_zero frobenius_zeroₓ'. -/
 theorem frobenius_zero : frobenius R p 0 = 0 :=
   (frobenius R p).map_zero
@@ -660,7 +660,7 @@ theorem frobenius_zero : frobenius R p 0 = 0 :=
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) y))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) y) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) y))
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) y) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) y))
 Case conversion may be inaccurate. Consider using '#align frobenius_add frobenius_addₓ'. -/
 theorem frobenius_add : frobenius R p (x + y) = frobenius R p x + frobenius R p y :=
   (frobenius R p).map_add x y
@@ -670,7 +670,7 @@ theorem frobenius_add : frobenius R p (x + y) = frobenius R p x + frobenius R p
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) n)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) n)
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (Nat.cast.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (Semiring.toNatCast.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) _inst_1)) n)
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (Nat.cast.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (Semiring.toNatCast.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) _inst_1)) n)
 Case conversion may be inaccurate. Consider using '#align frobenius_nat_cast frobenius_nat_castₓ'. -/
 theorem frobenius_nat_cast (n : ℕ) : frobenius R p n = n :=
   map_natCast (frobenius R p) n
@@ -714,7 +714,7 @@ variable [CommRing R] {S : Type v} [CommRing S] (f : R →* S) (g : R →+* S) (
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) x)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) x)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x))
 Case conversion may be inaccurate. Consider using '#align frobenius_neg frobenius_negₓ'. -/
 theorem frobenius_neg : frobenius R p (-x) = -frobenius R p x :=
   (frobenius R p).map_neg x
@@ -724,7 +724,7 @@ theorem frobenius_neg : frobenius R p (-x) = -frobenius R p x :=
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x y)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) y))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R) (y : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) y) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (Ring.toSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) y))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R) (y : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) y) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (Ring.toSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) y))
 Case conversion may be inaccurate. Consider using '#align frobenius_sub frobenius_subₓ'. -/
 theorem frobenius_sub : frobenius R p (x - y) = frobenius R p x - frobenius R p y :=
   (frobenius R p).map_sub x y
@@ -738,7 +738,7 @@ end frobenius
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p], Function.Injective.{succ u1, succ u1} R R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p], Function.Injective.{succ u1, succ u1} R R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p], Function.Injective.{succ u1, succ u1} R R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4))
 Case conversion may be inaccurate. Consider using '#align frobenius_inj frobenius_injₓ'. -/
 theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP R p] :
     Function.Injective (frobenius R p) := fun x h H =>

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -443,7 +443,7 @@ theorem add_pow_char_pow [CommSemiring R] {p : ℕ} [Fact p.Prime] [CharP R p] {
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x y) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y p))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R) (y : R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) y p))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R) (y : R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) y p))
 Case conversion may be inaccurate. Consider using '#align sub_pow_char sub_pow_charₓ'. -/
 theorem sub_pow_char [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R) :
     (x - y) ^ p = x ^ p - y ^ p :=
@@ -454,7 +454,7 @@ theorem sub_pow_char [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R)
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] {n : Nat} (x : R) (y : R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] {n : Nat} (x : R) (y : R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] {n : Nat} (x : R) (y : R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)))
 Case conversion may be inaccurate. Consider using '#align sub_pow_char_pow sub_pow_char_powₓ'. -/
 theorem sub_pow_char_pow [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] {n : ℕ} (x y : R) :
     (x - y) ^ p ^ n = x ^ p ^ n - y ^ p ^ n :=
@@ -465,7 +465,7 @@ theorem sub_pow_char_pow [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] {n :
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) p] [_inst_3 : Fact (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) p)], Ne.{succ u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) p] [_inst_3 : Fact (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) p)], Ne.{succ u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))
+  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) p] [_inst_3 : Fact (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) p)], Ne.{succ u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align char_p.neg_one_ne_one CharP.neg_one_ne_oneₓ'. -/
 theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1 : R) ≠ (1 : R) :=
   by
@@ -485,7 +485,7 @@ theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) p) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) p) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) p) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align char_p.neg_one_pow_char CharP.neg_one_pow_charₓ'. -/
 theorem CharP.neg_one_pow_char [CommRing R] (p : ℕ) [CharP R p] [Fact p.Prime] :
     (-1 : R) ^ p = -1 := by
@@ -498,7 +498,7 @@ theorem CharP.neg_one_pow_char [CommRing R] (p : ℕ) [CharP R p] [Fact p.Prime]
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) (n : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) (n : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) (n : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align char_p.neg_one_pow_char_pow CharP.neg_one_pow_char_powₓ'. -/
 theorem CharP.neg_one_pow_char_pow [CommRing R] (p n : ℕ) [CharP R p] [Fact p.Prime] :
     (-1 : R) ^ p ^ n = -1 := by
@@ -511,7 +511,7 @@ theorem CharP.neg_one_pow_char_pow [CommRing R] (p n : ℕ) [CharP R p] [Fact p.
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : Semiring.{u2} L] [_inst_3 : Nontrivial.{u2} L], (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L _inst_2)) -> (forall (p : Nat), Iff (CharP.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) p) (CharP.{u2} L (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} L (NonAssocSemiring.toAddCommMonoidWithOne.{u2} L (Semiring.toNonAssocSemiring.{u2} L _inst_2))) p))
 but is expected to have type
-  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : Semiring.{u1} L] [_inst_3 : Nontrivial.{u1} L], (RingHom.{u2, u1} K L (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} L _inst_2)) -> (forall (p : Nat), Iff (CharP.{u2} K (AddGroupWithOne.toAddMonoidWithOne.{u2} K (Ring.toAddGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K _inst_1))) p) (CharP.{u1} L (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} L (NonAssocSemiring.toAddCommMonoidWithOne.{u1} L (Semiring.toNonAssocSemiring.{u1} L _inst_2))) p))
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : Semiring.{u1} L] [_inst_3 : Nontrivial.{u1} L], (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} L _inst_2)) -> (forall (p : Nat), Iff (CharP.{u2} K (AddGroupWithOne.toAddMonoidWithOne.{u2} K (Ring.toAddGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K _inst_1))) p) (CharP.{u1} L (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} L (NonAssocSemiring.toAddCommMonoidWithOne.{u1} L (Semiring.toNonAssocSemiring.{u1} L _inst_2))) p))
 Case conversion may be inaccurate. Consider using '#align ring_hom.char_p_iff_char_p RingHom.charP_iff_charPₓ'. -/
 theorem RingHom.charP_iff_charP {K L : Type _} [DivisionRing K] [Semiring L] [Nontrivial L]
     (f : K →+* L) (p : ℕ) : CharP K p ↔ CharP L p := by
@@ -738,7 +738,7 @@ end frobenius
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p], Function.Injective.{succ u1, succ u1} R R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p], Function.Injective.{succ u1, succ u1} R R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p], Function.Injective.{succ u1, succ u1} R R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4))
 Case conversion may be inaccurate. Consider using '#align frobenius_inj frobenius_injₓ'. -/
 theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP R p] :
     Function.Injective (frobenius R p) := fun x h H =>
@@ -752,7 +752,7 @@ theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Finite.{succ u1} R] [_inst_2 : CommRing.{u1} R] [_inst_3 : IsReduced.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_2)))] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))] (a : R), IsSquare.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_2))) a
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Finite.{succ u1} R] [_inst_2 : CommRing.{u1} R] [_inst_3 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_2))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))] (a : R), IsSquare.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2)))) a
+  forall {R : Type.{u1}} [_inst_1 : Finite.{succ u1} R] [_inst_2 : CommRing.{u1} R] [_inst_3 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_2))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))] (a : R), IsSquare.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2)))) a
 Case conversion may be inaccurate. Consider using '#align is_square_of_char_two' isSquare_of_charTwo'ₓ'. -/
 /-- If `ring_char R = 2`, where `R` is a finite reduced commutative ring,
 then every `a : R` is a square. -/
@@ -812,7 +812,7 @@ variable [CommRing R] [IsReduced R] {R}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Nat) (k : Nat) (m : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R), Iff (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat Nat.hasMul) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k) m)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x m) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))] (p : Nat) (k : Nat) (m : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R), Iff (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k) m)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x m) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))] (p : Nat) (k : Nat) (m : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R), Iff (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k) m)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x m) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align char_p.pow_prime_pow_mul_eq_one_iff CharP.pow_prime_pow_mul_eq_one_iffₓ'. -/
 @[simp]
 theorem pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [Fact p.Prime] [CharP R p] (x : R) :
@@ -1055,7 +1055,7 @@ theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_3 : Ring.{u1} R] [_inst_4 : Fintype.{u1} R] (p : Nat) [hp : Fact (Nat.Prime p)] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_4) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) -> (forall (i : Nat), (LE.le.{0} Nat Nat.hasLe i n) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_3))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_3))))))) p) i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3))))))))) -> (Eq.{1} Nat i n)) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_3))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_3 : Ring.{u1} R] [_inst_4 : Fintype.{u1} R] (p : Nat) [hp : Fact (Nat.Prime p)] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_4) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) -> (forall (i : Nat), (LE.le.{0} Nat instLENat i n) -> (Eq.{succ u1} R (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p i)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_3)))))) -> (Eq.{1} Nat i n)) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_3)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n))
+  forall (R : Type.{u1}) [_inst_3 : Ring.{u1} R] [_inst_4 : Fintype.{u1} R] (p : Nat) [hp : Fact (Nat.Prime p)] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_4) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) -> (forall (i : Nat), (LE.le.{0} Nat instLENat i n) -> (Eq.{succ u1} R (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p i)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_3)))))) -> (Eq.{1} Nat i n)) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_3)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n))
 Case conversion may be inaccurate. Consider using '#align char_p_of_prime_pow_injective charP_of_prime_pow_injectiveₓ'. -/
 theorem charP_of_prime_pow_injective (R) [Ring R] [Fintype R] (p : ℕ) [hp : Fact p.Prime] (n : ℕ)
     (hn : Fintype.card R = p ^ n) (hR : ∀ i ≤ n, (p ^ i : R) = 0 → i = n) : CharP R (p ^ n) :=

bump to nightly-2023-04-24-06

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

ff662d55

Diff

@@ -148,7 +148,7 @@ end CommSemiring
 variable (R)
 
 #print CharP /-
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
 /-- The generator of the kernel of the unique homomorphism ℕ → R for a semiring R.
 
 *Warning*: for a semiring `R`, `char_p R 0` and `char_zero R` need not coincide.

bump to nightly-2023-04-06-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

86c1d414

Diff

@@ -211,17 +211,25 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
     rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
 #align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff
 
-theorem CharP.int_cast_eq_int_cast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℤ} :
+/- warning: char_p.int_cast_eq_int_cast -> CharP.intCast_eq_intCast is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] {a : Int} {b : Int}, Iff (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R _inst_1)))) a) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R _inst_1)))) b)) (Int.ModEq ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) a b)
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] {a : Int} {b : Int}, Iff (Eq.{succ u1} R (Int.cast.{u1} R (AddGroupWithOne.toIntCast.{u1} R _inst_1) a) (Int.cast.{u1} R (AddGroupWithOne.toIntCast.{u1} R _inst_1) b)) (Int.ModEq (Nat.cast.{0} Int instNatCastInt p) a b)
+Case conversion may be inaccurate. Consider using '#align char_p.int_cast_eq_int_cast CharP.intCast_eq_intCastₓ'. -/
+theorem CharP.intCast_eq_intCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℤ} :
     (a : R) = b ↔ a ≡ b [ZMOD p] := by
   rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.int_cast_eq_zero_iff R p, Int.modEq_iff_dvd]
-#align char_p.int_cast_eq_int_cast CharP.int_cast_eq_int_cast
+#align char_p.int_cast_eq_int_cast CharP.intCast_eq_intCast
 
-theorem CharP.nat_cast_eq_nat_cast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℕ} :
+#print CharP.natCast_eq_natCast /-
+theorem CharP.natCast_eq_natCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℕ} :
     (a : R) = b ↔ a ≡ b [MOD p] :=
   by
   rw [← Int.cast_ofNat, ← Int.cast_ofNat b]
-  exact (CharP.int_cast_eq_int_cast _ _).trans Int.coe_nat_modEq_iff
-#align char_p.nat_cast_eq_nat_cast CharP.nat_cast_eq_nat_cast
+  exact (CharP.intCast_eq_intCast _ _).trans Int.coe_nat_modEq_iff
+#align char_p.nat_cast_eq_nat_cast CharP.natCast_eq_natCast
+-/
 
 #print CharP.eq /-
 theorem CharP.eq [AddMonoidWithOne R] {p q : ℕ} (c1 : CharP R p) (c2 : CharP R q) : p = q :=

bump to nightly-2023-04-04-02

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

2ee17135

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Joey van Langen, Casper Putz
 
 ! This file was ported from Lean 3 source module algebra.char_p.basic
-! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
+! leanprover-community/mathlib commit 47a1a73351de8dd6c8d3d32b569c8e434b03ca47
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -211,16 +211,17 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
     rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
 #align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff
 
-/- warning: char_p.int_coe_eq_int_coe_iff -> CharP.int_cast_eq_int_cast_iff is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R _inst_1)))) a) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R _inst_1)))) b)) (Int.ModEq ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) a b)
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R (Int.cast.{u1} R (AddGroupWithOne.toIntCast.{u1} R _inst_1) a) (Int.cast.{u1} R (AddGroupWithOne.toIntCast.{u1} R _inst_1) b)) (Int.ModEq (Nat.cast.{0} Int instNatCastInt p) a b)
-Case conversion may be inaccurate. Consider using '#align char_p.int_coe_eq_int_coe_iff CharP.int_cast_eq_int_cast_iffₓ'. -/
-theorem CharP.int_cast_eq_int_cast_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a b : ℤ) :
-    (a : R) = (b : R) ↔ a ≡ b [ZMOD p] := by
+theorem CharP.int_cast_eq_int_cast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℤ} :
+    (a : R) = b ↔ a ≡ b [ZMOD p] := by
   rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.int_cast_eq_zero_iff R p, Int.modEq_iff_dvd]
-#align char_p.int_coe_eq_int_coe_iff CharP.int_cast_eq_int_cast_iff
+#align char_p.int_cast_eq_int_cast CharP.int_cast_eq_int_cast
+
+theorem CharP.nat_cast_eq_nat_cast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℕ} :
+    (a : R) = b ↔ a ≡ b [MOD p] :=
+  by
+  rw [← Int.cast_ofNat, ← Int.cast_ofNat b]
+  exact (CharP.int_cast_eq_int_cast _ _).trans Int.coe_nat_modEq_iff
+#align char_p.nat_cast_eq_nat_cast CharP.nat_cast_eq_nat_cast
 
 #print CharP.eq /-
 theorem CharP.eq [AddMonoidWithOne R] {p q : ℕ} (c1 : CharP R p) (c2 : CharP R q) : p = q :=
@@ -452,16 +453,6 @@ theorem sub_pow_char_pow [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] {n :
   sub_pow_char_pow_of_commute _ _ _ (Commute.all _ _)
 #align sub_pow_char_pow sub_pow_char_pow
 
-/- warning: eq_iff_modeq_int -> eq_iff_modEq_int is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) a) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) b)) (Int.ModEq ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) a b)
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R (Int.cast.{u1} R (Ring.toIntCast.{u1} R _inst_1) a) (Int.cast.{u1} R (Ring.toIntCast.{u1} R _inst_1) b)) (Int.ModEq (Nat.cast.{0} Int instNatCastInt p) a b)
-Case conversion may be inaccurate. Consider using '#align eq_iff_modeq_int eq_iff_modEq_intₓ'. -/
-theorem eq_iff_modEq_int [Ring R] (p : ℕ) [CharP R p] (a b : ℤ) : (a : R) = b ↔ a ≡ b [ZMOD p] := by
-  rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.int_cast_eq_zero_iff R p, Int.modEq_iff_dvd]
-#align eq_iff_modeq_int eq_iff_modEq_int
-
 /- warning: char_p.neg_one_ne_one -> CharP.neg_one_ne_one is a dubious translation:
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) p] [_inst_3 : Fact (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) p)], Ne.{succ u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))

bump to nightly-2023-04-01-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9

fc2d4474

Diff

@@ -33,6 +33,12 @@ namespace Commute
 
 variable [Semiring R] {p : ℕ} {x y : R}
 
+/- warning: commute.add_pow_prime_pow_eq -> Commute.add_pow_prime_pow_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Nat} {x : R} {y : R}, (Nat.Prime p) -> (Commute.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x y) -> (forall (n : Nat), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) p) (Finset.sum.{u1, 0} R Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finset.Ioo.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (fun (k : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n) k))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.hasDiv) (Nat.choose (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n) k) p)))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align commute.add_pow_prime_pow_eq Commute.add_pow_prime_pow_eqₓ'. -/
 protected theorem add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ) :
     (x + y) ^ p ^ n =
       x ^ p ^ n + y ^ p ^ n +
@@ -50,17 +56,35 @@ protected theorem add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ
     rw [Nat.div_mul_cancel (hp.dvd_choose_pow hi.1.ne' hi.2.Ne)]
 #align commute.add_pow_prime_pow_eq Commute.add_pow_prime_pow_eq
 
+/- warning: commute.add_pow_prime_eq -> Commute.add_pow_prime_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align commute.add_pow_prime_eq Commute.add_pow_prime_eqₓ'. -/
 protected theorem add_pow_prime_eq (hp : p.Prime) (h : Commute x y) :
     (x + y) ^ p =
       x ^ p + y ^ p + p * ∑ k in Finset.Ioo 0 p, x ^ k * y ^ (p - k) * ↑(p.choose k / p) :=
   by simpa using h.add_pow_prime_pow_eq hp 1
 #align commute.add_pow_prime_eq Commute.add_pow_prime_eq
 
+/- warning: commute.exists_add_pow_prime_pow_eq -> Commute.exists_add_pow_prime_pow_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Nat} {x : R} {y : R}, (Nat.Prime p) -> (Commute.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x y) -> (forall (n : Nat), Exists.{succ u1} R (fun (r : R) => Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) p) r))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Nat} {x : R} {y : R}, (Nat.Prime p) -> (Commute.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) x y) -> (forall (n : Nat), Exists.{succ u1} R (fun (r : R) => Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) p) r))))
+Case conversion may be inaccurate. Consider using '#align commute.exists_add_pow_prime_pow_eq Commute.exists_add_pow_prime_pow_eqₓ'. -/
 protected theorem exists_add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ) :
     ∃ r, (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n + p * r :=
   ⟨_, h.add_pow_prime_pow_eq hp n⟩
 #align commute.exists_add_pow_prime_pow_eq Commute.exists_add_pow_prime_pow_eq
 
+/- warning: commute.exists_add_pow_prime_eq -> Commute.exists_add_pow_prime_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Nat} {x : R} {y : R}, (Nat.Prime p) -> (Commute.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x y) -> (Exists.{succ u1} R (fun (r : R) => Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) p) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y p)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) p) r))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Nat} {x : R} {y : R}, (Nat.Prime p) -> (Commute.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) x y) -> (Exists.{succ u1} R (fun (r : R) => Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) p) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y p)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) p) r))))
+Case conversion may be inaccurate. Consider using '#align commute.exists_add_pow_prime_eq Commute.exists_add_pow_prime_eqₓ'. -/
 protected theorem exists_add_pow_prime_eq (hp : p.Prime) (h : Commute x y) :
     ∃ r, (x + y) ^ p = x ^ p + y ^ p + p * r :=
   ⟨_, h.add_pow_prime_eq hp⟩
@@ -72,6 +96,12 @@ section CommSemiring
 
 variable [CommSemiring R] {p : ℕ} {x y : R}
 
+/- warning: add_pow_prime_pow_eq -> add_pow_prime_pow_eq is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align add_pow_prime_pow_eq add_pow_prime_pow_eqₓ'. -/
 theorem add_pow_prime_pow_eq (hp : p.Prime) (x y : R) (n : ℕ) :
     (x + y) ^ p ^ n =
       x ^ p ^ n + y ^ p ^ n +
@@ -79,17 +109,35 @@ theorem add_pow_prime_pow_eq (hp : p.Prime) (x y : R) (n : ℕ) :
   (Commute.all x y).add_pow_prime_pow_eq hp n
 #align add_pow_prime_pow_eq add_pow_prime_pow_eq
 
+/- warning: add_pow_prime_eq -> add_pow_prime_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align add_pow_prime_eq add_pow_prime_eqₓ'. -/
 theorem add_pow_prime_eq (hp : p.Prime) (x y : R) :
     (x + y) ^ p =
       x ^ p + y ^ p + p * ∑ k in Finset.Ioo 0 p, x ^ k * y ^ (p - k) * ↑(p.choose k / p) :=
   (Commute.all x y).add_pow_prime_eq hp
 #align add_pow_prime_eq add_pow_prime_eq
 
+/- warning: exists_add_pow_prime_pow_eq -> exists_add_pow_prime_pow_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {p : Nat}, (Nat.Prime p) -> (forall (x : R) (y : R) (n : Nat), Exists.{succ u1} R (fun (r : R) => Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) p) r))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {p : Nat}, (Nat.Prime p) -> (forall (x : R) (y : R) (n : Nat), Exists.{succ u1} R (fun (r : R) => Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p) r))))
+Case conversion may be inaccurate. Consider using '#align exists_add_pow_prime_pow_eq exists_add_pow_prime_pow_eqₓ'. -/
 theorem exists_add_pow_prime_pow_eq (hp : p.Prime) (x y : R) (n : ℕ) :
     ∃ r, (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n + p * r :=
   (Commute.all x y).exists_add_pow_prime_pow_eq hp n
 #align exists_add_pow_prime_pow_eq exists_add_pow_prime_pow_eq
 
+/- warning: exists_add_pow_prime_eq -> exists_add_pow_prime_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {p : Nat}, (Nat.Prime p) -> (forall (x : R) (y : R), Exists.{succ u1} R (fun (r : R) => Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y) p) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) y p)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) p) r))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {p : Nat}, (Nat.Prime p) -> (forall (x : R) (y : R), Exists.{succ u1} R (fun (r : R) => Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y) p) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) y p)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p) r))))
+Case conversion may be inaccurate. Consider using '#align exists_add_pow_prime_eq exists_add_pow_prime_eqₓ'. -/
 theorem exists_add_pow_prime_eq (hp : p.Prime) (x y : R) :
     ∃ r, (x + y) ^ p = x ^ p + y ^ p + p * r :=
   (Commute.all x y).exists_add_pow_prime_eq hp
@@ -324,7 +372,7 @@ theorem add_pow_char_of_commute [Semiring R] {p : ℕ} [hp : Fact p.Prime] [Char
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {p : Nat} {n : Nat} [hp : Fact (Nat.Prime p)] [_inst_2 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) p] (x : R) (y : R), (Commute.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {p : Nat} [n : Fact (Nat.Prime p)] [hp : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) p] {_inst_2 : Nat} (x : R) (y : R), (Commute.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p _inst_2)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p _inst_2))))
+  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {p : Nat} {n : Nat} [hp : Fact (Nat.Prime p)] [_inst_2 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) p] (x : R) (y : R), (Commute.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n))))
 Case conversion may be inaccurate. Consider using '#align add_pow_char_pow_of_commute add_pow_char_pow_of_commuteₓ'. -/
 theorem add_pow_char_pow_of_commute [Semiring R] {p n : ℕ} [hp : Fact p.Prime] [CharP R p] (x y : R)
     (h : Commute x y) : (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n :=
@@ -537,7 +585,7 @@ theorem frobenius_one : frobenius R p 1 = 1 :=
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] (f : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] [_inst_5 : CharP.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) p] (x : R), Eq.{succ u1} S (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (fun (_x : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) f (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (frobenius.{u2} R _inst_1 p _inst_3 _inst_4) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (frobenius.{u1} S _inst_2 p _inst_3 _inst_5) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (fun (_x : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) f x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f x))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.map_frobenius MonoidHom.map_frobeniusₓ'. -/
 theorem MonoidHom.map_frobenius : f (frobenius R p x) = frobenius S p (f x) :=
   f.map_pow x p
@@ -547,7 +595,7 @@ theorem MonoidHom.map_frobenius : f (frobenius R p x) = frobenius S p (f x) :=
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] (g : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] [_inst_5 : CharP.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) p] (x : R), Eq.{succ u1} S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) g (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (frobenius.{u2} R _inst_1 p _inst_3 _inst_4) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (frobenius.{u1} S _inst_2 p _inst_3 _inst_5) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) g x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g x))
 Case conversion may be inaccurate. Consider using '#align ring_hom.map_frobenius RingHom.map_frobeniusₓ'. -/
 theorem RingHom.map_frobenius : g (frobenius R p x) = frobenius S p (g x) :=
   g.map_pow x p
@@ -557,7 +605,7 @@ theorem RingHom.map_frobenius : g (frobenius R p x) = frobenius S p (g x) :=
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] (f : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] [_inst_5 : CharP.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u1} S (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (fun (_x : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) f (Nat.iterate.{succ u2} R (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (frobenius.{u2} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u1} S (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (frobenius.{u1} S _inst_2 p _inst_3 _inst_5)) n (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (fun (_x : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) f x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) 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(CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S 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_inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f x))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.map_iterate_frobenius MonoidHom.map_iterate_frobeniusₓ'. -/
 theorem MonoidHom.map_iterate_frobenius (n : ℕ) :
     f ((frobenius R p^[n]) x) = (frobenius S p^[n]) (f x) :=
@@ -568,7 +616,7 @@ theorem MonoidHom.map_iterate_frobenius (n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] (g : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] [_inst_5 : CharP.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u1} S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) g (Nat.iterate.{succ u2} R (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (frobenius.{u2} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u1} S (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (frobenius.{u1} S _inst_2 p _inst_3 _inst_5)) n (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) g x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g x))
 Case conversion may be inaccurate. Consider using '#align ring_hom.map_iterate_frobenius RingHom.map_iterate_frobeniusₓ'. -/
 theorem RingHom.map_iterate_frobenius (n : ℕ) :
     g ((frobenius R p^[n]) x) = (frobenius S p^[n]) (g x) :=
@@ -649,16 +697,12 @@ theorem multiset_sum_pow_char (s : Multiset R) : s.Sum ^ p = (s.map (· ^ p)).Su
 #align multiset_sum_pow_char multiset_sum_pow_char
 -/
 
-/- warning: sum_pow_char -> sum_pow_char is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] {ι : Type.{u2}} (s : Finset.{u2} ι) (f : ι -> R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finset.sum.{u1, u2} R ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) s (fun (i : ι) => f i)) p) (Finset.sum.{u1, u2} R ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) s (fun (i : ι) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (f i) p))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> R), Eq.{succ u2} R (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Finset.sum.{u2, u1} R ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) s (fun (i : ι) => f i)) p) (Finset.sum.{u2, u1} R ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (f i) p))
-Case conversion may be inaccurate. Consider using '#align sum_pow_char sum_pow_charₓ'. -/
+#print sum_pow_char /-
 theorem sum_pow_char {ι : Type _} (s : Finset ι) (f : ι → R) :
     (∑ i in s, f i) ^ p = ∑ i in s, f i ^ p :=
   (frobenius R p).map_sum _ _
 #align sum_pow_char sum_pow_char
+-/
 
 end CommSemiring
 
@@ -1043,7 +1087,7 @@ instance [CharP S q] : CharP (R × S) (Nat.lcm p q)
 lean 3 declaration is
   forall (R : Type.{u2}) (S : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u2} R] [_inst_2 : AddMonoidWithOne.{u1} S] (p : Nat) [_inst_3 : CharP.{u2} R _inst_1 p] [_inst_4 : CharP.{u1} S _inst_2 p], CharP.{max u2 u1} (Prod.{u2, u1} R S) (Prod.addMonoidWithOne.{u2, u1} R S _inst_1 _inst_2) p
 but is expected to have type
-  forall (R : Type.{u1}) (S : Type.{u2}) [_inst_1 : AddMonoidWithOne.{u1} R] [_inst_2 : AddMonoidWithOne.{u2} S] (p : Nat) [_inst_3 : CharP.{u1} R _inst_1 p] [_inst_4 : CharP.{u2} S _inst_2 p], CharP.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instAddMonoidWithOneProd.{u1, u2} R S _inst_1 _inst_2) p
+  forall (R : Type.{u2}) (S : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u2} R] [_inst_2 : AddMonoidWithOne.{u1} S] (p : Nat) [_inst_3 : CharP.{u2} R _inst_1 p] [_inst_4 : CharP.{u1} S _inst_2 p], CharP.{max u1 u2} (Prod.{u2, u1} R S) (Prod.instAddMonoidWithOneProd.{u2, u1} R S _inst_1 _inst_2) p
 Case conversion may be inaccurate. Consider using '#align prod.char_p Prod.charPₓ'. -/
 /-- The characteristic of the product of two rings of the same characteristic
   is the same as the characteristic of the rings -/
@@ -1052,15 +1096,11 @@ instance Prod.charP [CharP S p] : CharP (R × S) p := by convert Nat.lcm.charP R
 
 end Prod
 
-/- warning: ulift.char_p -> ULift.charP is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u2}) [_inst_1 : AddMonoidWithOne.{u2} R] (p : Nat) [_inst_2 : CharP.{u2} R _inst_1 p], CharP.{max u2 u1} (ULift.{u1, u2} R) (ULift.addMonoidWithOne.{u2, u1} R _inst_1) p
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R _inst_1 p], CharP.{max u2 u1} (ULift.{u2, u1} R) (ULift.addMonoidWithOne.{u1, u2} R _inst_1) p
-Case conversion may be inaccurate. Consider using '#align ulift.char_p ULift.charPₓ'. -/
+#print ULift.charP /-
 instance ULift.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP (ULift.{v} R) p
     where cast_eq_zero_iff n := Iff.trans (ULift.ext_iff _ _) <| CharP.cast_eq_zero_iff R p n
 #align ulift.char_p ULift.charP
+-/
 
 #print MulOpposite.charP /-
 instance MulOpposite.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP Rᵐᵒᵖ p

bump to nightly-2023-03-27-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

0e4ebd8c

Diff

@@ -335,7 +335,7 @@ theorem add_pow_char_pow_of_commute [Semiring R] {p n : ℕ} [hp : Fact p.Prime]
 
 /- warning: sub_pow_char_of_commute -> sub_pow_char_of_commute is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) p] (x : R) (y : R), (Commute.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) x y) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) y p)))
+  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) p] (x : R) (y : R), (Commute.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) x y) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) y p)))
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) p] (x : R) (y : R), (Commute.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) x y) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) y p)))
 Case conversion may be inaccurate. Consider using '#align sub_pow_char_of_commute sub_pow_char_of_commuteₓ'. -/
@@ -348,7 +348,7 @@ theorem sub_pow_char_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p] (x
 
 /- warning: sub_pow_char_pow_of_commute -> sub_pow_char_pow_of_commute is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) p] {n : Nat} (x : R) (y : R), (Commute.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n))))
+  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) p] {n : Nat} (x : R) (y : R), (Commute.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n))))
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) p] {n : Nat} (x : R) (y : R), (Commute.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n))))
 Case conversion may be inaccurate. Consider using '#align sub_pow_char_pow_of_commute sub_pow_char_pow_of_commuteₓ'. -/
@@ -384,7 +384,7 @@ theorem add_pow_char_pow [CommSemiring R] {p : ℕ} [Fact p.Prime] [CharP R p] {
 
 /- warning: sub_pow_char -> sub_pow_char is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x y) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y p))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x y) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y p))
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R) (y : R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) y p))
 Case conversion may be inaccurate. Consider using '#align sub_pow_char sub_pow_charₓ'. -/
@@ -395,7 +395,7 @@ theorem sub_pow_char [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R)
 
 /- warning: sub_pow_char_pow -> sub_pow_char_pow is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] {n : Nat} (x : R) (y : R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] {n : Nat} (x : R) (y : R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)))
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] {n : Nat} (x : R) (y : R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)))
 Case conversion may be inaccurate. Consider using '#align sub_pow_char_pow sub_pow_char_powₓ'. -/
@@ -406,7 +406,7 @@ theorem sub_pow_char_pow [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] {n :
 
 /- warning: eq_iff_modeq_int -> eq_iff_modEq_int is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) a) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) b)) (Int.ModEq ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) a b)
+  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) a) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) b)) (Int.ModEq ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) a b)
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R (Int.cast.{u1} R (Ring.toIntCast.{u1} R _inst_1) a) (Int.cast.{u1} R (Ring.toIntCast.{u1} R _inst_1) b)) (Int.ModEq (Nat.cast.{0} Int instNatCastInt p) a b)
 Case conversion may be inaccurate. Consider using '#align eq_iff_modeq_int eq_iff_modEq_intₓ'. -/
@@ -416,7 +416,7 @@ theorem eq_iff_modEq_int [Ring R] (p : ℕ) [CharP R p] (a b : ℤ) : (a : R) =
 
 /- warning: char_p.neg_one_ne_one -> CharP.neg_one_ne_one is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) p] [_inst_3 : Fact (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) p)], Ne.{succ u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))
+  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) p] [_inst_3 : Fact (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) p)], Ne.{succ u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) p] [_inst_3 : Fact (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) p)], Ne.{succ u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align char_p.neg_one_ne_one CharP.neg_one_ne_oneₓ'. -/
@@ -436,7 +436,7 @@ theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1
 
 /- warning: char_p.neg_one_pow_char -> CharP.neg_one_pow_char is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) p) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) p) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) p) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align char_p.neg_one_pow_char CharP.neg_one_pow_charₓ'. -/
@@ -449,7 +449,7 @@ theorem CharP.neg_one_pow_char [CommRing R] (p : ℕ) [CharP R p] [Fact p.Prime]
 
 /- warning: char_p.neg_one_pow_char_pow -> CharP.neg_one_pow_char_pow is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) (n : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) (n : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) (n : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align char_p.neg_one_pow_char_pow CharP.neg_one_pow_char_powₓ'. -/
@@ -462,7 +462,7 @@ theorem CharP.neg_one_pow_char_pow [CommRing R] (p n : ℕ) [CharP R p] [Fact p.
 
 /- warning: ring_hom.char_p_iff_char_p -> RingHom.charP_iff_charP is a dubious translation:
 lean 3 declaration is
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : Semiring.{u2} L] [_inst_3 : Nontrivial.{u2} L], (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L _inst_2)) -> (forall (p : Nat), Iff (CharP.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) p) (CharP.{u2} L (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} L (NonAssocSemiring.toAddCommMonoidWithOne.{u2} L (Semiring.toNonAssocSemiring.{u2} L _inst_2))) p))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : Semiring.{u2} L] [_inst_3 : Nontrivial.{u2} L], (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L _inst_2)) -> (forall (p : Nat), Iff (CharP.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) p) (CharP.{u2} L (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} L (NonAssocSemiring.toAddCommMonoidWithOne.{u2} L (Semiring.toNonAssocSemiring.{u2} L _inst_2))) p))
 but is expected to have type
   forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : Semiring.{u1} L] [_inst_3 : Nontrivial.{u1} L], (RingHom.{u2, u1} K L (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} L _inst_2)) -> (forall (p : Nat), Iff (CharP.{u2} K (AddGroupWithOne.toAddMonoidWithOne.{u2} K (Ring.toAddGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K _inst_1))) p) (CharP.{u1} L (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} L (NonAssocSemiring.toAddCommMonoidWithOne.{u1} L (Semiring.toNonAssocSemiring.{u1} L _inst_2))) p))
 Case conversion may be inaccurate. Consider using '#align ring_hom.char_p_iff_char_p RingHom.charP_iff_charPₓ'. -/
@@ -669,7 +669,7 @@ variable [CommRing R] {S : Type v} [CommRing S] (f : R →* S) (g : R →+* S) (
 
 /- warning: frobenius_neg -> frobenius_neg is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x))
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) x)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x))
 Case conversion may be inaccurate. Consider using '#align frobenius_neg frobenius_negₓ'. -/
@@ -679,7 +679,7 @@ theorem frobenius_neg : frobenius R p (-x) = -frobenius R p x :=
 
 /- warning: frobenius_sub -> frobenius_sub is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x y)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) y))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x y)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) y))
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R) (y : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) y) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (Ring.toSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) y))
 Case conversion may be inaccurate. Consider using '#align frobenius_sub frobenius_subₓ'. -/
@@ -693,7 +693,7 @@ end frobenius
 
 /- warning: frobenius_inj -> frobenius_inj is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p], Function.Injective.{succ u1, succ u1} R R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p], Function.Injective.{succ u1, succ u1} R R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4))
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p], Function.Injective.{succ u1, succ u1} R R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4))
 Case conversion may be inaccurate. Consider using '#align frobenius_inj frobenius_injₓ'. -/
@@ -707,7 +707,7 @@ theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP
 
 /- warning: is_square_of_char_two' -> isSquare_of_charTwo' is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Finite.{succ u1} R] [_inst_2 : CommRing.{u1} R] [_inst_3 : IsReduced.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_2)))] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))] (a : R), IsSquare.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_2))) a
+  forall {R : Type.{u1}} [_inst_1 : Finite.{succ u1} R] [_inst_2 : CommRing.{u1} R] [_inst_3 : IsReduced.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_2)))] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))] (a : R), IsSquare.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_2))) a
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Finite.{succ u1} R] [_inst_2 : CommRing.{u1} R] [_inst_3 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_2))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))] (a : R), IsSquare.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2)))) a
 Case conversion may be inaccurate. Consider using '#align is_square_of_char_two' isSquare_of_charTwo'ₓ'. -/
@@ -733,25 +733,16 @@ theorem charP_to_charZero (R : Type _) [AddGroupWithOne R] [CharP R 0] : CharZer
 #align char_p.char_p_to_char_zero CharP.charP_to_charZero
 -/
 
-/- warning: char_p.cast_eq_mod -> CharP.cast_eq_mod is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)) p] (k : Nat), Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))))) k) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))))) (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) k p))
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))) p] (k : Nat), Eq.{succ u1} R (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R _inst_1) k) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R _inst_1) (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) k p))
-Case conversion may be inaccurate. Consider using '#align char_p.cast_eq_mod CharP.cast_eq_modₓ'. -/
+#print CharP.cast_eq_mod /-
 theorem cast_eq_mod (p : ℕ) [CharP R p] (k : ℕ) : (k : R) = (k % p : ℕ) :=
   calc
     (k : R) = ↑(k % p + p * (k / p)) := by rw [Nat.mod_add_div]
     _ = ↑(k % p) := by simp [cast_eq_zero]
     
 #align char_p.cast_eq_mod CharP.cast_eq_mod
+-/
 
-/- warning: char_p.char_ne_zero_of_finite -> CharP.char_ne_zero_of_finite is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)) p] [_inst_3 : Finite.{succ u1} R], Ne.{1} Nat p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))) p] [_inst_3 : Finite.{succ u1} R], Ne.{1} Nat p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))
-Case conversion may be inaccurate. Consider using '#align char_p.char_ne_zero_of_finite CharP.char_ne_zero_of_finiteₓ'. -/
+#print CharP.char_ne_zero_of_finite /-
 /-- The characteristic of a finite ring cannot be zero. -/
 theorem char_ne_zero_of_finite (p : ℕ) [CharP R p] [Finite R] : p ≠ 0 :=
   by
@@ -760,6 +751,7 @@ theorem char_ne_zero_of_finite (p : ℕ) [CharP R p] [Finite R] : p ≠ 0 :=
   cases nonempty_fintype R
   exact absurd Nat.cast_injective (not_injective_infinite_finite (coe : ℕ → R))
 #align char_p.char_ne_zero_of_finite CharP.char_ne_zero_of_finite
+-/
 
 #print CharP.ringChar_ne_zero_of_finite /-
 theorem ringChar_ne_zero_of_finite [Finite R] : ringChar R ≠ 0 :=
@@ -775,7 +767,7 @@ variable [CommRing R] [IsReduced R] {R}
 
 /- warning: char_p.pow_prime_pow_mul_eq_one_iff -> CharP.pow_prime_pow_mul_eq_one_iff is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Nat) (k : Nat) (m : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R), Iff (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat Nat.hasMul) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k) m)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x m) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Nat) (k : Nat) (m : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R), Iff (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat Nat.hasMul) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k) m)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x m) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))] (p : Nat) (k : Nat) (m : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R), Iff (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k) m)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x m) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align char_p.pow_prime_pow_mul_eq_one_iff CharP.pow_prime_pow_mul_eq_one_iffₓ'. -/
@@ -875,7 +867,7 @@ variable (R) [Ring R] [NoZeroDivisors R] [Nontrivial R] [Finite R]
 
 /- warning: char_p.char_is_prime -> CharP.char_is_prime is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))] [_inst_3 : Nontrivial.{u1} R] [_inst_4 : Finite.{succ u1} R] (p : Nat) [_inst_5 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) p], Nat.Prime p
+  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))] [_inst_3 : Nontrivial.{u1} R] [_inst_4 : Finite.{succ u1} R] (p : Nat) [_inst_5 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) p], Nat.Prime p
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))] [_inst_3 : Nontrivial.{u1} R] [_inst_4 : Finite.{succ u1} R] (p : Nat) [_inst_5 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) p], Nat.Prime p
 Case conversion may be inaccurate. Consider using '#align char_p.char_is_prime CharP.char_is_primeₓ'. -/
@@ -958,7 +950,7 @@ theorem Ring.two_ne_zero {R : Type _} [NonAssocSemiring R] [Nontrivial R] (hR :
 
 /- warning: ring.neg_one_ne_one_of_char_ne_two -> Ring.neg_one_ne_one_of_char_ne_two is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (Ne.{succ u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))))))
+  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (Ne.{succ u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> (Ne.{succ u1} R (Neg.neg.{u1} R (AddGroupWithOne.toNeg.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align ring.neg_one_ne_one_of_char_ne_two Ring.neg_one_ne_one_of_char_ne_twoₓ'. -/
@@ -972,7 +964,7 @@ theorem Ring.neg_one_ne_one_of_char_ne_two {R : Type _} [NonAssocRing R] [Nontri
 
 /- warning: ring.eq_self_iff_eq_zero_of_char_ne_two -> Ring.eq_self_iff_eq_zero_of_char_ne_two is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1))))], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (forall {a : R}, Iff (Eq.{succ u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))) a) a) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)))))))))
+  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1))))], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (forall {a : R}, Iff (Eq.{succ u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))))) a) a) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)))))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)) (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)))], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> (forall {a : R}, Iff (Eq.{succ u1} R (Neg.neg.{u1} R (AddGroupWithOne.toNeg.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))) a) a) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align ring.eq_self_iff_eq_zero_of_char_ne_two Ring.eq_self_iff_eq_zero_of_char_ne_twoₓ'. -/
@@ -993,7 +985,7 @@ variable (R) [NonAssocRing R] [Fintype R] (n : ℕ)
 
 /- warning: char_p_of_ne_zero -> charP_of_ne_zero is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Fintype.{u1} R] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_2) n) -> (forall (i : Nat), (LT.lt.{0} Nat Nat.hasLt i n) -> (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))))) i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)))))))) -> (Eq.{1} Nat i (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)) n)
+  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Fintype.{u1} R] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_2) n) -> (forall (i : Nat), (LT.lt.{0} Nat Nat.hasLt i n) -> (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))))))) i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)))))))) -> (Eq.{1} Nat i (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))) n)
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Fintype.{u1} R] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_2) n) -> (forall (i : Nat), (LT.lt.{0} Nat instLTNat i n) -> (Eq.{succ u1} R (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R _inst_1) i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)))))) -> (Eq.{1} Nat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))) n)
 Case conversion may be inaccurate. Consider using '#align char_p_of_ne_zero charP_of_ne_zeroₓ'. -/
@@ -1018,7 +1010,7 @@ theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0
 
 /- warning: char_p_of_prime_pow_injective -> charP_of_prime_pow_injective is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_3 : Ring.{u1} R] [_inst_4 : Fintype.{u1} R] (p : Nat) [hp : Fact (Nat.Prime p)] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_4) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) -> (forall (i : Nat), (LE.le.{0} Nat Nat.hasLe i n) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_3))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3))))))) p) i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3))))))))) -> (Eq.{1} Nat i n)) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n))
+  forall (R : Type.{u1}) [_inst_3 : Ring.{u1} R] [_inst_4 : Fintype.{u1} R] (p : Nat) [hp : Fact (Nat.Prime p)] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_4) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) -> (forall (i : Nat), (LE.le.{0} Nat Nat.hasLe i n) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_3))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_3))))))) p) i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3))))))))) -> (Eq.{1} Nat i n)) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_3))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n))
 but is expected to have type
   forall (R : Type.{u1}) [_inst_3 : Ring.{u1} R] [_inst_4 : Fintype.{u1} R] (p : Nat) [hp : Fact (Nat.Prime p)] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_4) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) -> (forall (i : Nat), (LE.le.{0} Nat instLENat i n) -> (Eq.{succ u1} R (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p i)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_3)))))) -> (Eq.{1} Nat i n)) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_3)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n))
 Case conversion may be inaccurate. Consider using '#align char_p_of_prime_pow_injective charP_of_prime_pow_injectiveₓ'. -/
@@ -1080,7 +1072,7 @@ section
 
 /- warning: int.cast_inj_on_of_ring_char_ne_two -> Int.cast_injOn_of_ringChar_ne_two is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (Set.InjOn.{0, u1} Int R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))))) (Insert.insert.{0, 0} Int (Set.{0} Int) (Set.hasInsert.{0} Int) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) (Insert.insert.{0, 0} Int (Set.{0} Int) (Set.hasInsert.{0} Int) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))) (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.hasSingleton.{0} Int) (Neg.neg.{0} Int Int.hasNeg (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
+  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (Set.InjOn.{0, u1} Int R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))))))) (Insert.insert.{0, 0} Int (Set.{0} Int) (Set.hasInsert.{0} Int) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) (Insert.insert.{0, 0} Int (Set.{0} Int) (Set.hasInsert.{0} Int) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))) (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.hasSingleton.{0} Int) (Neg.neg.{0} Int Int.hasNeg (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> (Set.InjOn.{0, u1} Int R (Int.cast.{u1} R (NonAssocRing.toIntCast.{u1} R _inst_1)) (Insert.insert.{0, 0} Int (Set.{0} Int) (Set.instInsertSet.{0} Int) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) (Insert.insert.{0, 0} Int (Set.{0} Int) (Set.instInsertSet.{0} Int) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)) (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.instSingletonSet.{0} Int) (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
 Case conversion may be inaccurate. Consider using '#align int.cast_inj_on_of_ring_char_ne_two Int.cast_injOn_of_ringChar_ne_twoₓ'. -/

bump to nightly-2023-03-24-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479

6eace303

Diff

@@ -733,16 +733,25 @@ theorem charP_to_charZero (R : Type _) [AddGroupWithOne R] [CharP R 0] : CharZer
 #align char_p.char_p_to_char_zero CharP.charP_to_charZero
 -/
 
-#print CharP.cast_eq_mod /-
+/- warning: char_p.cast_eq_mod -> CharP.cast_eq_mod is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)) p] (k : Nat), Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))))) k) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))))) (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) k p))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))) p] (k : Nat), Eq.{succ u1} R (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R _inst_1) k) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R _inst_1) (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) k p))
+Case conversion may be inaccurate. Consider using '#align char_p.cast_eq_mod CharP.cast_eq_modₓ'. -/
 theorem cast_eq_mod (p : ℕ) [CharP R p] (k : ℕ) : (k : R) = (k % p : ℕ) :=
   calc
     (k : R) = ↑(k % p + p * (k / p)) := by rw [Nat.mod_add_div]
     _ = ↑(k % p) := by simp [cast_eq_zero]
     
 #align char_p.cast_eq_mod CharP.cast_eq_mod
--/
 
-#print CharP.char_ne_zero_of_finite /-
+/- warning: char_p.char_ne_zero_of_finite -> CharP.char_ne_zero_of_finite is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)) p] [_inst_3 : Finite.{succ u1} R], Ne.{1} Nat p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))) p] [_inst_3 : Finite.{succ u1} R], Ne.{1} Nat p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))
+Case conversion may be inaccurate. Consider using '#align char_p.char_ne_zero_of_finite CharP.char_ne_zero_of_finiteₓ'. -/
 /-- The characteristic of a finite ring cannot be zero. -/
 theorem char_ne_zero_of_finite (p : ℕ) [CharP R p] [Finite R] : p ≠ 0 :=
   by
@@ -751,7 +760,6 @@ theorem char_ne_zero_of_finite (p : ℕ) [CharP R p] [Finite R] : p ≠ 0 :=
   cases nonempty_fintype R
   exact absurd Nat.cast_injective (not_injective_infinite_finite (coe : ℕ → R))
 #align char_p.char_ne_zero_of_finite CharP.char_ne_zero_of_finite
--/
 
 #print CharP.ringChar_ne_zero_of_finite /-
 theorem ringChar_ne_zero_of_finite [Finite R] : ringChar R ≠ 0 :=
@@ -952,7 +960,7 @@ theorem Ring.two_ne_zero {R : Type _} [NonAssocSemiring R] [Nontrivial R] (hR :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (Ne.{succ u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> (Ne.{succ u1} R (Neg.neg.{u1} R (AddGroupWithOne.toNeg.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> (Ne.{succ u1} R (Neg.neg.{u1} R (AddGroupWithOne.toNeg.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align ring.neg_one_ne_one_of_char_ne_two Ring.neg_one_ne_one_of_char_ne_twoₓ'. -/
 -- We have `char_p.neg_one_ne_one`, which assumes `[ring R] (p : ℕ) [char_p R p] [fact (2 < p)]`.
 -- This is a version using `ring_char` instead.
@@ -966,7 +974,7 @@ theorem Ring.neg_one_ne_one_of_char_ne_two {R : Type _} [NonAssocRing R] [Nontri
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1))))], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (forall {a : R}, Iff (Eq.{succ u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))) a) a) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)) (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)))], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> (forall {a : R}, Iff (Eq.{succ u1} R (Neg.neg.{u1} R (AddGroupWithOne.toNeg.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)) a) a) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)))))))
+  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)) (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)))], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> (forall {a : R}, Iff (Eq.{succ u1} R (Neg.neg.{u1} R (AddGroupWithOne.toNeg.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))) a) a) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align ring.eq_self_iff_eq_zero_of_char_ne_two Ring.eq_self_iff_eq_zero_of_char_ne_twoₓ'. -/
 /-- Characteristic `≠ 2` in a domain implies that `-a = a` iff `a = 0`. -/
 theorem Ring.eq_self_iff_eq_zero_of_char_ne_two {R : Type _} [NonAssocRing R] [Nontrivial R]
@@ -987,7 +995,7 @@ variable (R) [NonAssocRing R] [Fintype R] (n : ℕ)
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Fintype.{u1} R] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_2) n) -> (forall (i : Nat), (LT.lt.{0} Nat Nat.hasLt i n) -> (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))))) i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)))))))) -> (Eq.{1} Nat i (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)) n)
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Fintype.{u1} R] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_2) n) -> (forall (i : Nat), (LT.lt.{0} Nat instLTNat i n) -> (Eq.{succ u1} R (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R _inst_1) i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)))))) -> (Eq.{1} Nat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)) n)
+  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Fintype.{u1} R] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_2) n) -> (forall (i : Nat), (LT.lt.{0} Nat instLTNat i n) -> (Eq.{succ u1} R (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R _inst_1) i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)))))) -> (Eq.{1} Nat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (NonAssocRing.toAddCommGroupWithOne.{u1} R _inst_1))) n)
 Case conversion may be inaccurate. Consider using '#align char_p_of_ne_zero charP_of_ne_zeroₓ'. -/
 theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0 → i = 0) :
     CharP R n :=

bump to nightly-2023-03-24-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479

5b87f9bb

Diff

@@ -1062,15 +1062,11 @@ instance ULift.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP (ULift.{
     where cast_eq_zero_iff n := Iff.trans (ULift.ext_iff _ _) <| CharP.cast_eq_zero_iff R p n
 #align ulift.char_p ULift.charP
 
-/- warning: mul_opposite.char_p -> MulOpposite.charP is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R _inst_1 p], CharP.{u1} (MulOpposite.{u1} R) (MulOpposite.addMonoidWithOne.{u1} R _inst_1) p
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R _inst_1 p], CharP.{u1} (MulOpposite.{u1} R) (MulOpposite.instAddMonoidWithOneMulOpposite.{u1} R _inst_1) p
-Case conversion may be inaccurate. Consider using '#align mul_opposite.char_p MulOpposite.charPₓ'. -/
+#print MulOpposite.charP /-
 instance MulOpposite.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP Rᵐᵒᵖ p
     where cast_eq_zero_iff n := MulOpposite.unop_inj.symm.trans <| CharP.cast_eq_zero_iff R p n
 #align mul_opposite.char_p MulOpposite.charP
+-/
 
 section

bump to nightly-2023-03-17-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

11391fe2

Diff

@@ -149,7 +149,7 @@ theorem CharP.addOrderOf_one (R) [Semiring R] : CharP R (addOrderOf (1 : R)) :=
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] (a : Int), Iff (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R _inst_1)))) a) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1)))))))) (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) a)
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] (a : Int), Iff (Eq.{succ u1} R (Int.cast.{u1} R (AddGroupWithOne.toIntCast.{u1} R _inst_1) a) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (NegZeroClass.toZero.{u1} R (SubNegZeroMonoid.toNegZeroClass.{u1} R (SubtractionMonoid.toSubNegZeroMonoid.{u1} R (AddGroup.toSubtractionMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R _inst_1)))))))) (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int Int.instNatCastInt p) a)
+  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] (a : Int), Iff (Eq.{succ u1} R (Int.cast.{u1} R (AddGroupWithOne.toIntCast.{u1} R _inst_1) a) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (NegZeroClass.toZero.{u1} R (SubNegZeroMonoid.toNegZeroClass.{u1} R (SubtractionMonoid.toSubNegZeroMonoid.{u1} R (AddGroup.toSubtractionMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R _inst_1)))))))) (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) a)
 Case conversion may be inaccurate. Consider using '#align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iffₓ'. -/
 theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a : ℤ) :
     (a : R) = 0 ↔ (p : ℤ) ∣ a :=
@@ -167,7 +167,7 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R _inst_1)))) a) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R _inst_1)))) b)) (Int.ModEq ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) a b)
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R (Int.cast.{u1} R (AddGroupWithOne.toIntCast.{u1} R _inst_1) a) (Int.cast.{u1} R (AddGroupWithOne.toIntCast.{u1} R _inst_1) b)) (Int.ModEq (Nat.cast.{0} Int Int.instNatCastInt p) a b)
+  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R (Int.cast.{u1} R (AddGroupWithOne.toIntCast.{u1} R _inst_1) a) (Int.cast.{u1} R (AddGroupWithOne.toIntCast.{u1} R _inst_1) b)) (Int.ModEq (Nat.cast.{0} Int instNatCastInt p) a b)
 Case conversion may be inaccurate. Consider using '#align char_p.int_coe_eq_int_coe_iff CharP.int_cast_eq_int_cast_iffₓ'. -/
 theorem CharP.int_cast_eq_int_cast_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a b : ℤ) :
     (a : R) = (b : R) ↔ a ≡ b [ZMOD p] := by
@@ -408,7 +408,7 @@ theorem sub_pow_char_pow [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] {n :
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) a) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) b)) (Int.ModEq ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) a b)
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R (Int.cast.{u1} R (Ring.toIntCast.{u1} R _inst_1) a) (Int.cast.{u1} R (Ring.toIntCast.{u1} R _inst_1) b)) (Int.ModEq (Nat.cast.{0} Int Int.instNatCastInt p) a b)
+  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R (Int.cast.{u1} R (Ring.toIntCast.{u1} R _inst_1) a) (Int.cast.{u1} R (Ring.toIntCast.{u1} R _inst_1) b)) (Int.ModEq (Nat.cast.{0} Int instNatCastInt p) a b)
 Case conversion may be inaccurate. Consider using '#align eq_iff_modeq_int eq_iff_modEq_intₓ'. -/
 theorem eq_iff_modEq_int [Ring R] (p : ℕ) [CharP R p] (a b : ℤ) : (a : R) = b ↔ a ≡ b [ZMOD p] := by
   rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.int_cast_eq_zero_iff R p, Int.modEq_iff_dvd]

bump to nightly-2023-03-16-03

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

8ae28b0b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Joey van Langen, Casper Putz
 
 ! This file was ported from Lean 3 source module algebra.char_p.basic
-! leanprover-community/mathlib commit ceb887ddf3344dab425292e497fa2af91498437c
+! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.Nilpotent
 
 /-!
 # Characteristic of semirings
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 -/

ceb887dd

bump to nightly-2023-03-15-03

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

4e269297

Diff

@@ -4,14 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Joey van Langen, Casper Putz
 
 ! This file was ported from Lean 3 source module algebra.char_p.basic
-! leanprover-community/mathlib commit 05a78c9451101108e638a0f213fb1bed82483545
+! leanprover-community/mathlib commit ceb887ddf3344dab425292e497fa2af91498437c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Algebra.Hom.Iterate
 import Mathbin.Data.Int.Modeq
-import Mathbin.Data.Nat.Choose.Dvd
-import Mathbin.Data.Nat.Choose.Sum
+import Mathbin.Data.Nat.Multiplicity
 import Mathbin.GroupTheory.OrderOfElement
 import Mathbin.RingTheory.Nilpotent
 
@@ -22,7 +20,81 @@ import Mathbin.RingTheory.Nilpotent
 
 universe u v
 
-variable (R : Type u)
+open Finset
+
+open BigOperators
+
+variable {R : Type _}
+
+namespace Commute
+
+variable [Semiring R] {p : ℕ} {x y : R}
+
+protected theorem add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ) :
+    (x + y) ^ p ^ n =
+      x ^ p ^ n + y ^ p ^ n +
+        p * ∑ k in Ioo 0 (p ^ n), x ^ k * y ^ (p ^ n - k) * ↑((p ^ n).choose k / p) :=
+  by
+  trans x ^ p ^ n + y ^ p ^ n + ∑ k in Ioo 0 (p ^ n), x ^ k * y ^ (p ^ n - k) * (p ^ n).choose k
+  ·
+    simp_rw [h.add_pow, ← Nat.Ico_zero_eq_range, Nat.Ico_succ_right, Icc_eq_cons_Ico (zero_le _),
+      Finset.sum_cons, Ico_eq_cons_Ioo (pow_pos hp.pos _), Finset.sum_cons, tsub_self, tsub_zero,
+      pow_zero, Nat.choose_zero_right, Nat.choose_self, Nat.cast_one, mul_one, one_mul, ← add_assoc]
+  · congr 1
+    simp_rw [Finset.mul_sum, Nat.cast_comm, mul_assoc _ _ (p : R), ← Nat.cast_mul]
+    refine' Finset.sum_congr rfl fun i hi => _
+    rw [mem_Ioo] at hi
+    rw [Nat.div_mul_cancel (hp.dvd_choose_pow hi.1.ne' hi.2.Ne)]
+#align commute.add_pow_prime_pow_eq Commute.add_pow_prime_pow_eq
+
+protected theorem add_pow_prime_eq (hp : p.Prime) (h : Commute x y) :
+    (x + y) ^ p =
+      x ^ p + y ^ p + p * ∑ k in Finset.Ioo 0 p, x ^ k * y ^ (p - k) * ↑(p.choose k / p) :=
+  by simpa using h.add_pow_prime_pow_eq hp 1
+#align commute.add_pow_prime_eq Commute.add_pow_prime_eq
+
+protected theorem exists_add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ) :
+    ∃ r, (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n + p * r :=
+  ⟨_, h.add_pow_prime_pow_eq hp n⟩
+#align commute.exists_add_pow_prime_pow_eq Commute.exists_add_pow_prime_pow_eq
+
+protected theorem exists_add_pow_prime_eq (hp : p.Prime) (h : Commute x y) :
+    ∃ r, (x + y) ^ p = x ^ p + y ^ p + p * r :=
+  ⟨_, h.add_pow_prime_eq hp⟩
+#align commute.exists_add_pow_prime_eq Commute.exists_add_pow_prime_eq
+
+end Commute
+
+section CommSemiring
+
+variable [CommSemiring R] {p : ℕ} {x y : R}
+
+theorem add_pow_prime_pow_eq (hp : p.Prime) (x y : R) (n : ℕ) :
+    (x + y) ^ p ^ n =
+      x ^ p ^ n + y ^ p ^ n +
+        p * ∑ k in Finset.Ioo 0 (p ^ n), x ^ k * y ^ (p ^ n - k) * ↑((p ^ n).choose k / p) :=
+  (Commute.all x y).add_pow_prime_pow_eq hp n
+#align add_pow_prime_pow_eq add_pow_prime_pow_eq
+
+theorem add_pow_prime_eq (hp : p.Prime) (x y : R) :
+    (x + y) ^ p =
+      x ^ p + y ^ p + p * ∑ k in Finset.Ioo 0 p, x ^ k * y ^ (p - k) * ↑(p.choose k / p) :=
+  (Commute.all x y).add_pow_prime_eq hp
+#align add_pow_prime_eq add_pow_prime_eq
+
+theorem exists_add_pow_prime_pow_eq (hp : p.Prime) (x y : R) (n : ℕ) :
+    ∃ r, (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n + p * r :=
+  (Commute.all x y).exists_add_pow_prime_pow_eq hp n
+#align exists_add_pow_prime_pow_eq exists_add_pow_prime_pow_eq
+
+theorem exists_add_pow_prime_eq (hp : p.Prime) (x y : R) :
+    ∃ r, (x + y) ^ p = x ^ p + y ^ p + p * r :=
+  (Commute.all x y).exists_add_pow_prime_eq hp
+#align exists_add_pow_prime_eq exists_add_pow_prime_eq
+
+end CommSemiring
+
+variable (R)
 
 #print CharP /-
 /- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
@@ -48,6 +120,7 @@ lean 3 declaration is
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R _inst_1 p], Eq.{succ u1} R (Nat.cast.{u1} R (AddMonoidWithOne.toNatCast.{u1} R _inst_1) p) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (AddMonoid.toZero.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align char_p.cast_eq_zero CharP.cast_eq_zeroₓ'. -/
+@[simp]
 theorem CharP.cast_eq_zero [AddMonoidWithOne R] (p : ℕ) [CharP R p] : (p : R) = 0 :=
   (CharP.cast_eq_zero_iff R p p).2 (dvd_refl p)
 #align char_p.cast_eq_zero CharP.cast_eq_zero
@@ -233,41 +306,28 @@ end ringChar
 
 /- warning: add_pow_char_of_commute -> add_pow_char_of_commute is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) p] (x : R) (y : R), (Commute.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) p) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y p)))
+  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {p : Nat} [hp : Fact (Nat.Prime p)] [_inst_2 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) p] (x : R) (y : R), (Commute.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) p) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y p)))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) p] (x : R) (y : R), (Commute.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) p) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y p)))
+  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {p : Nat} [hp : Fact (Nat.Prime p)] [_inst_2 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) p] (x : R) (y : R), (Commute.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) p) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y p)))
 Case conversion may be inaccurate. Consider using '#align add_pow_char_of_commute add_pow_char_of_commuteₓ'. -/
-theorem add_pow_char_of_commute [Semiring R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R)
+theorem add_pow_char_of_commute [Semiring R] {p : ℕ} [hp : Fact p.Prime] [CharP R p] (x y : R)
     (h : Commute x y) : (x + y) ^ p = x ^ p + y ^ p :=
   by
-  rw [Commute.add_pow h, Finset.sum_range_succ_comm, tsub_self, pow_zero, Nat.choose_self]
-  rw [Nat.cast_one, mul_one, mul_one]; congr 1
-  convert Finset.sum_eq_single 0 _ _
-  · simp only [mul_one, one_mul, Nat.choose_zero_right, tsub_zero, Nat.cast_one, pow_zero]
-  · intro b h1 h2
-    suffices (p.choose b : R) = 0 by
-      rw [this]
-      simp
-    rw [CharP.cast_eq_zero_iff R p]
-    exact Nat.Prime.dvd_choose_self (Fact.out _) h2 (Finset.mem_range.1 h1)
-  · intro h1
-    contrapose! h1
-    rw [Finset.mem_range]
-    exact Nat.Prime.pos (Fact.out _)
+  let ⟨r, hr⟩ := h.exists_add_pow_prime_eq hp.out
+  simp [hr]
 #align add_pow_char_of_commute add_pow_char_of_commute
 
 /- warning: add_pow_char_pow_of_commute -> add_pow_char_pow_of_commute is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) p] {n : Nat} (x : R) (y : R), (Commute.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n))))
+  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {p : Nat} {n : Nat} [hp : Fact (Nat.Prime p)] [_inst_2 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) p] (x : R) (y : R), (Commute.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {p : Nat} [_inst_2 : Fact (Nat.Prime p)] [_inst_3 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) p] {n : Nat} (x : R) (y : R), (Commute.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n))))
+  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {p : Nat} [n : Fact (Nat.Prime p)] [hp : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) p] {_inst_2 : Nat} (x : R) (y : R), (Commute.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) x y) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x y) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p _inst_2)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p _inst_2))))
 Case conversion may be inaccurate. Consider using '#align add_pow_char_pow_of_commute add_pow_char_pow_of_commuteₓ'. -/
-theorem add_pow_char_pow_of_commute [Semiring R] {p : ℕ} [Fact p.Prime] [CharP R p] {n : ℕ}
-    (x y : R) (h : Commute x y) : (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n :=
+theorem add_pow_char_pow_of_commute [Semiring R] {p n : ℕ} [hp : Fact p.Prime] [CharP R p] (x y : R)
+    (h : Commute x y) : (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n :=
   by
-  induction n; · simp
-  rw [pow_succ', pow_mul, pow_mul, pow_mul, n_ih]
-  apply add_pow_char_of_commute; apply Commute.pow_pow h
+  let ⟨r, hr⟩ := h.exists_add_pow_prime_pow_eq hp.out n
+  simp [hr]
 #align add_pow_char_pow_of_commute add_pow_char_pow_of_commute
 
 /- warning: sub_pow_char_of_commute -> sub_pow_char_of_commute is a dubious translation:
@@ -472,7 +532,7 @@ theorem frobenius_one : frobenius R p 1 = 1 :=
 
 /- warning: monoid_hom.map_frobenius -> MonoidHom.map_frobenius is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} S (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (fun (_x : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (fun (_x : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) f x))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] (f : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] [_inst_5 : CharP.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) p] (x : R), Eq.{succ u1} S (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (fun (_x : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) f (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (frobenius.{u2} R _inst_1 p _inst_3 _inst_4) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (frobenius.{u1} S _inst_2 p _inst_3 _inst_5) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (fun (_x : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) f x))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f x))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.map_frobenius MonoidHom.map_frobeniusₓ'. -/
@@ -482,7 +542,7 @@ theorem MonoidHom.map_frobenius : f (frobenius R p x) = frobenius S p (f x) :=
 
 /- warning: ring_hom.map_frobenius -> RingHom.map_frobenius is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) g (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) g x))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] (g : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] [_inst_5 : CharP.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) p] (x : R), Eq.{succ u1} S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) g (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (frobenius.{u2} R _inst_1 p _inst_3 _inst_4) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (frobenius.{u1} S _inst_2 p _inst_3 _inst_5) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) g x))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (FunLike.coe.{max (succ u1) (succ u2), succ u1, 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(Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g x))
 Case conversion may be inaccurate. Consider using '#align ring_hom.map_frobenius RingHom.map_frobeniusₓ'. -/
@@ -492,7 +552,7 @@ theorem RingHom.map_frobenius : g (frobenius R p x) = frobenius S p (g x) :=
 
 /- warning: monoid_hom.map_iterate_frobenius -> MonoidHom.map_iterate_frobenius is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} S (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (fun (_x : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) f (Nat.iterate.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (fun (_x : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) f x))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] (f : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] [_inst_5 : CharP.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u1} S (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (fun (_x : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) f (Nat.iterate.{succ u2} R (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (frobenius.{u2} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u1} S (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (frobenius.{u1} S _inst_2 p _inst_3 _inst_5)) n (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (fun (_x : MonoidHom.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u2, u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) f x))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f x))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.map_iterate_frobenius MonoidHom.map_iterate_frobeniusₓ'. -/
@@ -503,7 +563,7 @@ theorem MonoidHom.map_iterate_frobenius (n : ℕ) :
 
 /- warning: ring_hom.map_iterate_frobenius -> RingHom.map_iterate_frobenius is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) g (Nat.iterate.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) g x))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] (g : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] [_inst_5 : CharP.{u1} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} S (NonAssocSemiring.toAddCommMonoidWithOne.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u1} S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) g (Nat.iterate.{succ u2} R (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (fun (_x : RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (frobenius.{u2} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u1} S (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (frobenius.{u1} S _inst_2 p _inst_3 _inst_5)) n (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) g x))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S 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(CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S 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(CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g x))
 Case conversion may be inaccurate. Consider using '#align ring_hom.map_iterate_frobenius RingHom.map_iterate_frobeniusₓ'. -/
@@ -978,7 +1038,7 @@ instance [CharP S q] : CharP (R × S) (Nat.lcm p q)
 
 /- warning: prod.char_p -> Prod.charP is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) (S : Type.{u2}) [_inst_1 : AddMonoidWithOne.{u1} R] [_inst_2 : AddMonoidWithOne.{u2} S] (p : Nat) [_inst_3 : CharP.{u1} R _inst_1 p] [_inst_4 : CharP.{u2} S _inst_2 p], CharP.{max u1 u2} (Prod.{u1, u2} R S) (Prod.addMonoidWithOne.{u1, u2} R S _inst_1 _inst_2) p
+  forall (R : Type.{u2}) (S : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u2} R] [_inst_2 : AddMonoidWithOne.{u1} S] (p : Nat) [_inst_3 : CharP.{u2} R _inst_1 p] [_inst_4 : CharP.{u1} S _inst_2 p], CharP.{max u2 u1} (Prod.{u2, u1} R S) (Prod.addMonoidWithOne.{u2, u1} R S _inst_1 _inst_2) p
 but is expected to have type
   forall (R : Type.{u1}) (S : Type.{u2}) [_inst_1 : AddMonoidWithOne.{u1} R] [_inst_2 : AddMonoidWithOne.{u2} S] (p : Nat) [_inst_3 : CharP.{u1} R _inst_1 p] [_inst_4 : CharP.{u2} S _inst_2 p], CharP.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instAddMonoidWithOneProd.{u1, u2} R S _inst_1 _inst_2) p
 Case conversion may be inaccurate. Consider using '#align prod.char_p Prod.charPₓ'. -/
@@ -989,11 +1049,15 @@ instance Prod.charP [CharP S p] : CharP (R × S) p := by convert Nat.lcm.charP R
 
 end Prod
 
-#print ULift.charP /-
+/- warning: ulift.char_p -> ULift.charP is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u2}) [_inst_1 : AddMonoidWithOne.{u2} R] (p : Nat) [_inst_2 : CharP.{u2} R _inst_1 p], CharP.{max u2 u1} (ULift.{u1, u2} R) (ULift.addMonoidWithOne.{u2, u1} R _inst_1) p
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R _inst_1 p], CharP.{max u2 u1} (ULift.{u2, u1} R) (ULift.addMonoidWithOne.{u1, u2} R _inst_1) p
+Case conversion may be inaccurate. Consider using '#align ulift.char_p ULift.charPₓ'. -/
 instance ULift.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP (ULift.{v} R) p
     where cast_eq_zero_iff n := Iff.trans (ULift.ext_iff _ _) <| CharP.cast_eq_zero_iff R p n
 #align ulift.char_p ULift.charP
--/
 
 /- warning: mul_opposite.char_p -> MulOpposite.charP is a dubious translation:
 lean 3 declaration is

bump to nightly-2023-03-14-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

f296636f

Diff

@@ -24,6 +24,7 @@ universe u v
 
 variable (R : Type u)
 
+#print CharP /-
 /- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`cast_eq_zero_iff] [] -/
 /-- The generator of the kernel of the unique homomorphism ℕ → R for a semiring R.
 
@@ -39,20 +40,41 @@ This example is formalized in `counterexamples/char_p_zero_ne_char_zero`.
 class CharP [AddMonoidWithOne R] (p : ℕ) : Prop where
   cast_eq_zero_iff : ∀ x : ℕ, (x : R) = 0 ↔ p ∣ x
 #align char_p CharP
+-/
 
+/- warning: char_p.cast_eq_zero -> CharP.cast_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R _inst_1 p], Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R _inst_1)))) p) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R _inst_1))))))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R _inst_1 p], Eq.{succ u1} R (Nat.cast.{u1} R (AddMonoidWithOne.toNatCast.{u1} R _inst_1) p) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (AddMonoid.toZero.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align char_p.cast_eq_zero CharP.cast_eq_zeroₓ'. -/
 theorem CharP.cast_eq_zero [AddMonoidWithOne R] (p : ℕ) [CharP R p] : (p : R) = 0 :=
   (CharP.cast_eq_zero_iff R p p).2 (dvd_refl p)
 #align char_p.cast_eq_zero CharP.cast_eq_zero
 
+/- warning: char_p.cast_card_eq_zero -> CharP.cast_card_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] [_inst_2 : Fintype.{u1} R], Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1))))) (Fintype.card.{u1} R _inst_2)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1)))))))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] [_inst_2 : Fintype.{u1} R], Eq.{succ u1} R (Nat.cast.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1)) (Fintype.card.{u1} R _inst_2)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (NegZeroClass.toZero.{u1} R (SubNegZeroMonoid.toNegZeroClass.{u1} R (SubtractionMonoid.toSubNegZeroMonoid.{u1} R (AddGroup.toSubtractionMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align char_p.cast_card_eq_zero CharP.cast_card_eq_zeroₓ'. -/
 @[simp]
 theorem CharP.cast_card_eq_zero [AddGroupWithOne R] [Fintype R] : (Fintype.card R : R) = 0 := by
   rw [← nsmul_one, card_nsmul_eq_zero]
 #align char_p.cast_card_eq_zero CharP.cast_card_eq_zero
 
+#print CharP.addOrderOf_one /-
 theorem CharP.addOrderOf_one (R) [Semiring R] : CharP R (addOrderOf (1 : R)) :=
   ⟨fun n => by rw [← Nat.smul_one_eq_coe, addOrderOf_dvd_iff_nsmul_eq_zero]⟩
 #align char_p.add_order_of_one CharP.addOrderOf_one
+-/
 
+/- warning: char_p.int_cast_eq_zero_iff -> CharP.int_cast_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] (a : Int), Iff (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R _inst_1)))) a) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1)))))))) (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) a)
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] (a : Int), Iff (Eq.{succ u1} R (Int.cast.{u1} R (AddGroupWithOne.toIntCast.{u1} R _inst_1) a) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (NegZeroClass.toZero.{u1} R (SubNegZeroMonoid.toNegZeroClass.{u1} R (SubtractionMonoid.toSubNegZeroMonoid.{u1} R (AddGroup.toSubtractionMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R _inst_1)))))))) (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int Int.instNatCastInt p) a)
+Case conversion may be inaccurate. Consider using '#align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iffₓ'. -/
 theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a : ℤ) :
     (a : R) = 0 ↔ (p : ℤ) ∣ a :=
   by
@@ -65,20 +87,31 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
     rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
 #align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff
 
-theorem CharP.int_coe_eq_int_coe_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a b : ℤ) :
+/- warning: char_p.int_coe_eq_int_coe_iff -> CharP.int_cast_eq_int_cast_iff is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R _inst_1)))) a) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R _inst_1)))) b)) (Int.ModEq ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) a b)
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : AddGroupWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R _inst_1) p] (a : Int) (b : Int), Iff (Eq.{succ u1} R (Int.cast.{u1} R (AddGroupWithOne.toIntCast.{u1} R _inst_1) a) (Int.cast.{u1} R (AddGroupWithOne.toIntCast.{u1} R _inst_1) b)) (Int.ModEq (Nat.cast.{0} Int Int.instNatCastInt p) a b)
+Case conversion may be inaccurate. Consider using '#align char_p.int_coe_eq_int_coe_iff CharP.int_cast_eq_int_cast_iffₓ'. -/
+theorem CharP.int_cast_eq_int_cast_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a b : ℤ) :
     (a : R) = (b : R) ↔ a ≡ b [ZMOD p] := by
   rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.int_cast_eq_zero_iff R p, Int.modEq_iff_dvd]
-#align char_p.int_coe_eq_int_coe_iff CharP.int_coe_eq_int_coe_iff
+#align char_p.int_coe_eq_int_coe_iff CharP.int_cast_eq_int_cast_iff
 
+#print CharP.eq /-
 theorem CharP.eq [AddMonoidWithOne R] {p q : ℕ} (c1 : CharP R p) (c2 : CharP R q) : p = q :=
   Nat.dvd_antisymm ((CharP.cast_eq_zero_iff R p q).1 (CharP.cast_eq_zero _ _))
     ((CharP.cast_eq_zero_iff R q p).1 (CharP.cast_eq_zero _ _))
 #align char_p.eq CharP.eq
+-/
 
-instance CharP.of_charZero [AddMonoidWithOne R] [CharZero R] : CharP R 0 :=
+#print CharP.ofCharZero /-
+instance CharP.ofCharZero [AddMonoidWithOne R] [CharZero R] : CharP R 0 :=
   ⟨fun x => by rw [zero_dvd_iff, ← Nat.cast_zero, Nat.cast_inj]⟩
-#align char_p.of_char_zero CharP.of_charZero
+#align char_p.of_char_zero CharP.ofCharZero
+-/
 
+#print CharP.exists /-
 theorem CharP.exists [NonAssocSemiring R] : ∃ p, CharP R p :=
   letI := Classical.decEq R
   by_cases
@@ -105,64 +138,105 @@ theorem CharP.exists [NonAssocSemiring R] : ∃ p, CharP R p :=
             of_not_not (not_not_of_not_imp <| Nat.find_spec (not_forall.1 H)),
             MulZeroClass.zero_mul]⟩⟩⟩
 #align char_p.exists CharP.exists
+-/
 
-theorem CharP.existsUnique [NonAssocSemiring R] : ∃! p, CharP R p :=
+#print CharP.exists_unique /-
+theorem CharP.exists_unique [NonAssocSemiring R] : ∃! p, CharP R p :=
   let ⟨c, H⟩ := CharP.exists R
   ⟨c, H, fun y H2 => CharP.eq R H2 H⟩
-#align char_p.exists_unique CharP.existsUnique
+#align char_p.exists_unique CharP.exists_unique
+-/
 
+#print CharP.congr /-
 theorem CharP.congr {R : Type u} [AddMonoidWithOne R] {p : ℕ} (q : ℕ) [hq : CharP R q] (h : q = p) :
     CharP R p :=
   h ▸ hq
 #align char_p.congr CharP.congr
+-/
 
+#print ringChar /-
 /-- Noncomputable function that outputs the unique characteristic of a semiring. -/
 noncomputable def ringChar [NonAssocSemiring R] : ℕ :=
-  Classical.choose (CharP.existsUnique R)
+  Classical.choose (CharP.exists_unique R)
 #align ring_char ringChar
+-/
 
 namespace ringChar
 
 variable [NonAssocSemiring R]
 
+/- warning: ring_char.spec -> ringChar.spec is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : NonAssocSemiring.{u1} R] (x : Nat), Iff (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_1)))))) x) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))))))) (Dvd.Dvd.{0} Nat Nat.hasDvd (ringChar.{u1} R _inst_1) x)
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : NonAssocSemiring.{u1} R] (x : Nat), Iff (Eq.{succ u1} R (Nat.cast.{u1} R (NonAssocSemiring.toNatCast.{u1} R _inst_1) x) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_1))))) (Dvd.dvd.{0} Nat Nat.instDvdNat (ringChar.{u1} R _inst_1) x)
+Case conversion may be inaccurate. Consider using '#align ring_char.spec ringChar.specₓ'. -/
 theorem spec : ∀ x : ℕ, (x : R) = 0 ↔ ringChar R ∣ x := by
-  letI := (Classical.choose_spec (CharP.existsUnique R)).1 <;> unfold ringChar <;>
+  letI := (Classical.choose_spec (CharP.exists_unique R)).1 <;> unfold ringChar <;>
     exact CharP.cast_eq_zero_iff R (ringChar R)
 #align ring_char.spec ringChar.spec
 
+#print ringChar.eq /-
 theorem eq (p : ℕ) [C : CharP R p] : ringChar R = p :=
-  ((Classical.choose_spec (CharP.existsUnique R)).2 p C).symm
+  ((Classical.choose_spec (CharP.exists_unique R)).2 p C).symm
 #align ring_char.eq ringChar.eq
+-/
 
+#print ringChar.charP /-
 instance charP : CharP R (ringChar R) :=
   ⟨spec R⟩
 #align ring_char.char_p ringChar.charP
+-/
 
 variable {R}
 
+#print ringChar.of_eq /-
 theorem of_eq {p : ℕ} (h : ringChar R = p) : CharP R p :=
   CharP.congr (ringChar R) h
 #align ring_char.of_eq ringChar.of_eq
+-/
 
+#print ringChar.eq_iff /-
 theorem eq_iff {p : ℕ} : ringChar R = p ↔ CharP R p :=
   ⟨of_eq, @eq R _ p⟩
 #align ring_char.eq_iff ringChar.eq_iff
+-/
 
+/- warning: ring_char.dvd -> ringChar.dvd is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NonAssocSemiring.{u1} R] {x : Nat}, (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_1)))))) x) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))))))) -> (Dvd.Dvd.{0} Nat Nat.hasDvd (ringChar.{u1} R _inst_1) x)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NonAssocSemiring.{u1} R] {x : Nat}, (Eq.{succ u1} R (Nat.cast.{u1} R (NonAssocSemiring.toNatCast.{u1} R _inst_1) x) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_1))))) -> (Dvd.dvd.{0} Nat Nat.instDvdNat (ringChar.{u1} R _inst_1) x)
+Case conversion may be inaccurate. Consider using '#align ring_char.dvd ringChar.dvdₓ'. -/
 theorem dvd {x : ℕ} (hx : (x : R) = 0) : ringChar R ∣ x :=
   (spec R x).1 hx
 #align ring_char.dvd ringChar.dvd
 
+#print ringChar.eq_zero /-
 @[simp]
 theorem eq_zero [CharZero R] : ringChar R = 0 :=
   eq R 0
 #align ring_char.eq_zero ringChar.eq_zero
+-/
 
+/- warning: ring_char.nat.cast_ring_char -> ringChar.Nat.cast_ringChar is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NonAssocSemiring.{u1} R], Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_1)))))) (ringChar.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NonAssocSemiring.{u1} R], Eq.{succ u1} R (Nat.cast.{u1} R (NonAssocSemiring.toNatCast.{u1} R _inst_1) (ringChar.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align ring_char.nat.cast_ring_char ringChar.Nat.cast_ringCharₓ'. -/
 @[simp]
 theorem Nat.cast_ringChar : (ringChar R : R) = 0 := by rw [ringChar.spec]
 #align ring_char.nat.cast_ring_char ringChar.Nat.cast_ringChar
 
 end ringChar
 
+/- warning: add_pow_char_of_commute -> add_pow_char_of_commute is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align add_pow_char_of_commute add_pow_char_of_commuteₓ'. -/
 theorem add_pow_char_of_commute [Semiring R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R)
     (h : Commute x y) : (x + y) ^ p = x ^ p + y ^ p :=
   by
@@ -182,6 +256,12 @@ theorem add_pow_char_of_commute [Semiring R] {p : ℕ} [Fact p.Prime] [CharP R p
     exact Nat.Prime.pos (Fact.out _)
 #align add_pow_char_of_commute add_pow_char_of_commute
 
+/- warning: add_pow_char_pow_of_commute -> add_pow_char_pow_of_commute is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align add_pow_char_pow_of_commute add_pow_char_pow_of_commuteₓ'. -/
 theorem add_pow_char_pow_of_commute [Semiring R] {p : ℕ} [Fact p.Prime] [CharP R p] {n : ℕ}
     (x y : R) (h : Commute x y) : (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n :=
   by
@@ -190,6 +270,12 @@ theorem add_pow_char_pow_of_commute [Semiring R] {p : ℕ} [Fact p.Prime] [CharP
   apply add_pow_char_of_commute; apply Commute.pow_pow h
 #align add_pow_char_pow_of_commute add_pow_char_pow_of_commute
 
+/- warning: sub_pow_char_of_commute -> sub_pow_char_of_commute is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align sub_pow_char_of_commute sub_pow_char_of_commuteₓ'. -/
 theorem sub_pow_char_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R)
     (h : Commute x y) : (x - y) ^ p = x ^ p - y ^ p :=
   by
@@ -197,6 +283,12 @@ theorem sub_pow_char_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p] (x
   simp; repeat' infer_instance
 #align sub_pow_char_of_commute sub_pow_char_of_commute
 
+/- warning: sub_pow_char_pow_of_commute -> sub_pow_char_pow_of_commute is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align sub_pow_char_pow_of_commute sub_pow_char_pow_of_commuteₓ'. -/
 theorem sub_pow_char_pow_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p] {n : ℕ} (x y : R)
     (h : Commute x y) : (x - y) ^ p ^ n = x ^ p ^ n - y ^ p ^ n :=
   by
@@ -205,30 +297,66 @@ theorem sub_pow_char_pow_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p
   apply sub_pow_char_of_commute; apply Commute.pow_pow h
 #align sub_pow_char_pow_of_commute sub_pow_char_pow_of_commute
 
+/- warning: add_pow_char -> add_pow_char is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align add_pow_char add_pow_charₓ'. -/
 theorem add_pow_char [CommSemiring R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R) :
     (x + y) ^ p = x ^ p + y ^ p :=
   add_pow_char_of_commute _ _ _ (Commute.all _ _)
 #align add_pow_char add_pow_char
 
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+Case conversion may be inaccurate. Consider using '#align add_pow_char_pow add_pow_char_powₓ'. -/
 theorem add_pow_char_pow [CommSemiring R] {p : ℕ} [Fact p.Prime] [CharP R p] {n : ℕ} (x y : R) :
     (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n :=
   add_pow_char_pow_of_commute _ _ _ (Commute.all _ _)
 #align add_pow_char_pow add_pow_char_pow
 
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+Case conversion may be inaccurate. Consider using '#align sub_pow_char sub_pow_charₓ'. -/
 theorem sub_pow_char [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R) :
     (x - y) ^ p = x ^ p - y ^ p :=
   sub_pow_char_of_commute _ _ _ (Commute.all _ _)
 #align sub_pow_char sub_pow_char
 
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+Case conversion may be inaccurate. Consider using '#align sub_pow_char_pow sub_pow_char_powₓ'. -/
 theorem sub_pow_char_pow [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] {n : ℕ} (x y : R) :
     (x - y) ^ p ^ n = x ^ p ^ n - y ^ p ^ n :=
   sub_pow_char_pow_of_commute _ _ _ (Commute.all _ _)
 #align sub_pow_char_pow sub_pow_char_pow
 
+/- warning: eq_iff_modeq_int -> eq_iff_modEq_int is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align eq_iff_modeq_int eq_iff_modEq_intₓ'. -/
 theorem eq_iff_modEq_int [Ring R] (p : ℕ) [CharP R p] (a b : ℤ) : (a : R) = b ↔ a ≡ b [ZMOD p] := by
   rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.int_cast_eq_zero_iff R p, Int.modEq_iff_dvd]
 #align eq_iff_modeq_int eq_iff_modEq_int
 
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+Case conversion may be inaccurate. Consider using '#align char_p.neg_one_ne_one CharP.neg_one_ne_oneₓ'. -/
 theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1 : R) ≠ (1 : R) :=
   by
   suffices (2 : R) ≠ 0 by
@@ -243,6 +371,12 @@ theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1
   linarith
 #align char_p.neg_one_ne_one CharP.neg_one_ne_one
 
+/- warning: char_p.neg_one_pow_char -> CharP.neg_one_pow_char is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) p) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) p) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align char_p.neg_one_pow_char CharP.neg_one_pow_charₓ'. -/
 theorem CharP.neg_one_pow_char [CommRing R] (p : ℕ) [CharP R p] [Fact p.Prime] :
     (-1 : R) ^ p = -1 := by
   rw [eq_neg_iff_add_eq_zero]
@@ -250,6 +384,12 @@ theorem CharP.neg_one_pow_char [CommRing R] (p : ℕ) [CharP R p] [Fact p.Prime]
   rw [← add_pow_char, add_left_neg, zero_pow (Fact.out (Nat.Prime p)).Pos]
 #align char_p.neg_one_pow_char CharP.neg_one_pow_char
 
+/- warning: char_p.neg_one_pow_char_pow -> CharP.neg_one_pow_char_pow is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) (n : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) (n : Nat) [_inst_2 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] [_inst_3 : Fact (Nat.Prime p)], Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align char_p.neg_one_pow_char_pow CharP.neg_one_pow_char_powₓ'. -/
 theorem CharP.neg_one_pow_char_pow [CommRing R] (p n : ℕ) [CharP R p] [Fact p.Prime] :
     (-1 : R) ^ p ^ n = -1 := by
   rw [eq_neg_iff_add_eq_zero]
@@ -257,6 +397,12 @@ theorem CharP.neg_one_pow_char_pow [CommRing R] (p n : ℕ) [CharP R p] [Fact p.
   rw [← add_pow_char_pow, add_left_neg, zero_pow (pow_pos (Fact.out (Nat.Prime p)).Pos _)]
 #align char_p.neg_one_pow_char_pow CharP.neg_one_pow_char_pow
 
+/- warning: ring_hom.char_p_iff_char_p -> RingHom.charP_iff_charP is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : Semiring.{u2} L] [_inst_3 : Nontrivial.{u2} L], (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L _inst_2)) -> (forall (p : Nat), Iff (CharP.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) p) (CharP.{u2} L (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} L (NonAssocSemiring.toAddCommMonoidWithOne.{u2} L (Semiring.toNonAssocSemiring.{u2} L _inst_2))) p))
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : Semiring.{u1} L] [_inst_3 : Nontrivial.{u1} L], (RingHom.{u2, u1} K L (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} L _inst_2)) -> (forall (p : Nat), Iff (CharP.{u2} K (AddGroupWithOne.toAddMonoidWithOne.{u2} K (Ring.toAddGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K _inst_1))) p) (CharP.{u1} L (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} L (NonAssocSemiring.toAddCommMonoidWithOne.{u1} L (Semiring.toNonAssocSemiring.{u1} L _inst_2))) p))
+Case conversion may be inaccurate. Consider using '#align ring_hom.char_p_iff_char_p RingHom.charP_iff_charPₓ'. -/
 theorem RingHom.charP_iff_charP {K L : Type _} [DivisionRing K] [Semiring L] [Nontrivial L]
     (f : K →+* L) (p : ℕ) : CharP K p ↔ CharP L p := by
   simp only [charP_iff, ← f.injective.eq_iff, map_natCast f, f.map_zero]
@@ -269,6 +415,7 @@ section CommSemiring
 variable [CommSemiring R] {S : Type v} [CommSemiring S] (f : R →* S) (g : R →+* S) (p : ℕ)
   [Fact p.Prime] [CharP R p] [CharP S p] (x y : R)
 
+#print frobenius /-
 /-- The frobenius map that sends x to x^p -/
 def frobenius : R →+* R where
   toFun x := x ^ p
@@ -277,50 +424,111 @@ def frobenius : R →+* R where
   map_zero' := zero_pow (Fact.out (Nat.Prime p)).Pos
   map_add' := add_pow_char R
 #align frobenius frobenius
+-/
 
 variable {R}
 
+/- warning: frobenius_def -> frobenius_def is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x p)
+Case conversion may be inaccurate. Consider using '#align frobenius_def frobenius_defₓ'. -/
 theorem frobenius_def : frobenius R p x = x ^ p :=
   rfl
 #align frobenius_def frobenius_def
 
+/- warning: iterate_frobenius -> iterate_frobenius is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align iterate_frobenius iterate_frobeniusₓ'. -/
 theorem iterate_frobenius (n : ℕ) : (frobenius R p^[n]) x = x ^ p ^ n :=
   by
   induction n; · simp
   rw [Function.iterate_succ', pow_succ', pow_mul, Function.comp_apply, frobenius_def, n_ih]
 #align iterate_frobenius iterate_frobenius
 
+/- warning: frobenius_mul -> frobenius_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) y))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x y)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) y) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) y))
+Case conversion may be inaccurate. Consider using '#align frobenius_mul frobenius_mulₓ'. -/
 theorem frobenius_mul : frobenius R p (x * y) = frobenius R p x * frobenius R p y :=
   (frobenius R p).map_mul x y
 #align frobenius_mul frobenius_mul
 
+/- warning: frobenius_one -> frobenius_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p], Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_1))))
+Case conversion may be inaccurate. Consider using '#align frobenius_one frobenius_oneₓ'. -/
 theorem frobenius_one : frobenius R p 1 = 1 :=
   one_pow _
 #align frobenius_one frobenius_one
 
+/- warning: monoid_hom.map_frobenius -> MonoidHom.map_frobenius is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} S (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (fun (_x : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (fun (_x : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) f x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) 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(CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} 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(CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R 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(CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) 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_inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f x))
+Case conversion may be inaccurate. Consider using '#align monoid_hom.map_frobenius MonoidHom.map_frobeniusₓ'. -/
 theorem MonoidHom.map_frobenius : f (frobenius R p x) = frobenius S p (f x) :=
   f.map_pow x p
 #align monoid_hom.map_frobenius MonoidHom.map_frobenius
 
+/- warning: ring_hom.map_frobenius -> RingHom.map_frobenius is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) g (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) g x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) g (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S 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+Case conversion may be inaccurate. Consider using '#align ring_hom.map_frobenius RingHom.map_frobeniusₓ'. -/
 theorem RingHom.map_frobenius : g (frobenius R p x) = frobenius S p (g x) :=
   g.map_pow x p
 #align ring_hom.map_frobenius RingHom.map_frobenius
 
+/- warning: monoid_hom.map_iterate_frobenius -> MonoidHom.map_iterate_frobenius is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} S (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (fun (_x : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) f (Nat.iterate.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (fun (_x : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) => R -> S) (MonoidHom.hasCoeToFun.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) f x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) 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(CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) 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_inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MonoidHom.monoidHomClass.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) f x))
+Case conversion may be inaccurate. Consider using '#align monoid_hom.map_iterate_frobenius MonoidHom.map_iterate_frobeniusₓ'. -/
 theorem MonoidHom.map_iterate_frobenius (n : ℕ) :
     f ((frobenius R p^[n]) x) = (frobenius S p^[n]) (f x) :=
   Function.Semiconj.iterate_right (f.map_frobenius p) n x
 #align monoid_hom.map_iterate_frobenius MonoidHom.map_iterate_frobenius
 
+/- warning: ring_hom.map_iterate_frobenius -> RingHom.map_iterate_frobenius is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) g (Nat.iterate.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (Nat.iterate.{succ u2} S (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (frobenius.{u2} S _inst_2 p _inst_3 _inst_5)) n (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) g x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] [_inst_5 : CharP.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) p] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4)) n x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S 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(CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (frobenius.{u2} 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(CommSemiring.toSemiring.{u2} S _inst_2)))))) g x))
+Case conversion may be inaccurate. Consider using '#align ring_hom.map_iterate_frobenius RingHom.map_iterate_frobeniusₓ'. -/
 theorem RingHom.map_iterate_frobenius (n : ℕ) :
     g ((frobenius R p^[n]) x) = (frobenius S p^[n]) (g x) :=
   g.toMonoidHom.map_iterate_frobenius p x n
 #align ring_hom.map_iterate_frobenius RingHom.map_iterate_frobenius
 
+/- warning: monoid_hom.iterate_map_frobenius -> MonoidHom.iterate_map_frobenius is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (x : R) (f : MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (p : Nat) [_inst_6 : Fact (Nat.Prime p)] [_inst_7 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} R (Nat.iterate.{succ u1} R (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (fun (_x : MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) => R -> R) (MonoidHom.hasCoeToFun.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) f) n (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) (Nat.iterate.{succ u1} R (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (fun (_x : MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) => R -> R) (MonoidHom.hasCoeToFun.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) f) n x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (x : R) (f : MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (p : Nat) [_inst_6 : Fact (Nat.Prime p)] [_inst_7 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} R (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R 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_inst_1))))) R R (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidHom.monoidHomClass.{u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f) n x))
+Case conversion may be inaccurate. Consider using '#align monoid_hom.iterate_map_frobenius MonoidHom.iterate_map_frobeniusₓ'. -/
 theorem MonoidHom.iterate_map_frobenius (f : R →* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
     (f^[n]) (frobenius R p x) = frobenius R p ((f^[n]) x) :=
   f.iterate_map_pow _ _ _
 #align monoid_hom.iterate_map_frobenius MonoidHom.iterate_map_frobenius
 
+/- warning: ring_hom.iterate_map_frobenius -> RingHom.iterate_map_frobenius is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (x : R) (f : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (p : Nat) [_inst_6 : Fact (Nat.Prime p)] [_inst_7 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} R (Nat.iterate.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f) n (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) (Nat.iterate.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f) n x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (x : R) (f : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (p : Nat) [_inst_6 : Fact (Nat.Prime p)] [_inst_7 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} R (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) f) n (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_6 _inst_7) (Nat.iterate.{succ u1} R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) f) n x))
+Case conversion may be inaccurate. Consider using '#align ring_hom.iterate_map_frobenius RingHom.iterate_map_frobeniusₓ'. -/
 theorem RingHom.iterate_map_frobenius (f : R →+* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
     (f^[n]) (frobenius R p x) = frobenius R p ((f^[n]) x) :=
   f.iterate_map_pow _ _ _
@@ -328,14 +536,32 @@ theorem RingHom.iterate_map_frobenius (f : R →+* R) (p : ℕ) [Fact p.Prime] [
 
 variable (R)
 
+/- warning: frobenius_zero -> frobenius_zero is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p], Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) _inst_1))))
+Case conversion may be inaccurate. Consider using '#align frobenius_zero frobenius_zeroₓ'. -/
 theorem frobenius_zero : frobenius R p 0 = 0 :=
   (frobenius R p).map_zero
 #align frobenius_zero frobenius_zero
 
+/- warning: frobenius_add -> frobenius_add is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) y))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) y) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) y))
+Case conversion may be inaccurate. Consider using '#align frobenius_add frobenius_addₓ'. -/
 theorem frobenius_add : frobenius R p (x + y) = frobenius R p x + frobenius R p y :=
   (frobenius R p).map_add x y
 #align frobenius_add frobenius_add
 
+/- warning: frobenius_nat_cast -> frobenius_nat_cast is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) n)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) n)
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (frobenius.{u1} R _inst_1 p _inst_3 _inst_4) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (Nat.cast.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (Semiring.toNatCast.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) _inst_1)) n)
+Case conversion may be inaccurate. Consider using '#align frobenius_nat_cast frobenius_nat_castₓ'. -/
 theorem frobenius_nat_cast (n : ℕ) : frobenius R p n = n :=
   map_natCast (frobenius R p) n
 #align frobenius_nat_cast frobenius_nat_cast
@@ -344,14 +570,28 @@ open BigOperators
 
 variable {R}
 
+/- warning: list_sum_pow_char -> list_sum_pow_char is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (l : List.{u1} R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (List.sum.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) l) p) (List.sum.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (List.map.{u1, u1} R R (fun (_x : R) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _x p) l))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] (l : List.{u1} R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (List.sum.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) l) p) (List.sum.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (List.map.{u1, u1} R R (fun (_x : R) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _x p) l))
+Case conversion may be inaccurate. Consider using '#align list_sum_pow_char list_sum_pow_charₓ'. -/
 theorem list_sum_pow_char (l : List R) : l.Sum ^ p = (l.map (· ^ p)).Sum :=
   (frobenius R p).map_list_sum _
 #align list_sum_pow_char list_sum_pow_char
 
+#print multiset_sum_pow_char /-
 theorem multiset_sum_pow_char (s : Multiset R) : s.Sum ^ p = (s.map (· ^ p)).Sum :=
   (frobenius R p).map_multiset_sum _
 #align multiset_sum_pow_char multiset_sum_pow_char
+-/
 
+/- warning: sum_pow_char -> sum_pow_char is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p] {ι : Type.{u2}} (s : Finset.{u2} ι) (f : ι -> R), Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finset.sum.{u1, u2} R ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) s (fun (i : ι) => f i)) p) (Finset.sum.{u1, u2} R ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) s (fun (i : ι) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (f i) p))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p] {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> R), Eq.{succ u2} R (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Finset.sum.{u2, u1} R ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) s (fun (i : ι) => f i)) p) (Finset.sum.{u2, u1} R ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (f i) p))
+Case conversion may be inaccurate. Consider using '#align sum_pow_char sum_pow_charₓ'. -/
 theorem sum_pow_char {ι : Type _} (s : Finset ι) (f : ι → R) :
     (∑ i in s, f i) ^ p = ∑ i in s, f i ^ p :=
   (frobenius R p).map_sum _ _
@@ -364,10 +604,22 @@ section CommRing
 variable [CommRing R] {S : Type v} [CommRing S] (f : R →* S) (g : R →+* S) (p : ℕ) [Fact p.Prime]
   [CharP R p] [CharP S p] (x y : R)
 
+/- warning: frobenius_neg -> frobenius_neg is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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+Case conversion may be inaccurate. Consider using '#align frobenius_neg frobenius_negₓ'. -/
 theorem frobenius_neg : frobenius R p (-x) = -frobenius R p x :=
   (frobenius R p).map_neg x
 #align frobenius_neg frobenius_neg
 
+/- warning: frobenius_sub -> frobenius_sub is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R) (y : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x y)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) y))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R) (y : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) y) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (Ring.toSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4) y))
+Case conversion may be inaccurate. Consider using '#align frobenius_sub frobenius_subₓ'. -/
 theorem frobenius_sub : frobenius R p (x - y) = frobenius R p x - frobenius R p y :=
   (frobenius R p).map_sub x y
 #align frobenius_sub frobenius_sub
@@ -376,6 +628,12 @@ end CommRing
 
 end frobenius
 
+/- warning: frobenius_inj -> frobenius_inj is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p], Function.Injective.{succ u1, succ u1} R R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))] (p : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p], Function.Injective.{succ u1, succ u1} R R (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (frobenius.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) p _inst_3 _inst_4))
+Case conversion may be inaccurate. Consider using '#align frobenius_inj frobenius_injₓ'. -/
 theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP R p] :
     Function.Injective (frobenius R p) := fun x h H =>
   by
@@ -384,15 +642,21 @@ theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP
   exact IsReduced.eq_zero _ ⟨_, H⟩
 #align frobenius_inj frobenius_inj
 
+/- warning: is_square_of_char_two' -> isSquare_of_charTwo' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Finite.{succ u1} R] [_inst_2 : CommRing.{u1} R] [_inst_3 : IsReduced.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2)))))) (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_2)))] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))] (a : R), IsSquare.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_2))) a
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Finite.{succ u1} R] [_inst_2 : CommRing.{u1} R] [_inst_3 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_2))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))] (a : R), IsSquare.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2)))) a
+Case conversion may be inaccurate. Consider using '#align is_square_of_char_two' isSquare_of_charTwo'ₓ'. -/
 /-- If `ring_char R = 2`, where `R` is a finite reduced commutative ring,
 then every `a : R` is a square. -/
-theorem isSquare_of_char_two' {R : Type _} [Finite R] [CommRing R] [IsReduced R] [CharP R 2]
+theorem isSquare_of_charTwo' {R : Type _} [Finite R] [CommRing R] [IsReduced R] [CharP R 2]
     (a : R) : IsSquare a := by
   cases nonempty_fintype R
   exact
     Exists.imp (fun b h => pow_two b ▸ Eq.symm h)
       (((Fintype.bijective_iff_injective_and_card _).mpr ⟨frobenius_inj R 2, rfl⟩).Surjective a)
-#align is_square_of_char_two' isSquare_of_char_two'
+#align is_square_of_char_two' isSquare_of_charTwo'
 
 namespace CharP
 
@@ -400,17 +664,22 @@ section
 
 variable [NonAssocRing R]
 
+#print CharP.charP_to_charZero /-
 theorem charP_to_charZero (R : Type _) [AddGroupWithOne R] [CharP R 0] : CharZero R :=
   charZero_of_inj_zero fun n h0 => eq_zero_of_zero_dvd ((cast_eq_zero_iff R 0 n).mp h0)
 #align char_p.char_p_to_char_zero CharP.charP_to_charZero
+-/
 
+#print CharP.cast_eq_mod /-
 theorem cast_eq_mod (p : ℕ) [CharP R p] (k : ℕ) : (k : R) = (k % p : ℕ) :=
   calc
     (k : R) = ↑(k % p + p * (k / p)) := by rw [Nat.mod_add_div]
     _ = ↑(k % p) := by simp [cast_eq_zero]
     
 #align char_p.cast_eq_mod CharP.cast_eq_mod
+-/
 
+#print CharP.char_ne_zero_of_finite /-
 /-- The characteristic of a finite ring cannot be zero. -/
 theorem char_ne_zero_of_finite (p : ℕ) [CharP R p] [Finite R] : p ≠ 0 :=
   by
@@ -419,10 +688,13 @@ theorem char_ne_zero_of_finite (p : ℕ) [CharP R p] [Finite R] : p ≠ 0 :=
   cases nonempty_fintype R
   exact absurd Nat.cast_injective (not_injective_infinite_finite (coe : ℕ → R))
 #align char_p.char_ne_zero_of_finite CharP.char_ne_zero_of_finite
+-/
 
+#print CharP.ringChar_ne_zero_of_finite /-
 theorem ringChar_ne_zero_of_finite [Finite R] : ringChar R ≠ 0 :=
   char_ne_zero_of_finite R (ringChar R)
 #align char_p.ring_char_ne_zero_of_finite CharP.ringChar_ne_zero_of_finite
+-/
 
 end
 
@@ -430,6 +702,12 @@ section CommRing
 
 variable [CommRing R] [IsReduced R] {R}
 
+/- warning: char_p.pow_prime_pow_mul_eq_one_iff -> CharP.pow_prime_pow_mul_eq_one_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Nat) (k : Nat) (m : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p] (x : R), Iff (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat Nat.hasMul) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k) m)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x m) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsReduced.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))] (p : Nat) (k : Nat) (m : Nat) [_inst_3 : Fact (Nat.Prime p)] [_inst_4 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) p] (x : R), Iff (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k) m)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x m) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align char_p.pow_prime_pow_mul_eq_one_iff CharP.pow_prime_pow_mul_eq_one_iffₓ'. -/
 @[simp]
 theorem pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [Fact p.Prime] [CharP R p] (x : R) :
     x ^ (p ^ k * m) = 1 ↔ x ^ m = 1 :=
@@ -450,15 +728,23 @@ open Nat
 
 variable [NonAssocSemiring R]
 
+#print CharP.char_ne_one /-
 theorem char_ne_one [Nontrivial R] (p : ℕ) [hc : CharP R p] : p ≠ 1 := fun hp : p = 1 =>
   have : (1 : R) = 0 := by simpa using (cast_eq_zero_iff R p 1).mpr (hp ▸ dvd_refl p)
   absurd this one_ne_zero
 #align char_p.char_ne_one CharP.char_ne_one
+-/
 
 section NoZeroDivisors
 
 variable [NoZeroDivisors R]
 
+/- warning: char_p.char_is_prime_of_two_le -> CharP.char_is_prime_of_two_le is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)))] (p : Nat) [hc : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_1)) p], (LE.le.{0} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) p) -> (Nat.Prime p)
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_1))] (p : Nat) [hc : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_1)) p], (LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) p) -> (Nat.Prime p)
+Case conversion may be inaccurate. Consider using '#align char_p.char_is_prime_of_two_le CharP.char_is_prime_of_two_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (d «expr ∣ » p) -/
 theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.Prime p :=
   suffices ∀ (d) (_ : d ∣ p), d = 1 ∨ d = p from Nat.prime_def_lt''.mpr ⟨hp, this⟩
@@ -483,6 +769,12 @@ section Nontrivial
 
 variable [Nontrivial R]
 
+/- warning: char_p.char_is_prime_or_zero -> CharP.char_is_prime_or_zero is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)))] [_inst_3 : Nontrivial.{u1} R] (p : Nat) [hc : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_1)) p], Or (Nat.Prime p) (Eq.{1} Nat p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_1))] [_inst_3 : Nontrivial.{u1} R] (p : Nat) [hc : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_1)) p], Or (Nat.Prime p) (Eq.{1} Nat p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+Case conversion may be inaccurate. Consider using '#align char_p.char_is_prime_or_zero CharP.char_is_prime_or_zeroₓ'. -/
 theorem char_is_prime_or_zero (p : ℕ) [hc : CharP R p] : Nat.Prime p ∨ p = 0 :=
   match p, hc with
   | 0, _ => Or.inr rfl
@@ -490,6 +782,12 @@ theorem char_is_prime_or_zero (p : ℕ) [hc : CharP R p] : Nat.Prime p ∨ p = 0
   | m + 2, hc => Or.inl (@char_is_prime_of_two_le R _ _ (m + 2) hc (Nat.le_add_left 2 m))
 #align char_p.char_is_prime_or_zero CharP.char_is_prime_or_zero
 
+/- warning: char_p.char_is_prime_of_pos -> CharP.char_is_prime_of_pos is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)))] [_inst_3 : Nontrivial.{u1} R] (p : Nat) [_inst_4 : NeZero.{0} Nat Nat.hasZero p] [_inst_5 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_1)) p], Fact (Nat.Prime p)
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_1))] [_inst_3 : Nontrivial.{u1} R] (p : Nat) [_inst_4 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) p] [_inst_5 : CharP.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_1)) p], Fact (Nat.Prime p)
+Case conversion may be inaccurate. Consider using '#align char_p.char_is_prime_of_pos CharP.char_is_prime_of_posₓ'. -/
 theorem char_is_prime_of_pos (p : ℕ) [NeZero p] [CharP R p] : Fact p.Prime :=
   ⟨(CharP.char_is_prime_or_zero R _).resolve_right <| NeZero.ne p⟩
 #align char_p.char_is_prime_of_pos CharP.char_is_prime_of_pos
@@ -504,6 +802,12 @@ section Ring
 
 variable (R) [Ring R] [NoZeroDivisors R] [Nontrivial R] [Finite R]
 
+/- warning: char_p.char_is_prime -> CharP.char_is_prime is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))] [_inst_3 : Nontrivial.{u1} R] [_inst_4 : Finite.{succ u1} R] (p : Nat) [_inst_5 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) p], Nat.Prime p
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))] [_inst_3 : Nontrivial.{u1} R] [_inst_4 : Finite.{succ u1} R] (p : Nat) [_inst_5 : CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) p], Nat.Prime p
+Case conversion may be inaccurate. Consider using '#align char_p.char_is_prime CharP.char_is_primeₓ'. -/
 theorem char_is_prime (p : ℕ) [CharP R p] : p.Prime :=
   Or.resolve_right (char_is_prime_or_zero R p) (char_ne_zero_of_finite R p)
 #align char_p.char_is_prime CharP.char_is_prime
@@ -526,10 +830,13 @@ instance (priority := 100) [CharP R 1] : Subsingleton R :=
       _ = 0 := by rw [MulZeroClass.zero_mul]
       
 
+#print CharP.false_of_nontrivial_of_char_one /-
 theorem false_of_nontrivial_of_char_one [Nontrivial R] [CharP R 1] : False :=
   false_of_nontrivial_of_subsingleton R
 #align char_p.false_of_nontrivial_of_char_one CharP.false_of_nontrivial_of_char_one
+-/
 
+#print CharP.ringChar_ne_one /-
 theorem ringChar_ne_one [Nontrivial R] : ringChar R ≠ 1 :=
   by
   intro h
@@ -537,12 +844,21 @@ theorem ringChar_ne_one [Nontrivial R] : ringChar R ≠ 1 :=
   symm
   rw [← Nat.cast_one, ringChar.spec, h]
 #align char_p.ring_char_ne_one CharP.ringChar_ne_one
+-/
 
+#print CharP.nontrivial_of_char_ne_one /-
 theorem nontrivial_of_char_ne_one {v : ℕ} (hv : v ≠ 1) [hr : CharP R v] : Nontrivial R :=
   ⟨⟨(1 : ℕ), 0, fun h =>
       hv <| by rwa [CharP.cast_eq_zero_iff _ v, Nat.dvd_one] at h <;> assumption⟩⟩
 #align char_p.nontrivial_of_char_ne_one CharP.nontrivial_of_char_ne_one
+-/
 
+/- warning: char_p.ring_char_of_prime_eq_zero -> CharP.ringChar_of_prime_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : Nontrivial.{u1} R] {p : Nat}, (Nat.Prime p) -> (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_1)))))) p) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))))))) -> (Eq.{1} Nat (ringChar.{u1} R _inst_1) p)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : Nontrivial.{u1} R] {p : Nat}, (Nat.Prime p) -> (Eq.{succ u1} R (Nat.cast.{u1} R (NonAssocSemiring.toNatCast.{u1} R _inst_1) p) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_1))))) -> (Eq.{1} Nat (ringChar.{u1} R _inst_1) p)
+Case conversion may be inaccurate. Consider using '#align char_p.ring_char_of_prime_eq_zero CharP.ringChar_of_prime_eq_zeroₓ'. -/
 theorem ringChar_of_prime_eq_zero [Nontrivial R] {p : ℕ} (hprime : Nat.Prime p)
     (hp0 : (p : R) = 0) : ringChar R = p :=
   Or.resolve_left ((Nat.dvd_prime hprime).1 (ringChar.dvd hp0)) ringChar_ne_one
@@ -554,6 +870,12 @@ end CharP
 
 section
 
+/- warning: ring.two_ne_zero -> Ring.two_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R _inst_1) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (Ne.{succ u1} R (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R _inst_1) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> (Ne.{succ u1} R (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (NonAssocSemiring.toNatCast.{u1} R _inst_1) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align ring.two_ne_zero Ring.two_ne_zeroₓ'. -/
 /-- We have `2 ≠ 0` in a nontrivial ring whose characteristic is not `2`. -/
 @[protected]
 theorem Ring.two_ne_zero {R : Type _} [NonAssocSemiring R] [Nontrivial R] (hR : ringChar R ≠ 2) :
@@ -563,6 +885,12 @@ theorem Ring.two_ne_zero {R : Type _} [NonAssocSemiring R] [Nontrivial R] (hR :
   exact mt (or_iff_left hR).mp CharP.ringChar_ne_one
 #align ring.two_ne_zero Ring.two_ne_zero
 
+/- warning: ring.neg_one_ne_one_of_char_ne_two -> Ring.neg_one_ne_one_of_char_ne_two is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (Ne.{succ u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> (Ne.{succ u1} R (Neg.neg.{u1} R (AddGroupWithOne.toNeg.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align ring.neg_one_ne_one_of_char_ne_two Ring.neg_one_ne_one_of_char_ne_twoₓ'. -/
 -- We have `char_p.neg_one_ne_one`, which assumes `[ring R] (p : ℕ) [char_p R p] [fact (2 < p)]`.
 -- This is a version using `ring_char` instead.
 /-- Characteristic `≠ 2` and nontrivial implies that `-1 ≠ 1`. -/
@@ -571,6 +899,12 @@ theorem Ring.neg_one_ne_one_of_char_ne_two {R : Type _} [NonAssocRing R] [Nontri
   Ring.two_ne_zero hR (neg_eq_iff_add_eq_zero.mp h)
 #align ring.neg_one_ne_one_of_char_ne_two Ring.neg_one_ne_one_of_char_ne_two
 
+/- warning: ring.eq_self_iff_eq_zero_of_char_ne_two -> Ring.eq_self_iff_eq_zero_of_char_ne_two is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1))))], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (forall {a : R}, Iff (Eq.{succ u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))) a) a) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)) (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)))], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> (forall {a : R}, Iff (Eq.{succ u1} R (Neg.neg.{u1} R (AddGroupWithOne.toNeg.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)) a) a) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align ring.eq_self_iff_eq_zero_of_char_ne_two Ring.eq_self_iff_eq_zero_of_char_ne_twoₓ'. -/
 /-- Characteristic `≠ 2` in a domain implies that `-a = a` iff `a = 0`. -/
 theorem Ring.eq_self_iff_eq_zero_of_char_ne_two {R : Type _} [NonAssocRing R] [Nontrivial R]
     [NoZeroDivisors R] (hR : ringChar R ≠ 2) {a : R} : -a = a ↔ a = 0 :=
@@ -586,6 +920,12 @@ section
 
 variable (R) [NonAssocRing R] [Fintype R] (n : ℕ)
 
+/- warning: char_p_of_ne_zero -> charP_of_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Fintype.{u1} R] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_2) n) -> (forall (i : Nat), (LT.lt.{0} Nat Nat.hasLt i n) -> (Eq.{succ u1} R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))))) i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R _inst_1)))))))) -> (Eq.{1} Nat i (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)) n)
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Fintype.{u1} R] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_2) n) -> (forall (i : Nat), (LT.lt.{0} Nat instLTNat i n) -> (Eq.{succ u1} R (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R _inst_1) i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)))))) -> (Eq.{1} Nat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)) n)
+Case conversion may be inaccurate. Consider using '#align char_p_of_ne_zero charP_of_ne_zeroₓ'. -/
 theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0 → i = 0) :
     CharP R n :=
   {
@@ -605,6 +945,12 @@ theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0
         rw [Nat.cast_mul, H, MulZeroClass.zero_mul] }
 #align char_p_of_ne_zero charP_of_ne_zero
 
+/- warning: char_p_of_prime_pow_injective -> charP_of_prime_pow_injective is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_3 : Ring.{u1} R] [_inst_4 : Fintype.{u1} R] (p : Nat) [hp : Fact (Nat.Prime p)] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_4) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) -> (forall (i : Nat), (LE.le.{0} Nat Nat.hasLe i n) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_3))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3))))))) p) i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3))))))))) -> (Eq.{1} Nat i n)) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_3 : Ring.{u1} R] [_inst_4 : Fintype.{u1} R] (p : Nat) [hp : Fact (Nat.Prime p)] (n : Nat), (Eq.{1} Nat (Fintype.card.{u1} R _inst_4) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) -> (forall (i : Nat), (LE.le.{0} Nat instLENat i n) -> (Eq.{succ u1} R (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p i)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_3)))))) -> (Eq.{1} Nat i n)) -> (CharP.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_3)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n))
+Case conversion may be inaccurate. Consider using '#align char_p_of_prime_pow_injective charP_of_prime_pow_injectiveₓ'. -/
 theorem charP_of_prime_pow_injective (R) [Ring R] [Fintype R] (p : ℕ) [hp : Fact p.Prime] (n : ℕ)
     (hn : Fintype.card R = p ^ n) (hR : ∀ i ≤ n, (p ^ i : R) = 0 → i = n) : CharP R (p ^ n) :=
   by
@@ -630,6 +976,12 @@ instance [CharP S q] : CharP (R × S) (Nat.lcm p q)
     where cast_eq_zero_iff := by
     simp [Prod.ext_iff, CharP.cast_eq_zero_iff R p, CharP.cast_eq_zero_iff S q, Nat.lcm_dvd_iff]
 
+/- warning: prod.char_p -> Prod.charP is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (S : Type.{u2}) [_inst_1 : AddMonoidWithOne.{u1} R] [_inst_2 : AddMonoidWithOne.{u2} S] (p : Nat) [_inst_3 : CharP.{u1} R _inst_1 p] [_inst_4 : CharP.{u2} S _inst_2 p], CharP.{max u1 u2} (Prod.{u1, u2} R S) (Prod.addMonoidWithOne.{u1, u2} R S _inst_1 _inst_2) p
+but is expected to have type
+  forall (R : Type.{u1}) (S : Type.{u2}) [_inst_1 : AddMonoidWithOne.{u1} R] [_inst_2 : AddMonoidWithOne.{u2} S] (p : Nat) [_inst_3 : CharP.{u1} R _inst_1 p] [_inst_4 : CharP.{u2} S _inst_2 p], CharP.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instAddMonoidWithOneProd.{u1, u2} R S _inst_1 _inst_2) p
+Case conversion may be inaccurate. Consider using '#align prod.char_p Prod.charPₓ'. -/
 /-- The characteristic of the product of two rings of the same characteristic
   is the same as the characteristic of the rings -/
 instance Prod.charP [CharP S p] : CharP (R × S) p := by convert Nat.lcm.charP R S p p <;> simp
@@ -637,16 +989,30 @@ instance Prod.charP [CharP S p] : CharP (R × S) p := by convert Nat.lcm.charP R
 
 end Prod
 
+#print ULift.charP /-
 instance ULift.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP (ULift.{v} R) p
     where cast_eq_zero_iff n := Iff.trans (ULift.ext_iff _ _) <| CharP.cast_eq_zero_iff R p n
 #align ulift.char_p ULift.charP
+-/
 
+/- warning: mul_opposite.char_p -> MulOpposite.charP is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R _inst_1 p], CharP.{u1} (MulOpposite.{u1} R) (MulOpposite.addMonoidWithOne.{u1} R _inst_1) p
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R _inst_1 p], CharP.{u1} (MulOpposite.{u1} R) (MulOpposite.instAddMonoidWithOneMulOpposite.{u1} R _inst_1) p
+Case conversion may be inaccurate. Consider using '#align mul_opposite.char_p MulOpposite.charPₓ'. -/
 instance MulOpposite.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP Rᵐᵒᵖ p
     where cast_eq_zero_iff n := MulOpposite.unop_inj.symm.trans <| CharP.cast_eq_zero_iff R p n
 #align mul_opposite.char_p MulOpposite.charP
 
 section
 
+/- warning: int.cast_inj_on_of_ring_char_ne_two -> Int.cast_injOn_of_ringChar_ne_two is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (Set.InjOn.{0, u1} Int R ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R _inst_1)))))) (Insert.insert.{0, 0} Int (Set.{0} Int) (Set.hasInsert.{0} Int) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) (Insert.insert.{0, 0} Int (Set.{0} Int) (Set.hasInsert.{0} Int) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))) (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.hasSingleton.{0} Int) (Neg.neg.{0} Int Int.hasNeg (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NonAssocRing.{u1} R] [_inst_2 : Nontrivial.{u1} R], (Ne.{1} Nat (ringChar.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R _inst_1)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> (Set.InjOn.{0, u1} Int R (Int.cast.{u1} R (NonAssocRing.toIntCast.{u1} R _inst_1)) (Insert.insert.{0, 0} Int (Set.{0} Int) (Set.instInsertSet.{0} Int) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) (Insert.insert.{0, 0} Int (Set.{0} Int) (Set.instInsertSet.{0} Int) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)) (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.instSingletonSet.{0} Int) (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
+Case conversion may be inaccurate. Consider using '#align int.cast_inj_on_of_ring_char_ne_two Int.cast_injOn_of_ringChar_ne_twoₓ'. -/
 /-- If two integers from `{0, 1, -1}` result in equal elements in a ring `R`
 that is nontrivial and of characteristic not `2`, then they are equal. -/
 theorem Int.cast_injOn_of_ringChar_ne_two {R : Type _} [NonAssocRing R] [Nontrivial R]
@@ -685,10 +1051,22 @@ namespace NeZero
 
 variable (R) [AddMonoidWithOne R] {r : R} {n p : ℕ} {a : ℕ+}
 
+/- warning: ne_zero.of_not_dvd -> NeZero.of_not_dvd is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] {n : Nat} {p : Nat} [_inst_2 : CharP.{u1} R _inst_1 p], (Not (Dvd.Dvd.{0} Nat Nat.hasDvd p n)) -> (NeZero.{u1} R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R _inst_1)))) n))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] {n : Nat} {p : Nat} [_inst_2 : CharP.{u1} R _inst_1 p], (Not (Dvd.dvd.{0} Nat Nat.instDvdNat p n)) -> (NeZero.{u1} R (AddMonoid.toZero.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R _inst_1)) (Nat.cast.{u1} R (AddMonoidWithOne.toNatCast.{u1} R _inst_1) n))
+Case conversion may be inaccurate. Consider using '#align ne_zero.of_not_dvd NeZero.of_not_dvdₓ'. -/
 theorem of_not_dvd [CharP R p] (h : ¬p ∣ n) : NeZero (n : R) :=
   ⟨(CharP.cast_eq_zero_iff R p n).Not.mpr h⟩
 #align ne_zero.of_not_dvd NeZero.of_not_dvd
 
+/- warning: ne_zero.not_char_dvd -> NeZero.not_char_dvd is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R _inst_1 p] (k : Nat) [h : NeZero.{u1} R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R _inst_1)))) k)], Not (Dvd.Dvd.{0} Nat Nat.hasDvd p k)
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : AddMonoidWithOne.{u1} R] (p : Nat) [_inst_2 : CharP.{u1} R _inst_1 p] (k : Nat) [h : NeZero.{u1} R (AddMonoid.toZero.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R _inst_1)) (Nat.cast.{u1} R (AddMonoidWithOne.toNatCast.{u1} R _inst_1) k)], Not (Dvd.dvd.{0} Nat Nat.instDvdNat p k)
+Case conversion may be inaccurate. Consider using '#align ne_zero.not_char_dvd NeZero.not_char_dvdₓ'. -/
 theorem not_char_dvd (p : ℕ) [CharP R p] (k : ℕ) [h : NeZero (k : R)] : ¬p ∣ k := by
   rwa [← CharP.cast_eq_zero_iff R p k, ← Ne.def, ← neZero_iff]
 #align ne_zero.not_char_dvd NeZero.not_char_dvd

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -97,12 +97,13 @@ theorem CharP.exists [NonAssocSemiring R] : ∃ p, CharP R p :=
                   ⟨by
                     rwa [← Nat.mod_add_div x (Nat.find (not_forall.1 H)), Nat.cast_add,
                       Nat.cast_mul,
-                      of_not_not (not_not_of_not_imp <| Nat.find_spec (not_forall.1 H)), zero_mul,
-                      add_zero] at H1,
+                      of_not_not (not_not_of_not_imp <| Nat.find_spec (not_forall.1 H)),
+                      MulZeroClass.zero_mul, add_zero] at H1,
                     H2⟩)),
           fun H1 => by
           rw [← Nat.mul_div_cancel' H1, Nat.cast_mul,
-            of_not_not (not_not_of_not_imp <| Nat.find_spec (not_forall.1 H)), zero_mul]⟩⟩⟩
+            of_not_not (not_not_of_not_imp <| Nat.find_spec (not_forall.1 H)),
+            MulZeroClass.zero_mul]⟩⟩⟩
 #align char_p.exists CharP.exists
 
 theorem CharP.existsUnique [NonAssocSemiring R] : ∃! p, CharP R p :=
@@ -522,7 +523,7 @@ instance (priority := 100) [CharP R 1] : Subsingleton R :=
       r = 1 * r := by rw [one_mul]
       _ = (1 : ℕ) * r := by rw [Nat.cast_one]
       _ = 0 * r := by rw [CharP.cast_eq_zero]
-      _ = 0 := by rw [zero_mul]
+      _ = 0 := by rw [MulZeroClass.zero_mul]
       
 
 theorem false_of_nontrivial_of_char_one [Nontrivial R] [CharP R 1] : False :=
@@ -594,13 +595,14 @@ theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0
       intro k
       constructor
       · intro h
-        rw [← Nat.mod_add_div k n, Nat.cast_add, Nat.cast_mul, H, zero_mul, add_zero] at h
+        rw [← Nat.mod_add_div k n, Nat.cast_add, Nat.cast_mul, H, MulZeroClass.zero_mul,
+          add_zero] at h
         rw [Nat.dvd_iff_mod_eq_zero]
         apply hR _ (Nat.mod_lt _ _) h
         rw [← hn, Fintype.card_pos_iff]
         exact ⟨0⟩
       · rintro ⟨k, rfl⟩
-        rw [Nat.cast_mul, H, zero_mul] }
+        rw [Nat.cast_mul, H, MulZeroClass.zero_mul] }
 #align char_p_of_ne_zero charP_of_ne_zero
 
 theorem charP_of_prime_pow_injective (R) [Ring R] [Fintype R] (p : ℕ) [hp : Fact p.Prime] (n : ℕ)

bump to nightly-2023-03-01-20

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

20cadee0

Diff

@@ -458,7 +458,7 @@ section NoZeroDivisors
 
 variable [NoZeroDivisors R]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (d «expr ∣ » p) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (d «expr ∣ » p) -/
 theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.Prime p :=
   suffices ∀ (d) (_ : d ∣ p), d = 1 ∨ d = p from Nat.prime_def_lt''.mpr ⟨hp, this⟩
   fun (d : ℕ) (hdvd : ∃ e, p = d * e) =>

bump to nightly-2023-02-22-21

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

0652cf4a

Diff

@@ -50,7 +50,7 @@ theorem CharP.cast_card_eq_zero [AddGroupWithOne R] [Fintype R] : (Fintype.card
 #align char_p.cast_card_eq_zero CharP.cast_card_eq_zero
 
 theorem CharP.addOrderOf_one (R) [Semiring R] : CharP R (addOrderOf (1 : R)) :=
-  ⟨fun n => by rw [← Nat.smul_one_eq_coe, add_orderOf_dvd_iff_nsmul_eq_zero]⟩
+  ⟨fun n => by rw [← Nat.smul_one_eq_coe, addOrderOf_dvd_iff_nsmul_eq_zero]⟩
 #align char_p.add_order_of_one CharP.addOrderOf_one
 
 theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a : ℤ) :

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: remove a subsingleton instance which leads to unreasonable instance search paths (#12445)

3877d4f0

Diff

@@ -466,8 +466,9 @@ section NonAssocSemiring
 
 variable {R} [NonAssocSemiring R]
 
--- see Note [lower instance priority]
-instance (priority := 100) CharOne.subsingleton [CharP R 1] : Subsingleton R :=
+-- This lemma is not an instance, to make sure that trying to prove `α` is a subsingleton does
+-- not try to find a ring structure on `α`, which can be expensive.
+lemma CharOne.subsingleton [CharP R 1] : Subsingleton R :=
   Subsingleton.intro <|
     suffices ∀ r : R, r = 0 from fun a b => show a = b by rw [this a, this b]
     fun r =>
@@ -477,8 +478,9 @@ instance (priority := 100) CharOne.subsingleton [CharP R 1] : Subsingleton R :=
       _ = 0 * r := by rw [CharP.cast_eq_zero]
       _ = 0 := by rw [zero_mul]
 
-theorem false_of_nontrivial_of_char_one [Nontrivial R] [CharP R 1] : False :=
-  false_of_nontrivial_of_subsingleton R
+theorem false_of_nontrivial_of_char_one [Nontrivial R] [CharP R 1] : False := by
+  have : Subsingleton R := CharOne.subsingleton
+  exact false_of_nontrivial_of_subsingleton R
 #align char_p.false_of_nontrivial_of_char_one CharP.false_of_nontrivial_of_char_one
 
 theorem ringChar_ne_one [Nontrivial R] : ringChar R ≠ 1 := by

chore: split RingTheory.Nilpotent (#12184)

Mathlib.RingTheory.Nilpotent has a few very simple definitions (Mathlib.Data.Nat.Lattice is sufficient to state them), but needs some pretty heavy imports (ideals, linear algebra) towards the end. This change moves the heavier parts into a new file.

bdfbc7fa

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Joey van Langen, Casper Putz
 -/
 import Mathlib.Algebra.CharP.ExpChar
-import Mathlib.RingTheory.Nilpotent
+import Mathlib.RingTheory.Nilpotent.Defs
 
 #align_import algebra.char_p.basic from "leanprover-community/mathlib"@"47a1a73351de8dd6c8d3d32b569c8e434b03ca47"

chore: use a variable in Data.Nat.Cast.Defs (#12254)

5efe4b85

Diff

@@ -521,7 +521,7 @@ protected theorem Ring.two_ne_zero {R : Type*} [NonAssocSemiring R] [Nontrivial
 /-- Characteristic `≠ 2` and nontrivial implies that `-1 ≠ 1`. -/
 theorem Ring.neg_one_ne_one_of_char_ne_two {R : Type*} [NonAssocRing R] [Nontrivial R]
     (hR : ringChar R ≠ 2) : (-1 : R) ≠ 1 := fun h =>
-  Ring.two_ne_zero hR (one_add_one_eq_two (α := R) ▸ neg_eq_iff_add_eq_zero.mp h)
+  Ring.two_ne_zero hR (one_add_one_eq_two (R := R) ▸ neg_eq_iff_add_eq_zero.mp h)
 #align ring.neg_one_ne_one_of_char_ne_two Ring.neg_one_ne_one_of_char_ne_two
 
 /-- Characteristic `≠ 2` in a domain implies that `-a = a` iff `a = 0`. -/

chore: Rename nat_cast/int_cast/rat_cast to natCast/intCast/ratCast (#11486)

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.

145460b9

Diff

@@ -140,7 +140,7 @@ theorem CharP.addOrderOf_one (R) [Semiring R] : CharP R (addOrderOf (1 : R)) :=
   ⟨fun n => by rw [← Nat.smul_one_eq_coe, addOrderOf_dvd_iff_nsmul_eq_zero]⟩
 #align char_p.add_order_of_one CharP.addOrderOf_one
 
-theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a : ℤ) :
+theorem CharP.intCast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a : ℤ) :
     (a : R) = 0 ↔ (p : ℤ) ∣ a := by
   rcases lt_trichotomy a 0 with (h | rfl | h)
   · rw [← neg_eq_zero, ← Int.cast_neg, ← dvd_neg]
@@ -149,11 +149,11 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
   · simp only [Int.cast_zero, eq_self_iff_true, dvd_zero]
   · lift a to ℕ using le_of_lt h with b
     rw [Int.cast_natCast, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
-#align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff
+#align char_p.int_cast_eq_zero_iff CharP.intCast_eq_zero_iff
 
 theorem CharP.intCast_eq_intCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℤ} :
     (a : R) = b ↔ a ≡ b [ZMOD p] := by
-  rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.int_cast_eq_zero_iff R p, Int.modEq_iff_dvd]
+  rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.intCast_eq_zero_iff R p, Int.modEq_iff_dvd]
 #align char_p.int_cast_eq_int_cast CharP.intCast_eq_intCast
 
 theorem CharP.natCast_eq_natCast' [AddMonoidWithOne R] (p : ℕ) [CharP R p] {a b : ℕ}

chore: backports from #11997, adaptations for nightly-2024-04-07 (#12176)

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>

02293f49

Diff

@@ -625,7 +625,7 @@ theorem of_not_dvd [CharP R p] (h : ¬p ∣ n) : NeZero (n : R) :=
 #align ne_zero.of_not_dvd NeZero.of_not_dvd
 
 theorem not_char_dvd (p : ℕ) [CharP R p] (k : ℕ) [h : NeZero (k : R)] : ¬p ∣ k := by
-  rwa [← CharP.cast_eq_zero_iff R p k, ← Ne.def, ← neZero_iff]
+  rwa [← CharP.cast_eq_zero_iff R p k, ← Ne, ← neZero_iff]
 #align ne_zero.not_char_dvd NeZero.not_char_dvd
 
 end NeZero

chore: remove porting notes about redundant binder updates (#12101)

All these are about some code (now commented out) which performs a (now) redundant binder information update. I don't see how this is useful information going forward, hence propose simply deleting them.

33c3101f

Diff

@@ -455,7 +455,6 @@ end Semiring
 section Ring
 
 variable [Ring R] [NoZeroDivisors R] [Nontrivial R] [Finite R]
--- Porting note: removed redundant binder annotation update `(R)`
 
 theorem char_is_prime (p : ℕ) [CharP R p] : p.Prime :=
   Or.resolve_right (char_is_prime_or_zero R p) (char_ne_zero_of_finite R p)
@@ -539,7 +538,6 @@ end
 section
 
 variable [NonAssocRing R] [Fintype R] (n : ℕ)
--- Porting note: removed redundant binder annotation update `(R)`
 
 theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0 → i = 0) :
     CharP R n :=
@@ -621,7 +619,6 @@ end
 namespace NeZero
 
 variable [AddMonoidWithOne R] {r : R} {n p : ℕ} {a : ℕ+}
--- Porting note: removed redundant binder annotation update `(R)`
 
 theorem of_not_dvd [CharP R p] (h : ¬p ∣ n) : NeZero (n : R) :=
   ⟨(CharP.cast_eq_zero_iff R p n).not.mpr h⟩

chore(Data/Int/Cast): fix confusion between OfNat and Nat.cast lemmas (#11861)

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.

a7ffab83

Diff

@@ -145,10 +145,10 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
   rcases lt_trichotomy a 0 with (h | rfl | h)
   · rw [← neg_eq_zero, ← Int.cast_neg, ← dvd_neg]
     lift -a to ℕ using neg_nonneg.mpr (le_of_lt h) with b
-    rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
+    rw [Int.cast_natCast, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
   · simp only [Int.cast_zero, eq_self_iff_true, dvd_zero]
   · lift a to ℕ using le_of_lt h with b
-    rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
+    rw [Int.cast_natCast, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
 #align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff
 
 theorem CharP.intCast_eq_intCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℤ} :

chore: remove some unnecessary 'open BigOperators' (#11880)

Could we have an open linter, that checked for unused opened namespaces?

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

16eb4bdf

Diff

@@ -15,8 +15,6 @@ import Mathlib.RingTheory.Nilpotent
 
 open Finset
 
-open BigOperators
-
 section
 
 variable (R : Type*) [CommRing R] [IsReduced R] (p n : ℕ) [ExpChar R p]

chore(Data/Int): Rename coe_nat to natCast (#11637)

Reduce the diff of #11499

Renames

All in the Int namespace:

ofNat_eq_cast → ofNat_eq_natCast
cast_eq_cast_iff_Nat → natCast_inj
natCast_eq_ofNat → ofNat_eq_natCast
coe_nat_sub → natCast_sub
coe_nat_nonneg → natCast_nonneg
sign_coe_add_one → sign_natCast_add_one
nat_succ_eq_int_succ → natCast_succ
succ_neg_nat_succ → succ_neg_natCast_succ
coe_pred_of_pos → natCast_pred_of_pos
coe_nat_div → natCast_div
coe_nat_ediv → natCast_ediv
sign_coe_nat_of_nonzero → sign_natCast_of_ne_zero
toNat_coe_nat → toNat_natCast
toNat_coe_nat_add_one → toNat_natCast_add_one
coe_nat_dvd → natCast_dvd_natCast
coe_nat_dvd_left → natCast_dvd
coe_nat_dvd_right → dvd_natCast
le_coe_nat_sub → le_natCast_sub
succ_coe_nat_pos → succ_natCast_pos
coe_nat_modEq_iff → natCast_modEq_iff
coe_natAbs → natCast_natAbs
coe_nat_eq_zero → natCast_eq_zero
coe_nat_ne_zero → natCast_ne_zero
coe_nat_ne_zero_iff_pos → natCast_ne_zero_iff_pos
abs_coe_nat → abs_natCast
coe_nat_nonpos_iff → natCast_nonpos_iff

Also rename Nat.coe_nat_dvd to Nat.cast_dvd_cast

392a24a9

Diff

@@ -145,10 +145,10 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
   rcases lt_trichotomy a 0 with (h | rfl | h)
   · rw [← neg_eq_zero, ← Int.cast_neg, ← dvd_neg]
     lift -a to ℕ using neg_nonneg.mpr (le_of_lt h) with b
-    rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
+    rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
   · simp only [Int.cast_zero, eq_self_iff_true, dvd_zero]
   · lift a to ℕ using le_of_lt h with b
-    rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
+    rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.natCast_dvd_natCast]
 #align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff
 
 theorem CharP.intCast_eq_intCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℤ} :

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

1b40c7bc

Diff

@@ -513,7 +513,7 @@ section
 /-- We have `2 ≠ 0` in a nontrivial ring whose characteristic is not `2`. -/
 protected theorem Ring.two_ne_zero {R : Type*} [NonAssocSemiring R] [Nontrivial R]
     (hR : ringChar R ≠ 2) : (2 : R) ≠ 0 := by
-  rw [Ne.def, (by norm_cast : (2 : R) = (2 : ℕ)), ringChar.spec, Nat.dvd_prime Nat.prime_two]
+  rw [Ne, (by norm_cast : (2 : R) = (2 : ℕ)), ringChar.spec, Nat.dvd_prime Nat.prime_two]
   exact mt (or_iff_left hR).mp CharP.ringChar_ne_one
 #align ring.two_ne_zero Ring.two_ne_zero

change the order of operation in zsmulRec and nsmulRec (#11451)

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

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

where the latter is more natural

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

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

but it seems to no longer apply.

Remarks on the PR :

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

9a3feeae

Diff

@@ -296,7 +296,7 @@ theorem sub_pow_char_pow_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p
   induction n with
   | zero => simp
   | succ n n_ih =>
-      rw [pow_succ', pow_mul, pow_mul, pow_mul, n_ih]
+      rw [pow_succ, pow_mul, pow_mul, pow_mul, n_ih]
       apply sub_pow_char_of_commute; apply Commute.pow_pow h
 #align sub_pow_char_pow_of_commute sub_pow_char_pow_of_commute

chore(*): migrate from RingHom.map_* to _root_.map_* (#11660)

Cherry-picked from #9607 Co-authored-by: @semorrison

859f3760

Diff

@@ -354,7 +354,7 @@ theorem CharP.neg_one_pow_char_pow [Ring R] (p n : ℕ) [CharP R p] [Fact p.Prim
 
 theorem RingHom.charP_iff_charP {K L : Type*} [DivisionRing K] [Semiring L] [Nontrivial L]
     (f : K →+* L) (p : ℕ) : CharP K p ↔ CharP L p := by
-  simp only [charP_iff, ← f.injective.eq_iff, map_natCast f, f.map_zero]
+  simp only [charP_iff, ← f.injective.eq_iff, map_natCast f, map_zero f]
 #align ring_hom.char_p_iff_char_p RingHom.charP_iff_charP
 
 namespace CharP

style: remove redundant instance arguments (#11581)

I removed some redundant instance arguments throughout Mathlib. To do this, I used VS Code's regex search. See https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/repeating.20instances.20from.20variable.20command I closed the previous PR for this and reopened it.

acda20c6

Diff

@@ -388,7 +388,7 @@ theorem ringChar_ne_zero_of_finite [Finite R] : ringChar R ≠ 0 :=
   char_ne_zero_of_finite R (ringChar R)
 #align char_p.ring_char_ne_zero_of_finite CharP.ringChar_ne_zero_of_finite
 
-theorem ringChar_zero_iff_CharZero [NonAssocRing R] : ringChar R = 0 ↔ CharZero R := by
+theorem ringChar_zero_iff_CharZero : ringChar R = 0 ↔ CharZero R := by
   rw [ringChar.eq_iff, charP_zero_iff_charZero]
 
 end

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -109,7 +109,7 @@ class CharP [AddMonoidWithOne R] (p : ℕ) : Prop where
 #align char_p CharP
 #align char_p_iff charP_iff
 
--- porting note: the field of the structure had implicit arguments where they were
+-- Porting note: the field of the structure had implicit arguments where they were
 -- explicit in Lean 3
 theorem CharP.cast_eq_zero_iff (R : Type u) [AddMonoidWithOne R] (p : ℕ) [CharP R p] (x : ℕ) :
     (x : R) = 0 ↔ p ∣ x :=
@@ -327,7 +327,7 @@ theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1
     rw [← sub_eq_zero, sub_neg_eq_add] at h
     norm_num at h
     exact this h
-    -- porting note: this could probably be golfed
+    -- Porting note: this could probably be golfed
   intro h
   rw [show (2 : R) = (2 : ℕ) by norm_cast] at h
   have := (CharP.cast_eq_zero_iff R p 2).mp h
@@ -455,7 +455,7 @@ end Semiring
 section Ring
 
 variable [Ring R] [NoZeroDivisors R] [Nontrivial R] [Finite R]
--- porting note: removed redundant binder annotation update `(R)`
+-- Porting note: removed redundant binder annotation update `(R)`
 
 theorem char_is_prime (p : ℕ) [CharP R p] : p.Prime :=
   Or.resolve_right (char_is_prime_or_zero R p) (char_ne_zero_of_finite R p)
@@ -539,7 +539,7 @@ end
 section
 
 variable [NonAssocRing R] [Fintype R] (n : ℕ)
--- porting note: removed redundant binder annotation update `(R)`
+-- Porting note: removed redundant binder annotation update `(R)`
 
 theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0 → i = 0) :
     CharP R n :=
@@ -621,7 +621,7 @@ end
 namespace NeZero
 
 variable [AddMonoidWithOne R] {r : R} {n p : ℕ} {a : ℕ+}
--- porting note: removed redundant binder annotation update `(R)`
+-- Porting note: removed redundant binder annotation update `(R)`
 
 theorem of_not_dvd [CharP R p] (h : ¬p ∣ n) : NeZero (n : R) :=
   ⟨(CharP.cast_eq_zero_iff R p n).not.mpr h⟩

refactor: optimize proofs with omega (#11093)

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.

37bc4aba

Diff

@@ -333,7 +333,7 @@ theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1
   have := (CharP.cast_eq_zero_iff R p 2).mp h
   have := Nat.le_of_dvd (by decide) this
   rw [fact_iff] at *
-  linarith
+  omega
 #align char_p.neg_one_ne_one CharP.neg_one_ne_one
 
 theorem CharP.neg_one_pow_char [Ring R] (p : ℕ) [CharP R p] [Fact p.Prime] :

chore(Init/Fin): deprecate Fin.eq_of_veq and Fin.veq_of_eq (#10626)

We have Fin.eq_of_val_eq and Fin.val_eq_of_eq in Lean core now. Also slightly shake the tree.

9a944835

Diff

@@ -652,6 +652,6 @@ namespace Fin
 
 instance charP (n : ℕ) : CharP (Fin (n + 1)) (n + 1) where
     cast_eq_zero_iff' := by
-      simp [Fin.eq_iff_veq, Nat.dvd_iff_mod_eq_zero]
+      simp [Fin.ext_iff, Nat.dvd_iff_mod_eq_zero]
 
 end Fin

chore: add lemmas for nat literals corresponding to lemmas for nat casts (#8006)

I loogled for every occurrence of "cast", Nat and "natCast" and where the casted nat was n, and made sure there were corresponding @[simp] lemmas for 0, 1, and OfNat.ofNat n. This is necessary in general for simp confluence. Example:

import Mathlib

variable {α : Type*} [LinearOrderedRing α] (m n : ℕ) [m.AtLeastTwo] [n.AtLeastTwo]

example : ((OfNat.ofNat m : ℕ) : α) ≤ ((OfNat.ofNat n : ℕ) : α) ↔ (OfNat.ofNat m : ℕ) ≤ (OfNat.ofNat n : ℕ) := by
  simp only [Nat.cast_le] -- this `@[simp]` lemma can apply

example : ((OfNat.ofNat m : ℕ) : α) ≤ ((OfNat.ofNat n : ℕ) : α) ↔ (OfNat.ofNat m : α) ≤ (OfNat.ofNat n : α) := by
  simp only [Nat.cast_ofNat] -- and so can this one

example : (OfNat.ofNat m : α) ≤ (OfNat.ofNat n : α) ↔ (OfNat.ofNat m : ℕ) ≤ (OfNat.ofNat n : ℕ) := by
  simp -- fails! `simp` doesn't have a lemma to bridge their results. confluence issue.

As far as I know, the only file this PR leaves with ofNat gaps is PartENat.lean. #8002 is addressing that file in parallel.

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

bbe9baad

Diff

@@ -120,6 +120,17 @@ theorem CharP.cast_eq_zero [AddMonoidWithOne R] (p : ℕ) [CharP R p] : (p : R)
   (CharP.cast_eq_zero_iff R p p).2 (dvd_refl p)
 #align char_p.cast_eq_zero CharP.cast_eq_zero
 
+-- See note [no_index around OfNat.ofNat]
+--
+-- TODO: This lemma needs to be `@[simp]` for confluence in the presence of `CharP.cast_eq_zero` and
+-- `Nat.cast_ofNat`, but with `no_index` on its entire LHS, it matches literally every expression so
+-- is too expensive. If lean4#2867 is fixed in a performant way, this can be made `@[simp]`.
+--
+-- @[simp]
+theorem CharP.ofNat_eq_zero [AddMonoidWithOne R] (p : ℕ) [p.AtLeastTwo] [CharP R p] :
+    (no_index (OfNat.ofNat p : R)) = 0 :=
+  cast_eq_zero R p
+
 @[simp]
 theorem CharP.cast_card_eq_zero [AddGroupWithOne R] [Fintype R] : (Fintype.card R : R) = 0 := by
   rw [← nsmul_one, card_nsmul_eq_zero]

chore: classify simp can do this porting notes (#10619)

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

de765f60

Diff

@@ -256,7 +256,7 @@ theorem eq_zero [CharZero R] : ringChar R = 0 :=
   eq R 0
 #align ring_char.eq_zero ringChar.eq_zero
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem Nat.cast_ringChar : (ringChar R : R) = 0 := by rw [ringChar.spec]
 #align ring_char.nat.cast_ring_char ringChar.Nat.cast_ringChar

feat(FieldTheory/PurelyInseparable): definition and basic results of purely inseparable extensions (#9488)

Main defintions:

IsPurelyInseparable: typeclass for purely inseparable field extension: an algebraic extension E / F is purely inseparable if and only if the minimal polynomial of every element of E ∖ F is not separable.

Main results (not exhaustive):

isPurelyInseparable_iff_mem_pow: a field extension E / F of exponential characteristic q is purely inseparable if and only if for every element x of E, there exists a natural number n such that x ^ (q ^ n) is contained in F.
IsPurelyInseparable.trans: if E / F and K / E are both purely inseparable extensions, then K / F is also purely inseparable.
isPurelyInseparable_iff_natSepDegree_eq_one: E / F is purely inseparable if and only if for every element x of E, its minimal polynomial has separable degree one.
isPurelyInseparable_iff_minpoly_eq_X_pow_sub_C: a field extension E / F of exponential characteristic q is purely inseparable if and only if for every element x of E, the minimal polynomial of x over F is of form X ^ (q ^ n) - y for some natural number n and some element y of F.
isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow: a field extension E / F of exponential characteristic q is purely inseparable if and only if for every element x of E, the minimal polynomial of x over F is of form (X - x) ^ (q ^ n) for some natural number n.
isPurelyInseparable_iff_finSepDegree_eq_one: an algebraic extension is purely inseparable if and only if it has (finite) separable degree one.

TODO: remove the algebraic assumption. (will be in later PR)
IsPurelyInseparable.normal: a purely inseparable extension is normal.
separableClosure.isPurelyInseparable: if E / F is algebraic, then E is purely inseparable over the (relative) separable closure of E / F.
IsPurelyInseparable.injective_comp_algebraMap: if E / F is purely inseparable, then for any reduced ring L, the map (E →+* L) → (F →+* L) induced by algebraMap F E is injective. In other words, a purely inseparable field extension is an epimorphism in the category of fields.
isPurelyInseparable_adjoin_iff_mem_pow: if F is of exponential characteristic q, then F(S) / F is a purely inseparable extension if and only if for any x ∈ S, x ^ (q ^ n) is contained in F for some n : ℕ.
Field.finSepDegree_eq: if E / F is algebraic, then the Field.finSepDegree F E is equal to Field.sepDegree F E as a natural number. This means that the cardinality of Field.Emb F E and the degree of (separableClosure F E) / F are both finite or infinite, and when they are finite, they coincide.

TODO: (will be in later PR)

IsPurelyInseparable.of_injective_comp_algebraMap: if L is an algebraically closed field containing E, such that the map (E →+* L) → (F →+* L) induced by algebraMap F E is injective, then E / F is purely inseparable. In other words, epimorphisms in the category of fields must be purely inseparable extensions. Need to use the fact that Emb F E is infintie when E / F is (purely) transcendental.
Prove that the (infinite) inseparable degree are multiplicative; linearly disjoint argument is needed.

Co-authored-by: Junyan Xu <junyanxumath@gmail.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

d172b397

Diff

@@ -17,13 +17,21 @@ open Finset
 
 open BigOperators
 
-theorem frobenius_inj (R : Type*) [CommRing R] [IsReduced R] (p : ℕ) [ExpChar R p] :
-    Function.Injective (frobenius R p) := fun x h H => by
+section
+
+variable (R : Type*) [CommRing R] [IsReduced R] (p n : ℕ) [ExpChar R p]
+
+theorem iterateFrobenius_inj : Function.Injective (iterateFrobenius R p n) := fun x y H ↦ by
   rw [← sub_eq_zero] at H ⊢
-  rw [← frobenius_sub] at H
+  simp_rw [iterateFrobenius_def, ← sub_pow_expChar_pow] at H
   exact IsReduced.eq_zero _ ⟨_, H⟩
+
+theorem frobenius_inj : Function.Injective (frobenius R p) :=
+  iterateFrobenius_one (R := R) p ▸ iterateFrobenius_inj R p 1
 #align frobenius_inj frobenius_inj
 
+end
+
 /-- If `ringChar R = 2`, where `R` is a finite reduced commutative ring,
 then every `a : R` is a square. -/
 theorem isSquare_of_charTwo' {R : Type*} [Finite R] [CommRing R] [IsReduced R] [CharP R 2]
@@ -39,12 +47,9 @@ variable {R : Type*} [CommRing R] [IsReduced R]
 @[simp]
 theorem ExpChar.pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [ExpChar R p] (x : R) :
     x ^ (p ^ k * m) = 1 ↔ x ^ m = 1 := by
-  induction' k with k hk
-  · rw [pow_zero, one_mul]
-  · refine' ⟨fun h => _, fun h => _⟩
-    · rw [pow_succ, mul_assoc, pow_mul', ← frobenius_def, ← frobenius_one p] at h
-      exact hk.1 (frobenius_inj R p h)
-    · rw [pow_mul', h, one_pow]
+  rw [pow_mul']
+  convert ← (iterateFrobenius_inj R p k).eq_iff
+  apply map_one
 #align char_p.pow_prime_pow_mul_eq_one_iff ExpChar.pow_prime_pow_mul_eq_one_iff
 
 @[deprecated] alias CharP.pow_prime_pow_mul_eq_one_iff := ExpChar.pow_prime_pow_mul_eq_one_iff

refactor: generalize CharP+Prime to ExpChar in frobenius (#10016)

Consequently, the part about frobenius in Algebra/CharP/Basic is moved to CharP/ExpChar, and imports are adjusted as necessary.

Add instances from CharP+Fact(Nat.Prime) and CharZero to ExpChar, to allow lemmas generalized to ExpChar still apply to CharP.
Remove lemmas in Algebra/CharP/ExpChar from [#9799](https://github.com/leanprover-community/mathlib4/commit/1e74fcfff8d5ffe5a3a9881864cf10fa39f619e6) because they coincide with the generalized lemmas, and golf the other lemmas (in Algebra/CharP/Basic).
Define the RingHom iterateFrobenius and the semilinear map LinearMap.(iterate)Frobenius for an algebra. When the characteristic is zero (ExpChar is 1), these are all equal to the identity map (· ^ 1). Also define iterateFrobeniusEquiv for perfect rings.
Fix and/or generalize other files.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: acmepjz <acme_pjz@hotmail.com>

96a6d295

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Joey van Langen, Casper Putz
 -/
-import Mathlib.Algebra.CharP.Basic
+import Mathlib.Algebra.CharP.ExpChar
 import Mathlib.RingTheory.Nilpotent
 
 #align_import algebra.char_p.basic from "leanprover-community/mathlib"@"47a1a73351de8dd6c8d3d32b569c8e434b03ca47"
@@ -17,7 +17,7 @@ open Finset
 
 open BigOperators
 
-theorem frobenius_inj (R : Type*) [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP R p] :
+theorem frobenius_inj (R : Type*) [CommRing R] [IsReduced R] (p : ℕ) [ExpChar R p] :
     Function.Injective (frobenius R p) := fun x h H => by
   rw [← sub_eq_zero] at H ⊢
   rw [← frobenius_sub] at H
@@ -34,12 +34,10 @@ theorem isSquare_of_charTwo' {R : Type*} [Finite R] [CommRing R] [IsReduced R] [
       (((Fintype.bijective_iff_injective_and_card _).mpr ⟨frobenius_inj R 2, rfl⟩).surjective a)
 #align is_square_of_char_two' isSquare_of_charTwo'
 
-namespace CharP
-
 variable {R : Type*} [CommRing R] [IsReduced R]
 
 @[simp]
-theorem pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [Fact p.Prime] [CharP R p] (x : R) :
+theorem ExpChar.pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [ExpChar R p] (x : R) :
     x ^ (p ^ k * m) = 1 ↔ x ^ m = 1 := by
   induction' k with k hk
   · rw [pow_zero, one_mul]
@@ -47,6 +45,6 @@ theorem pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [Fact p.Prime] [CharP R p] (x
     · rw [pow_succ, mul_assoc, pow_mul', ← frobenius_def, ← frobenius_one p] at h
       exact hk.1 (frobenius_inj R p h)
     · rw [pow_mul', h, one_pow]
-#align char_p.pow_prime_pow_mul_eq_one_iff CharP.pow_prime_pow_mul_eq_one_iff
+#align char_p.pow_prime_pow_mul_eq_one_iff ExpChar.pow_prime_pow_mul_eq_one_iff
 
-end CharP
+@[deprecated] alias CharP.pow_prime_pow_mul_eq_one_iff := ExpChar.pow_prime_pow_mul_eq_one_iff

refactor: generalize CharP+Prime to ExpChar in frobenius (#10016)

Consequently, the part about frobenius in Algebra/CharP/Basic is moved to CharP/ExpChar, and imports are adjusted as necessary.

Add instances from CharP+Fact(Nat.Prime) and CharZero to ExpChar, to allow lemmas generalized to ExpChar still apply to CharP.
Remove lemmas in Algebra/CharP/ExpChar from [#9799](https://github.com/leanprover-community/mathlib4/commit/1e74fcfff8d5ffe5a3a9881864cf10fa39f619e6) because they coincide with the generalized lemmas, and golf the other lemmas (in Algebra/CharP/Basic).
Define the RingHom iterateFrobenius and the semilinear map LinearMap.(iterate)Frobenius for an algebra. When the characteristic is zero (ExpChar is 1), these are all equal to the identity map (· ^ 1). Also define iterateFrobeniusEquiv for perfect rings.
Fix and/or generalize other files.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: acmepjz <acme_pjz@hotmail.com>

96a6d295

Diff

@@ -346,140 +346,6 @@ theorem RingHom.charP_iff_charP {K L : Type*} [DivisionRing K] [Semiring L] [Non
   simp only [charP_iff, ← f.injective.eq_iff, map_natCast f, f.map_zero]
 #align ring_hom.char_p_iff_char_p RingHom.charP_iff_charP
 
-section frobenius
-
-section CommSemiring
-
-variable [CommSemiring R] {S : Type v} [CommSemiring S] (f : R →* S) (g : R →+* S) (p : ℕ)
-  [Fact p.Prime] [CharP R p] [CharP S p] (x y : R)
-
-/-- The frobenius map that sends x to x^p -/
-def frobenius : R →+* R where
-  toFun x := x ^ p
-  map_one' := one_pow p
-  map_mul' x y := mul_pow x y p
-  map_zero' := zero_pow (Fact.out (p := Nat.Prime p)).ne_zero
-  map_add' := add_pow_char R
-#align frobenius frobenius
-
-variable {R}
-
-theorem frobenius_def : frobenius R p x = x ^ p :=
-  rfl
-#align frobenius_def frobenius_def
-
-theorem iterate_frobenius (n : ℕ) : (frobenius R p)^[n] x = x ^ p ^ n := by
-  induction n with
-  | zero => simp
-  | succ n n_ih =>
-      rw [Function.iterate_succ', pow_succ', pow_mul, Function.comp_apply, frobenius_def, n_ih]
-#align iterate_frobenius iterate_frobenius
-
-theorem frobenius_mul : frobenius R p (x * y) = frobenius R p x * frobenius R p y :=
-  (frobenius R p).map_mul x y
-#align frobenius_mul frobenius_mul
-
-theorem frobenius_one : frobenius R p 1 = 1 :=
-  one_pow _
-#align frobenius_one frobenius_one
-
-theorem MonoidHom.map_frobenius : f (frobenius R p x) = frobenius S p (f x) :=
-  f.map_pow x p
-#align monoid_hom.map_frobenius MonoidHom.map_frobenius
-
-theorem RingHom.map_frobenius : g (frobenius R p x) = frobenius S p (g x) :=
-  g.map_pow x p
-#align ring_hom.map_frobenius RingHom.map_frobenius
-
-theorem MonoidHom.map_iterate_frobenius (n : ℕ) :
-    f ((frobenius R p)^[n] x) = (frobenius S p)^[n] (f x) :=
-  Function.Semiconj.iterate_right (f.map_frobenius p) n x
-#align monoid_hom.map_iterate_frobenius MonoidHom.map_iterate_frobenius
-
-theorem RingHom.map_iterate_frobenius (n : ℕ) :
-    g ((frobenius R p)^[n] x) = (frobenius S p)^[n] (g x) :=
-  g.toMonoidHom.map_iterate_frobenius p x n
-#align ring_hom.map_iterate_frobenius RingHom.map_iterate_frobenius
-
-theorem MonoidHom.iterate_map_frobenius (f : R →* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
-    f^[n] (frobenius R p x) = frobenius R p (f^[n] x) :=
-  f.iterate_map_pow _ _ _
-#align monoid_hom.iterate_map_frobenius MonoidHom.iterate_map_frobenius
-
-theorem RingHom.iterate_map_frobenius (f : R →+* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
-    f^[n] (frobenius R p x) = frobenius R p (f^[n] x) :=
-  f.iterate_map_pow _ _ _
-#align ring_hom.iterate_map_frobenius RingHom.iterate_map_frobenius
-
-variable (R)
-
-theorem frobenius_zero : frobenius R p 0 = 0 :=
-  (frobenius R p).map_zero
-#align frobenius_zero frobenius_zero
-
-theorem frobenius_add : frobenius R p (x + y) = frobenius R p x + frobenius R p y :=
-  (frobenius R p).map_add x y
-#align frobenius_add frobenius_add
-
-theorem frobenius_nat_cast (n : ℕ) : frobenius R p n = n :=
-  map_natCast (frobenius R p) n
-#align frobenius_nat_cast frobenius_nat_cast
-
-open BigOperators
-
-variable {R}
-
-theorem list_sum_pow_char (l : List R) : l.sum ^ p = (l.map (· ^ p : R → R)).sum :=
-  (frobenius R p).map_list_sum _
-#align list_sum_pow_char list_sum_pow_char
-
-theorem multiset_sum_pow_char (s : Multiset R) : s.sum ^ p = (s.map (· ^ p : R → R)).sum :=
-  (frobenius R p).map_multiset_sum _
-#align multiset_sum_pow_char multiset_sum_pow_char
-
-theorem sum_pow_char {ι : Type*} (s : Finset ι) (f : ι → R) :
-    (∑ i in s, f i) ^ p = ∑ i in s, f i ^ p :=
-  (frobenius R p).map_sum _ _
-#align sum_pow_char sum_pow_char
-
-variable (n : ℕ)
-
-theorem list_sum_pow_char_pow (l : List R) : l.sum ^ p ^ n = (l.map (· ^ p ^ n : R → R)).sum := by
-  induction n with
-  | zero => simp_rw [pow_zero, pow_one, List.map_id']
-  | succ n ih => simp_rw [pow_succ', pow_mul, ih, list_sum_pow_char, List.map_map]; rfl
-
-theorem multiset_sum_pow_char_pow (s : Multiset R) :
-    s.sum ^ p ^ n = (s.map (· ^ p ^ n : R → R)).sum := by
-  induction n with
-  | zero => simp_rw [pow_zero, pow_one, Multiset.map_id']
-  | succ n ih => simp_rw [pow_succ', pow_mul, ih, multiset_sum_pow_char, Multiset.map_map]; rfl
-
-theorem sum_pow_char_pow {ι : Type*} (s : Finset ι) (f : ι → R) :
-    (∑ i in s, f i) ^ p ^ n = ∑ i in s, f i ^ p ^ n := by
-  induction n with
-  | zero => simp_rw [pow_zero, pow_one]
-  | succ n ih => simp_rw [pow_succ', pow_mul, ih, sum_pow_char]
-
-end CommSemiring
-
-section CommRing
-
-variable [CommRing R] {S : Type v} [CommRing S] (f : R →* S) (g : R →+* S) (p : ℕ) [Fact p.Prime]
-  [CharP R p] [CharP S p] (x y : R)
-
-theorem frobenius_neg : frobenius R p (-x) = -frobenius R p x :=
-  (frobenius R p).map_neg x
-#align frobenius_neg frobenius_neg
-
-theorem frobenius_sub : frobenius R p (x - y) = frobenius R p x - frobenius R p y :=
-  (frobenius R p).map_sub x y
-#align frobenius_sub frobenius_sub
-
-end CommRing
-
-end frobenius
-
 namespace CharP
 
 section
@@ -710,6 +576,12 @@ instance Prod.charP [CharP S p] : CharP (R × S) p := by
   convert Nat.lcm.charP R S p p; simp
 #align prod.char_p Prod.charP
 
+instance Prod.charZero_of_left [CharZero R] : CharZero (R × S) where
+  cast_injective _ _ h := CharZero.cast_injective congr(Prod.fst $h)
+
+instance Prod.charZero_of_right [CharZero S] : CharZero (R × S) where
+  cast_injective _ _ h := CharZero.cast_injective congr(Prod.snd $h)
+
 end Prod
 
 instance ULift.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP (ULift.{v} R) p where

feat: The support of f ^ n (#9617)

This involves moving lemmas from Algebra.GroupPower.Ring to Algebra.GroupWithZero.Basic and changing some 0 < n assumptions to n ≠ 0.

From LeanAPAP

9d1a7d26

Diff

@@ -330,7 +330,7 @@ theorem CharP.neg_one_pow_char [Ring R] (p : ℕ) [CharP R p] [Fact p.Prime] :
   rw [eq_neg_iff_add_eq_zero]
   nth_rw 2 [← one_pow p]
   rw [← add_pow_char_of_commute R _ _ (Commute.one_right _), add_left_neg,
-    zero_pow (Fact.out (p := Nat.Prime p)).pos]
+    zero_pow (Fact.out (p := Nat.Prime p)).ne_zero]
 #align char_p.neg_one_pow_char CharP.neg_one_pow_char
 
 theorem CharP.neg_one_pow_char_pow [Ring R] (p n : ℕ) [CharP R p] [Fact p.Prime] :
@@ -338,7 +338,7 @@ theorem CharP.neg_one_pow_char_pow [Ring R] (p n : ℕ) [CharP R p] [Fact p.Prim
   rw [eq_neg_iff_add_eq_zero]
   nth_rw 2 [← one_pow (p ^ n)]
   rw [← add_pow_char_pow_of_commute R _ _ (Commute.one_right _), add_left_neg,
-    zero_pow (pow_pos (Fact.out (p := Nat.Prime p)).pos _)]
+    zero_pow (pow_ne_zero _ (Fact.out (p := Nat.Prime p)).ne_zero)]
 #align char_p.neg_one_pow_char_pow CharP.neg_one_pow_char_pow
 
 theorem RingHom.charP_iff_charP {K L : Type*} [DivisionRing K] [Semiring L] [Nontrivial L]
@@ -358,7 +358,7 @@ def frobenius : R →+* R where
   toFun x := x ^ p
   map_one' := one_pow p
   map_mul' x y := mul_pow x y p
-  map_zero' := zero_pow (Fact.out (p := Nat.Prime p)).pos
+  map_zero' := zero_pow (Fact.out (p := Nat.Prime p)).ne_zero
   map_add' := add_pow_char R
 #align frobenius frobenius

chore: tidy various files (#9903)

8080f08c

Diff

@@ -445,21 +445,21 @@ theorem sum_pow_char {ι : Type*} (s : Finset ι) (f : ι → R) :
 variable (n : ℕ)
 
 theorem list_sum_pow_char_pow (l : List R) : l.sum ^ p ^ n = (l.map (· ^ p ^ n : R → R)).sum := by
-  induction n
-  case zero => simp_rw [pow_zero, pow_one, List.map_id']
-  case succ n ih => simp_rw [pow_succ', pow_mul, ih, list_sum_pow_char, List.map_map]; rfl
+  induction n with
+  | zero => simp_rw [pow_zero, pow_one, List.map_id']
+  | succ n ih => simp_rw [pow_succ', pow_mul, ih, list_sum_pow_char, List.map_map]; rfl
 
 theorem multiset_sum_pow_char_pow (s : Multiset R) :
     s.sum ^ p ^ n = (s.map (· ^ p ^ n : R → R)).sum := by
-  induction n
-  case zero => simp_rw [pow_zero, pow_one, Multiset.map_id']
-  case succ n ih => simp_rw [pow_succ', pow_mul, ih, multiset_sum_pow_char, Multiset.map_map]; rfl
+  induction n with
+  | zero => simp_rw [pow_zero, pow_one, Multiset.map_id']
+  | succ n ih => simp_rw [pow_succ', pow_mul, ih, multiset_sum_pow_char, Multiset.map_map]; rfl
 
 theorem sum_pow_char_pow {ι : Type*} (s : Finset ι) (f : ι → R) :
     (∑ i in s, f i) ^ p ^ n = ∑ i in s, f i ^ p ^ n := by
-  induction n
-  case zero => simp_rw [pow_zero, pow_one]
-  case succ n ih => simp_rw [pow_succ', pow_mul, ih, sum_pow_char]
+  induction n with
+  | zero => simp_rw [pow_zero, pow_one]
+  | succ n ih => simp_rw [pow_succ', pow_mul, ih, sum_pow_char]
 
 end CommSemiring

feat(Algebra/CharP/{Basic|ExpChar}): add sum_pow_{char|expChar}_pow (#9799)

1e74fcff

Diff

@@ -442,6 +442,25 @@ theorem sum_pow_char {ι : Type*} (s : Finset ι) (f : ι → R) :
   (frobenius R p).map_sum _ _
 #align sum_pow_char sum_pow_char
 
+variable (n : ℕ)
+
+theorem list_sum_pow_char_pow (l : List R) : l.sum ^ p ^ n = (l.map (· ^ p ^ n : R → R)).sum := by
+  induction n
+  case zero => simp_rw [pow_zero, pow_one, List.map_id']
+  case succ n ih => simp_rw [pow_succ', pow_mul, ih, list_sum_pow_char, List.map_map]; rfl
+
+theorem multiset_sum_pow_char_pow (s : Multiset R) :
+    s.sum ^ p ^ n = (s.map (· ^ p ^ n : R → R)).sum := by
+  induction n
+  case zero => simp_rw [pow_zero, pow_one, Multiset.map_id']
+  case succ n ih => simp_rw [pow_succ', pow_mul, ih, multiset_sum_pow_char, Multiset.map_map]; rfl
+
+theorem sum_pow_char_pow {ι : Type*} (s : Finset ι) (f : ι → R) :
+    (∑ i in s, f i) ^ p ^ n = ∑ i in s, f i ^ p ^ n := by
+  induction n
+  case zero => simp_rw [pow_zero, pow_one]
+  case succ n ih => simp_rw [pow_succ', pow_mul, ih, sum_pow_char]
+
 end CommSemiring
 
 section CommRing

feat(Algebra/CharP/ExpChar): add more results for ExpChar parallel to CharP (#9573)

fd4eb93d

Diff

@@ -540,6 +540,12 @@ theorem char_is_prime_or_zero (p : ℕ) [hc : CharP R p] : Nat.Prime p ∨ p = 0
   | m + 2, hc => Or.inl (@char_is_prime_of_two_le R _ _ (m + 2) hc (Nat.le_add_left 2 m))
 #align char_p.char_is_prime_or_zero CharP.char_is_prime_or_zero
 
+theorem exists' (R : Type*) [NonAssocRing R] [NoZeroDivisors R] [Nontrivial R] :
+    CharZero R ∨ ∃ p : ℕ, Fact p.Prime ∧ CharP R p := by
+  obtain ⟨p, hchar⟩ := CharP.exists R
+  rcases char_is_prime_or_zero R p with h | rfl
+  exacts [Or.inr ⟨p, Fact.mk h, hchar⟩, Or.inl (charP_to_charZero R)]
+
 theorem char_is_prime_of_pos (p : ℕ) [NeZero p] [CharP R p] : Fact p.Prime :=
   ⟨(CharP.char_is_prime_or_zero R _).resolve_right <| NeZero.ne p⟩
 #align char_p.char_is_prime_of_pos CharP.char_is_prime_of_pos

refactor: decapitalize names in @[mk_iff] (#9378)

@[mk_iff] class MyPred now generates myPred_iff, not MyPred_iff
add Lean.Name.decapitalize
fix indentation and a few typos in the docs/comments.

Partially addresses issue #9129

5192777c

Diff

@@ -103,7 +103,7 @@ For instance, endowing `{0, 1}` with addition given by `max` (i.e. `1` is absorb
 `CharZero {0, 1}` does not hold and yet `CharP {0, 1} 0` does.
 This example is formalized in `Counterexamples/CharPZeroNeCharZero.lean`.
 -/
-@[mk_iff charP_iff]
+@[mk_iff]
 class CharP [AddMonoidWithOne R] (p : ℕ) : Prop where
   cast_eq_zero_iff' : ∀ x : ℕ, (x : R) = 0 ↔ p ∣ x
 #align char_p CharP

feat: Fin CharP and lemmas for Fin rollover (#9033)

Co-authored-by: Yakov Pechersky <pechersky@users.noreply.github.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

7d31d033

Diff

@@ -739,3 +739,11 @@ theorem charZero_iff_forall_prime_ne_zero
     exact CharP.charP_to_charZero R
 
 end CharZero
+
+namespace Fin
+
+instance charP (n : ℕ) : CharP (Fin (n + 1)) (n + 1) where
+    cast_eq_zero_iff' := by
+      simp [Fin.eq_iff_veq, Nat.dvd_iff_mod_eq_zero]
+
+end Fin

feat: add CharP.natCast_eq_natCast_mod and relax typeclass assumptions (#9050)

27b7e3e7

Diff

@@ -145,12 +145,30 @@ theorem CharP.intCast_eq_intCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b
   rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.int_cast_eq_zero_iff R p, Int.modEq_iff_dvd]
 #align char_p.int_cast_eq_int_cast CharP.intCast_eq_intCast
 
-theorem CharP.natCast_eq_natCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℕ} :
-    (a : R) = b ↔ a ≡ b [MOD p] := by
-  rw [← Int.cast_ofNat, ← Int.cast_ofNat b]
-  exact (CharP.intCast_eq_intCast _ _).trans Int.coe_nat_modEq_iff
+theorem CharP.natCast_eq_natCast' [AddMonoidWithOne R] (p : ℕ) [CharP R p] {a b : ℕ}
+    (h : a ≡ b [MOD p]) : (a : R) = b := by
+  wlog hle : a ≤ b
+  · exact (this R p h.symm (le_of_not_le hle)).symm
+  rw [Nat.modEq_iff_dvd' hle] at h
+  rw [← Nat.sub_add_cancel hle, Nat.cast_add, (CharP.cast_eq_zero_iff R p _).mpr h, zero_add]
+
+theorem CharP.natCast_eq_natCast [AddMonoidWithOne R] [IsRightCancelAdd R] (p : ℕ) [CharP R p]
+    {a b : ℕ} : (a : R) = b ↔ a ≡ b [MOD p] := by
+  wlog hle : a ≤ b
+  · rw [eq_comm, this R p (le_of_not_le hle), Nat.ModEq.comm]
+  rw [Nat.modEq_iff_dvd' hle, ← CharP.cast_eq_zero_iff R p (b - a),
+    ← add_right_cancel_iff (G := R) (a := a) (b := b - a), zero_add, ← Nat.cast_add,
+    Nat.sub_add_cancel hle, eq_comm]
 #align char_p.nat_cast_eq_nat_cast CharP.natCast_eq_natCast
 
+theorem CharP.intCast_eq_intCast_mod [AddGroupWithOne R] (p : ℕ) [CharP R p] {a : ℤ} :
+    (a : R) = a % (p : ℤ) :=
+  (CharP.intCast_eq_intCast R p).mpr (Int.mod_modEq a p).symm
+
+theorem CharP.natCast_eq_natCast_mod [AddMonoidWithOne R] (p : ℕ) [CharP R p] {a : ℕ} :
+    (a : R) = a % p :=
+  CharP.natCast_eq_natCast' R p (Nat.mod_modEq a p).symm
+
 theorem CharP.eq [AddMonoidWithOne R] {p q : ℕ} (_c1 : CharP R p) (_c2 : CharP R q) : p = q :=
   Nat.dvd_antisymm ((CharP.cast_eq_zero_iff R p q).1 (CharP.cast_eq_zero _ _))
     ((CharP.cast_eq_zero_iff R q p).1 (CharP.cast_eq_zero _ _))

feat(Algebra/CharP/ExpChar): add some results parallel to CharP (#8860)

change the condition of CharP.neg_one_pow_char and CharP.neg_one_pow_char_pow from CommRing to Ring
add ExpChar.exists, expChar_of_injective_algebraMap
add add_pow_expChar and 9 similar functions parallel to that of CharP
add {charP|charZero|expChar}_of_injective_ringHom

1d5e93af

Diff

@@ -307,18 +307,20 @@ theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1
   linarith
 #align char_p.neg_one_ne_one CharP.neg_one_ne_one
 
-theorem CharP.neg_one_pow_char [CommRing R] (p : ℕ) [CharP R p] [Fact p.Prime] :
+theorem CharP.neg_one_pow_char [Ring R] (p : ℕ) [CharP R p] [Fact p.Prime] :
     (-1 : R) ^ p = -1 := by
   rw [eq_neg_iff_add_eq_zero]
   nth_rw 2 [← one_pow p]
-  rw [← add_pow_char, add_left_neg, zero_pow (Fact.out (p := Nat.Prime p)).pos]
+  rw [← add_pow_char_of_commute R _ _ (Commute.one_right _), add_left_neg,
+    zero_pow (Fact.out (p := Nat.Prime p)).pos]
 #align char_p.neg_one_pow_char CharP.neg_one_pow_char
 
-theorem CharP.neg_one_pow_char_pow [CommRing R] (p n : ℕ) [CharP R p] [Fact p.Prime] :
+theorem CharP.neg_one_pow_char_pow [Ring R] (p n : ℕ) [CharP R p] [Fact p.Prime] :
     (-1 : R) ^ p ^ n = -1 := by
   rw [eq_neg_iff_add_eq_zero]
   nth_rw 2 [← one_pow (p ^ n)]
-  rw [← add_pow_char_pow, add_left_neg, zero_pow (pow_pos (Fact.out (p := Nat.Prime p)).pos _)]
+  rw [← add_pow_char_pow_of_commute R _ _ (Commute.one_right _), add_left_neg,
+    zero_pow (pow_pos (Fact.out (p := Nat.Prime p)).pos _)]
 #align char_p.neg_one_pow_char_pow CharP.neg_one_pow_char_pow
 
 theorem RingHom.charP_iff_charP {K L : Type*} [DivisionRing K] [Semiring L] [Nontrivial L]

chore: split Algebra.CharP.Basic, reduce imports in RingTheory.Multiplicity (#8637)

This was adding unnecessary imports to Data.ZMod.Basic.

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

90d520aa

chore: split Algebra.CharP.Basic, reduce imports in RingTheory.Multiplicity (#8637)

This was adding unnecessary imports to Data.ZMod.Basic.

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

90d520aa

Diff

@@ -5,8 +5,10 @@ Authors: Kenny Lau, Joey van Langen, Casper Putz
 -/
 import Mathlib.Data.Int.ModEq
 import Mathlib.Data.Nat.Multiplicity
+import Mathlib.Data.Nat.Choose.Sum
+import Mathlib.Data.Nat.Cast.Prod
+import Mathlib.Algebra.Group.ULift
 import Mathlib.GroupTheory.OrderOfElement
-import Mathlib.RingTheory.Nilpotent
 
 #align_import algebra.char_p.basic from "leanprover-community/mathlib"@"47a1a73351de8dd6c8d3d32b569c8e434b03ca47"
 
@@ -439,23 +441,6 @@ end CommRing
 
 end frobenius
 
-theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP R p] :
-    Function.Injective (frobenius R p) := fun x h H => by
-  rw [← sub_eq_zero] at H ⊢
-  rw [← frobenius_sub] at H
-  exact IsReduced.eq_zero _ ⟨_, H⟩
-#align frobenius_inj frobenius_inj
-
-/-- If `ringChar R = 2`, where `R` is a finite reduced commutative ring,
-then every `a : R` is a square. -/
-theorem isSquare_of_charTwo' {R : Type*} [Finite R] [CommRing R] [IsReduced R] [CharP R 2]
-    (a : R) : IsSquare a := by
-  cases nonempty_fintype R
-  exact
-    Exists.imp (fun b h => pow_two b ▸ Eq.symm h)
-      (((Fintype.bijective_iff_injective_and_card _).mpr ⟨frobenius_inj R 2, rfl⟩).surjective a)
-#align is_square_of_char_two' isSquare_of_charTwo'
-
 namespace CharP
 
 section
@@ -492,23 +477,6 @@ theorem ringChar_zero_iff_CharZero [NonAssocRing R] : ringChar R = 0 ↔ CharZer
 
 end
 
-section CommRing
-
-variable [CommRing R] [IsReduced R] {R}
-
-@[simp]
-theorem pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [Fact p.Prime] [CharP R p] (x : R) :
-    x ^ (p ^ k * m) = 1 ↔ x ^ m = 1 := by
-  induction' k with k hk
-  · rw [pow_zero, one_mul]
-  · refine' ⟨fun h => _, fun h => _⟩
-    · rw [pow_succ, mul_assoc, pow_mul', ← frobenius_def, ← frobenius_one p] at h
-      exact hk.1 (frobenius_inj R p h)
-    · rw [pow_mul', h, one_pow]
-#align char_p.pow_prime_pow_mul_eq_one_iff CharP.pow_prime_pow_mul_eq_one_iff
-
-end CommRing
-
 section Semiring
 
 variable [NonAssocSemiring R]

chore: bump to v4.3.0-rc2 (#8366)

PR contents

This is the supremum of

#8284
#8056
#8023
#8332
#8226 (already approved)
#7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

switching to using explicit lemmas that have the intended level of application
(config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

40b64f79

Diff

@@ -716,8 +716,8 @@ theorem Int.cast_injOn_of_ringChar_ne_two {R : Type*} [NonAssocRing R] [Nontrivi
   rintro _ (rfl | rfl | rfl) _ (rfl | rfl | rfl) h <;>
   simp only
     [cast_neg, cast_one, cast_zero, neg_eq_zero, one_ne_zero, zero_ne_one, zero_eq_neg] at h ⊢
-  · exact (Ring.neg_one_ne_one_of_char_ne_two hR).symm h
-  · exact (Ring.neg_one_ne_one_of_char_ne_two hR) h
+  · exact ((Ring.neg_one_ne_one_of_char_ne_two hR).symm h).elim
+  · exact ((Ring.neg_one_ne_one_of_char_ne_two hR) h).elim
 #align int.cast_inj_on_of_ring_char_ne_two Int.cast_injOn_of_ringChar_ne_two
 
 end

fix: patch for std4#195 (more succ/pred lemmas for Nat) (#6203)

cdcad962

Diff

@@ -511,8 +511,6 @@ end CommRing
 
 section Semiring
 
-open Nat
-
 variable [NonAssocSemiring R]
 
 theorem char_ne_one [Nontrivial R] (p : ℕ) [hc : CharP R p] : p ≠ 1 := fun hp : p = 1 =>
@@ -529,7 +527,7 @@ theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.
   fun (d : ℕ) (hdvd : ∃ e, p = d * e) =>
   let ⟨e, hmul⟩ := hdvd
   have : (p : R) = 0 := (cast_eq_zero_iff R p p).mpr (dvd_refl p)
-  have : (d : R) * e = 0 := @cast_mul R _ d e ▸ hmul ▸ this
+  have : (d : R) * e = 0 := @Nat.cast_mul R _ d e ▸ hmul ▸ this
   Or.elim (eq_zero_or_eq_zero_of_mul_eq_zero this)
     (fun hd : (d : R) = 0 =>
       have : p ∣ d := (cast_eq_zero_iff R p d).mp hd

chore: only four spaces for subsequent lines (#7286)

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

0c7d6fa5

Diff

@@ -110,7 +110,7 @@ class CharP [AddMonoidWithOne R] (p : ℕ) : Prop where
 -- porting note: the field of the structure had implicit arguments where they were
 -- explicit in Lean 3
 theorem CharP.cast_eq_zero_iff (R : Type u) [AddMonoidWithOne R] (p : ℕ) [CharP R p] (x : ℕ) :
-  (x : R) = 0 ↔ p ∣ x :=
+    (x : R) = 0 ↔ p ∣ x :=
 CharP.cast_eq_zero_iff' (R := R) (p := p) x
 
 @[simp]

chore: fix doc-strings about (c vs C)ounterexamples (#6691)

This PR just touches doc-strings. It fixes capitalization issues involving Counterexamples and adds a missing line-break for better display.

0b511e95

Diff

@@ -99,8 +99,8 @@ variable (R)
 
 For instance, endowing `{0, 1}` with addition given by `max` (i.e. `1` is absorbing), shows that
 `CharZero {0, 1}` does not hold and yet `CharP {0, 1} 0` does.
-This example is formalized in `counterexamples/char_p_zero_ne_char_zero`.
- -/
+This example is formalized in `Counterexamples/CharPZeroNeCharZero.lean`.
+-/
 @[mk_iff charP_iff]
 class CharP [AddMonoidWithOne R] (p : ℕ) : Prop where
   cast_eq_zero_iff' : ∀ x : ℕ, (x : R) = 0 ↔ p ∣ x

feat(Mathlib/Algebra/CharP/Basic): add ringChar_zero_iff_CharZero (#6572)

Zulip discussion

a1bb5932

Diff

@@ -466,6 +466,9 @@ theorem charP_to_charZero (R : Type*) [AddGroupWithOne R] [CharP R 0] : CharZero
   charZero_of_inj_zero fun n h0 => eq_zero_of_zero_dvd ((cast_eq_zero_iff R 0 n).mp h0)
 #align char_p.char_p_to_char_zero CharP.charP_to_charZero
 
+theorem charP_zero_iff_charZero (R : Type*) [AddGroupWithOne R] : CharP R 0 ↔ CharZero R :=
+  ⟨fun _ ↦ charP_to_charZero R, fun _ ↦ ofCharZero R⟩
+
 theorem cast_eq_mod (p : ℕ) [CharP R p] (k : ℕ) : (k : R) = (k % p : ℕ) :=
   calc
     (k : R) = ↑(k % p + p * (k / p)) := by rw [Nat.mod_add_div]
@@ -484,6 +487,9 @@ theorem ringChar_ne_zero_of_finite [Finite R] : ringChar R ≠ 0 :=
   char_ne_zero_of_finite R (ringChar R)
 #align char_p.ring_char_ne_zero_of_finite CharP.ringChar_ne_zero_of_finite
 
+theorem ringChar_zero_iff_CharZero [NonAssocRing R] : ringChar R = 0 ↔ CharZero R := by
+  rw [ringChar.eq_iff, charP_zero_iff_charZero]
+
 end
 
 section CommRing

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

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

277dea95

Diff

@@ -177,12 +177,12 @@ theorem CharP.exists [NonAssocSemiring R] : ∃ p, CharP R p :=
                     rwa [← Nat.mod_add_div x (Nat.find (not_forall.1 H)), Nat.cast_add,
                       Nat.cast_mul,
                       of_not_not (not_not_of_not_imp <| Nat.find_spec (not_forall.1 H)),
-                      MulZeroClass.zero_mul, add_zero] at H1,
+                      zero_mul, add_zero] at H1,
                     H2⟩)),
           fun H1 => by
           rw [← Nat.mul_div_cancel' H1, Nat.cast_mul,
             of_not_not (not_not_of_not_imp <| Nat.find_spec (not_forall.1 H)),
-            MulZeroClass.zero_mul]⟩⟩⟩
+            zero_mul]⟩⟩⟩
 #align char_p.exists CharP.exists
 
 theorem CharP.exists_unique [NonAssocSemiring R] : ∃! p, CharP R p :=
@@ -582,7 +582,7 @@ instance (priority := 100) CharOne.subsingleton [CharP R 1] : Subsingleton R :=
       r = 1 * r := by rw [one_mul]
       _ = (1 : ℕ) * r := by rw [Nat.cast_one]
       _ = 0 * r := by rw [CharP.cast_eq_zero]
-      _ = 0 := by rw [MulZeroClass.zero_mul]
+      _ = 0 := by rw [zero_mul]
 
 theorem false_of_nontrivial_of_char_one [Nontrivial R] [CharP R 1] : False :=
   false_of_nontrivial_of_subsingleton R
@@ -654,14 +654,14 @@ theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0
       intro k
       constructor
       · intro h
-        rw [← Nat.mod_add_div k n, Nat.cast_add, Nat.cast_mul, H, MulZeroClass.zero_mul,
+        rw [← Nat.mod_add_div k n, Nat.cast_add, Nat.cast_mul, H, zero_mul,
           add_zero] at h
         rw [Nat.dvd_iff_mod_eq_zero]
         apply hR _ (Nat.mod_lt _ _) h
         rw [← hn, gt_iff_lt, Fintype.card_pos_iff]
         exact ⟨0⟩
       · rintro ⟨k, rfl⟩
-        rw [Nat.cast_mul, H, MulZeroClass.zero_mul] }
+        rw [Nat.cast_mul, H, zero_mul] }
 #align char_p_of_ne_zero charP_of_ne_zero
 
 theorem charP_of_prime_pow_injective (R) [Ring R] [Fintype R] (p : ℕ) [hp : Fact p.Prime] (n : ℕ)

feat: charZero_iff_forall_prime_ne_zero (#6518)

4e823e1a

Diff

@@ -732,3 +732,18 @@ theorem not_char_dvd (p : ℕ) [CharP R p] (k : ℕ) [h : NeZero (k : R)] : ¬p
 #align ne_zero.not_char_dvd NeZero.not_char_dvd
 
 end NeZero
+
+namespace CharZero
+
+theorem charZero_iff_forall_prime_ne_zero
+    [NonAssocRing R] [NoZeroDivisors R] [Nontrivial R] :
+    CharZero R ↔ ∀ p : ℕ, p.Prime → (p : R) ≠ 0 := by
+  refine ⟨fun h p hp => by simp [hp.ne_zero], fun h => ?_⟩
+  let p := ringChar R
+  cases CharP.char_is_prime_or_zero R p with
+  | inl hp => simpa using h p hp
+  | inr h =>
+    haveI : CharP R 0 := h ▸ inferInstance
+    exact CharP.charP_to_charZero R
+
+end CharZero

chore(Mathlib/Algebra/CharP/Basic): golf cast_injOn_of_ringChar_ne_two (#6573)

Just the shortening of a proof, letting simp do the work.

ea2fa166

Diff

@@ -709,30 +709,11 @@ section
 that is nontrivial and of characteristic not `2`, then they are equal. -/
 theorem Int.cast_injOn_of_ringChar_ne_two {R : Type*} [NonAssocRing R] [Nontrivial R]
     (hR : ringChar R ≠ 2) : ({0, 1, -1} : Set ℤ).InjOn ((↑) : ℤ → R) := by
-  intro a ha b hb h
-  apply eq_of_sub_eq_zero
-  by_contra hf
-  replace ha : a = 0 ∨ a = 1 ∨ a = -1 := ha
-  replace hb : b = 0 ∨ b = 1 ∨ b = -1 := hb
-  have hh : a - b = 1 ∨ b - a = 1 ∨ a - b = 2 ∨ b - a = 2 := by
-    rcases ha with (ha | ha | ha) <;> rcases hb with (hb | hb | hb)
-    pick_goal 5
-    pick_goal 9
-    -- move goals with `a = b` to the front
-    iterate 3 rw [ha, hb, sub_self] at hf; tauto
-    -- 6 goals remain
-    all_goals rw [ha, hb]; norm_num
-  have h' : ((a - b : ℤ) : R) = 0 := by exact_mod_cast sub_eq_zero_of_eq h
-  have h'' : ((b - a : ℤ) : R) = 0 := by exact_mod_cast sub_eq_zero_of_eq h.symm
-  rcases hh with (hh | hh | hh | hh)
-  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h'
-    exact one_ne_zero h'
-  · rw [hh, (by norm_cast : ((1 : ℤ) : R) = 1)] at h''
-    exact one_ne_zero h''
-  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h'
-    exact Ring.two_ne_zero hR h'
-  · rw [hh, (by norm_cast : ((2 : ℤ) : R) = 2)] at h''
-    exact Ring.two_ne_zero hR h''
+  rintro _ (rfl | rfl | rfl) _ (rfl | rfl | rfl) h <;>
+  simp only
+    [cast_neg, cast_one, cast_zero, neg_eq_zero, one_ne_zero, zero_ne_one, zero_eq_neg] at h ⊢
+  · exact (Ring.neg_one_ne_one_of_char_ne_two hR).symm h
+  · exact (Ring.neg_one_ne_one_of_char_ne_two hR) h
 #align int.cast_inj_on_of_ring_char_ne_two Int.cast_injOn_of_ringChar_ne_two
 
 end

feat: charP_iff_prime_eq_zero (#6516)

4eabdeb3

Diff

@@ -569,7 +569,7 @@ theorem char_is_prime (p : ℕ) [CharP R p] : p.Prime :=
 
 end Ring
 
-section CharOne
+section NonAssocSemiring
 
 variable {R} [NonAssocSemiring R]
 
@@ -605,7 +605,12 @@ theorem ringChar_of_prime_eq_zero [Nontrivial R] {p : ℕ} (hprime : Nat.Prime p
   Or.resolve_left ((Nat.dvd_prime hprime).1 (ringChar.dvd hp0)) ringChar_ne_one
 #align char_p.ring_char_of_prime_eq_zero CharP.ringChar_of_prime_eq_zero
 
-end CharOne
+theorem charP_iff_prime_eq_zero [Nontrivial R] {p : ℕ} (hp : p.Prime) :
+    CharP R p ↔ (p : R) = 0 :=
+  ⟨fun _ => cast_eq_zero R p,
+   fun hp0 => (ringChar_of_prime_eq_zero hp hp0) ▸ inferInstance⟩
+
+end NonAssocSemiring
 
 end CharP

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -21,7 +21,7 @@ open Finset
 
 open BigOperators
 
-variable {R : Type _}
+variable {R : Type*}
 
 namespace Commute
 
@@ -319,7 +319,7 @@ theorem CharP.neg_one_pow_char_pow [CommRing R] (p n : ℕ) [CharP R p] [Fact p.
   rw [← add_pow_char_pow, add_left_neg, zero_pow (pow_pos (Fact.out (p := Nat.Prime p)).pos _)]
 #align char_p.neg_one_pow_char_pow CharP.neg_one_pow_char_pow
 
-theorem RingHom.charP_iff_charP {K L : Type _} [DivisionRing K] [Semiring L] [Nontrivial L]
+theorem RingHom.charP_iff_charP {K L : Type*} [DivisionRing K] [Semiring L] [Nontrivial L]
     (f : K →+* L) (p : ℕ) : CharP K p ↔ CharP L p := by
   simp only [charP_iff, ← f.injective.eq_iff, map_natCast f, f.map_zero]
 #align ring_hom.char_p_iff_char_p RingHom.charP_iff_charP
@@ -415,7 +415,7 @@ theorem multiset_sum_pow_char (s : Multiset R) : s.sum ^ p = (s.map (· ^ p : R
   (frobenius R p).map_multiset_sum _
 #align multiset_sum_pow_char multiset_sum_pow_char
 
-theorem sum_pow_char {ι : Type _} (s : Finset ι) (f : ι → R) :
+theorem sum_pow_char {ι : Type*} (s : Finset ι) (f : ι → R) :
     (∑ i in s, f i) ^ p = ∑ i in s, f i ^ p :=
   (frobenius R p).map_sum _ _
 #align sum_pow_char sum_pow_char
@@ -448,7 +448,7 @@ theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP
 
 /-- If `ringChar R = 2`, where `R` is a finite reduced commutative ring,
 then every `a : R` is a square. -/
-theorem isSquare_of_charTwo' {R : Type _} [Finite R] [CommRing R] [IsReduced R] [CharP R 2]
+theorem isSquare_of_charTwo' {R : Type*} [Finite R] [CommRing R] [IsReduced R] [CharP R 2]
     (a : R) : IsSquare a := by
   cases nonempty_fintype R
   exact
@@ -462,7 +462,7 @@ section
 
 variable [NonAssocRing R]
 
-theorem charP_to_charZero (R : Type _) [AddGroupWithOne R] [CharP R 0] : CharZero R :=
+theorem charP_to_charZero (R : Type*) [AddGroupWithOne R] [CharP R 0] : CharZero R :=
   charZero_of_inj_zero fun n h0 => eq_zero_of_zero_dvd ((cast_eq_zero_iff R 0 n).mp h0)
 #align char_p.char_p_to_char_zero CharP.charP_to_charZero
 
@@ -612,7 +612,7 @@ end CharP
 section
 
 /-- We have `2 ≠ 0` in a nontrivial ring whose characteristic is not `2`. -/
-protected theorem Ring.two_ne_zero {R : Type _} [NonAssocSemiring R] [Nontrivial R]
+protected theorem Ring.two_ne_zero {R : Type*} [NonAssocSemiring R] [Nontrivial R]
     (hR : ringChar R ≠ 2) : (2 : R) ≠ 0 := by
   rw [Ne.def, (by norm_cast : (2 : R) = (2 : ℕ)), ringChar.spec, Nat.dvd_prime Nat.prime_two]
   exact mt (or_iff_left hR).mp CharP.ringChar_ne_one
@@ -621,13 +621,13 @@ protected theorem Ring.two_ne_zero {R : Type _} [NonAssocSemiring R] [Nontrivial
 -- We have `CharP.neg_one_ne_one`, which assumes `[Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)]`.
 -- This is a version using `ringChar` instead.
 /-- Characteristic `≠ 2` and nontrivial implies that `-1 ≠ 1`. -/
-theorem Ring.neg_one_ne_one_of_char_ne_two {R : Type _} [NonAssocRing R] [Nontrivial R]
+theorem Ring.neg_one_ne_one_of_char_ne_two {R : Type*} [NonAssocRing R] [Nontrivial R]
     (hR : ringChar R ≠ 2) : (-1 : R) ≠ 1 := fun h =>
   Ring.two_ne_zero hR (one_add_one_eq_two (α := R) ▸ neg_eq_iff_add_eq_zero.mp h)
 #align ring.neg_one_ne_one_of_char_ne_two Ring.neg_one_ne_one_of_char_ne_two
 
 /-- Characteristic `≠ 2` in a domain implies that `-a = a` iff `a = 0`. -/
-theorem Ring.eq_self_iff_eq_zero_of_char_ne_two {R : Type _} [NonAssocRing R] [Nontrivial R]
+theorem Ring.eq_self_iff_eq_zero_of_char_ne_two {R : Type*} [NonAssocRing R] [Nontrivial R]
     [NoZeroDivisors R] (hR : ringChar R ≠ 2) {a : R} : -a = a ↔ a = 0 :=
   ⟨fun h =>
     (mul_eq_zero.mp <| (two_mul a).trans <| neg_eq_iff_add_eq_zero.mp h).resolve_left
@@ -702,7 +702,7 @@ section
 
 /-- If two integers from `{0, 1, -1}` result in equal elements in a ring `R`
 that is nontrivial and of characteristic not `2`, then they are equal. -/
-theorem Int.cast_injOn_of_ringChar_ne_two {R : Type _} [NonAssocRing R] [Nontrivial R]
+theorem Int.cast_injOn_of_ringChar_ne_two {R : Type*} [NonAssocRing R] [Nontrivial R]
     (hR : ringChar R ≠ 2) : ({0, 1, -1} : Set ℤ).InjOn ((↑) : ℤ → R) := by
   intro a ha b hb h
   apply eq_of_sub_eq_zero

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Joey van Langen, Casper Putz
-
-! This file was ported from Lean 3 source module algebra.char_p.basic
-! leanprover-community/mathlib commit 47a1a73351de8dd6c8d3d32b569c8e434b03ca47
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Int.ModEq
 import Mathlib.Data.Nat.Multiplicity
 import Mathlib.GroupTheory.OrderOfElement
 import Mathlib.RingTheory.Nilpotent
 
+#align_import algebra.char_p.basic from "leanprover-community/mathlib"@"47a1a73351de8dd6c8d3d32b569c8e434b03ca47"
+
 /-!
 # Characteristic of semirings
 -/

chore: bump to nightly-2023-07-01 (#5409)

depends on: https://github.com/leanprover/std4/pull/163
depends on: #5584
depends on: #5715
depends on: #5729
depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

906f7221

Diff

@@ -587,7 +587,6 @@ instance (priority := 100) CharOne.subsingleton [CharP R 1] : Subsingleton R :=
       _ = 0 * r := by rw [CharP.cast_eq_zero]
       _ = 0 := by rw [MulZeroClass.zero_mul]
 
-
 theorem false_of_nontrivial_of_char_one [Nontrivial R] [CharP R 1] : False :=
   false_of_nontrivial_of_subsingleton R
 #align char_p.false_of_nontrivial_of_char_one CharP.false_of_nontrivial_of_char_one

chore: tidy various files (#5628)

3282e2f7

Diff

@@ -664,14 +664,13 @@ theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0
 #align char_p_of_ne_zero charP_of_ne_zero
 
 theorem charP_of_prime_pow_injective (R) [Ring R] [Fintype R] (p : ℕ) [hp : Fact p.Prime] (n : ℕ)
-    (hn : Fintype.card R = p ^ n) (hR : ∀ i ≤ n, (p ^ i : R) = 0 → i = n) : CharP R (p ^ n) := by
+    (hn : Fintype.card R = p ^ n) (hR : ∀ i ≤ n, (p : R) ^ i = 0 → i = n) : CharP R (p ^ n) := by
   obtain ⟨c, hc⟩ := CharP.exists R
-  skip
   have hcpn : c ∣ p ^ n := by rw [← CharP.cast_eq_zero_iff R c, ← hn, CharP.cast_card_eq_zero]
   obtain ⟨i, hi, hc⟩ : ∃ i ≤ n, c = p ^ i := by rwa [Nat.dvd_prime_pow hp.1] at hcpn
   obtain rfl : i = n := by
     apply hR i hi
-    rw [← hc, CharP.cast_eq_zero]
+    rw [← Nat.cast_pow, ← hc, CharP.cast_eq_zero]
   rwa [← hc]
 #align char_p_of_prime_pow_injective charP_of_prime_pow_injective
 
@@ -695,12 +694,12 @@ instance Prod.charP [CharP S p] : CharP (R × S) p := by
 
 end Prod
 
-instance ULift.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP (ULift.{v} R) p
-    where cast_eq_zero_iff' n := Iff.trans (ULift.ext_iff _ _) <| CharP.cast_eq_zero_iff R p n
+instance ULift.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP (ULift.{v} R) p where
+  cast_eq_zero_iff' n := Iff.trans (ULift.ext_iff _ _) <| CharP.cast_eq_zero_iff R p n
 #align ulift.char_p ULift.charP
 
-instance MulOpposite.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP Rᵐᵒᵖ p
-    where cast_eq_zero_iff' n := MulOpposite.unop_inj.symm.trans <| CharP.cast_eq_zero_iff R p n
+instance MulOpposite.charP [AddMonoidWithOne R] (p : ℕ) [CharP R p] : CharP Rᵐᵒᵖ p where
+  cast_eq_zero_iff' n := MulOpposite.unop_inj.symm.trans <| CharP.cast_eq_zero_iff R p n
 #align mul_opposite.char_p MulOpposite.charP
 
 section

fix precedence of Nat.iterate (#5589)

bd2fff86

Diff

@@ -349,7 +349,7 @@ theorem frobenius_def : frobenius R p x = x ^ p :=
   rfl
 #align frobenius_def frobenius_def
 
-theorem iterate_frobenius (n : ℕ) : (frobenius R p^[n]) x = x ^ p ^ n := by
+theorem iterate_frobenius (n : ℕ) : (frobenius R p)^[n] x = x ^ p ^ n := by
   induction n with
   | zero => simp
   | succ n n_ih =>
@@ -373,22 +373,22 @@ theorem RingHom.map_frobenius : g (frobenius R p x) = frobenius S p (g x) :=
 #align ring_hom.map_frobenius RingHom.map_frobenius
 
 theorem MonoidHom.map_iterate_frobenius (n : ℕ) :
-    f ((frobenius R p^[n]) x) = (frobenius S p^[n]) (f x) :=
+    f ((frobenius R p)^[n] x) = (frobenius S p)^[n] (f x) :=
   Function.Semiconj.iterate_right (f.map_frobenius p) n x
 #align monoid_hom.map_iterate_frobenius MonoidHom.map_iterate_frobenius
 
 theorem RingHom.map_iterate_frobenius (n : ℕ) :
-    g ((frobenius R p^[n]) x) = (frobenius S p^[n]) (g x) :=
+    g ((frobenius R p)^[n] x) = (frobenius S p)^[n] (g x) :=
   g.toMonoidHom.map_iterate_frobenius p x n
 #align ring_hom.map_iterate_frobenius RingHom.map_iterate_frobenius
 
 theorem MonoidHom.iterate_map_frobenius (f : R →* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
-    (f^[n]) (frobenius R p x) = frobenius R p ((f^[n]) x) :=
+    f^[n] (frobenius R p x) = frobenius R p (f^[n] x) :=
   f.iterate_map_pow _ _ _
 #align monoid_hom.iterate_map_frobenius MonoidHom.iterate_map_frobenius
 
 theorem RingHom.iterate_map_frobenius (f : R →+* R) (p : ℕ) [Fact p.Prime] [CharP R p] (n : ℕ) :
-    (f^[n]) (frobenius R p x) = frobenius R p ((f^[n]) x) :=
+    f^[n] (frobenius R p x) = frobenius R p (f^[n] x) :=
   f.iterate_map_pow _ _ _
 #align ring_hom.iterate_map_frobenius RingHom.iterate_map_frobenius

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

Changes are of the form

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

2a870323

Diff

@@ -444,7 +444,7 @@ end frobenius
 
 theorem frobenius_inj [CommRing R] [IsReduced R] (p : ℕ) [Fact p.Prime] [CharP R p] :
     Function.Injective (frobenius R p) := fun x h H => by
-  rw [← sub_eq_zero] at H⊢
+  rw [← sub_eq_zero] at H ⊢
   rw [← frobenius_sub] at H
   exact IsReduced.eq_zero _ ⟨_, H⟩
 #align frobenius_inj frobenius_inj

chore: fix #align lines (#3640)

This PR fixes two things:

Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

2b42dc7c

Diff

@@ -473,7 +473,6 @@ theorem cast_eq_mod (p : ℕ) [CharP R p] (k : ℕ) : (k : R) = (k % p : ℕ) :=
   calc
     (k : R) = ↑(k % p + p * (k / p)) := by rw [Nat.mod_add_div]
     _ = ↑(k % p) := by simp [cast_eq_zero]
-
 #align char_p.cast_eq_mod CharP.cast_eq_mod
 
 /-- The characteristic of a finite ring cannot be zero. -/

feat: Dot notation aliases (#3303)

Match https://github.com/leanprover-community/mathlib/pull/18698 and a bit of https://github.com/leanprover-community/mathlib/pull/18785.

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

4fa401fa

Diff

@@ -531,11 +531,11 @@ theorem char_is_prime_of_two_le (p : ℕ) [hc : CharP R p] (hp : 2 ≤ p) : Nat.
   Or.elim (eq_zero_or_eq_zero_of_mul_eq_zero this)
     (fun hd : (d : R) = 0 =>
       have : p ∣ d := (cast_eq_zero_iff R p d).mp hd
-      show d = 1 ∨ d = p from Or.inr (dvd_antisymm ⟨e, hmul⟩ this))
+      show d = 1 ∨ d = p from Or.inr (this.antisymm' ⟨e, hmul⟩))
     fun he : (e : R) = 0 =>
     have : p ∣ e := (cast_eq_zero_iff R p e).mp he
     have : e ∣ p := dvd_of_mul_left_eq d (Eq.symm hmul)
-    have : e = p := dvd_antisymm ‹e ∣ p› ‹p ∣ e›
+    have : e = p := ‹e ∣ p›.antisymm ‹p ∣ e›
     have h₀ : 0 < p := two_pos.trans_le hp
     have : d * p = 1 * p := by rw [‹e = p›] at hmul; rw [one_mul]; exact Eq.symm hmul
     show d = 1 ∨ d = p from Or.inl (mul_right_cancel₀ h₀.ne' this)

https://github.com/leanprover-community/mathlib/pull/18119, https://github.com/leanprover-community/mathlib/pull/18666.

feat: a/c ≡ b/c mod m/c → a ≡ b mod m (#3259)

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

9d339228

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Joey van Langen, Casper Putz
 
 ! This file was ported from Lean 3 source module algebra.char_p.basic
-! leanprover-community/mathlib commit ceb887ddf3344dab425292e497fa2af91498437c
+! leanprover-community/mathlib commit 47a1a73351de8dd6c8d3d32b569c8e434b03ca47
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -141,10 +141,16 @@ theorem CharP.int_cast_eq_zero_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a
     rw [Int.cast_ofNat, CharP.cast_eq_zero_iff R p, Int.coe_nat_dvd]
 #align char_p.int_cast_eq_zero_iff CharP.int_cast_eq_zero_iff
 
-theorem CharP.int_cast_eq_int_cast_iff [AddGroupWithOne R] (p : ℕ) [CharP R p] (a b : ℤ) :
-    (a : R) = (b : R) ↔ a ≡ b [ZMOD p] := by
+theorem CharP.intCast_eq_intCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℤ} :
+    (a : R) = b ↔ a ≡ b [ZMOD p] := by
   rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.int_cast_eq_zero_iff R p, Int.modEq_iff_dvd]
-#align char_p.int_coe_eq_int_coe_iff CharP.int_cast_eq_int_cast_iff
+#align char_p.int_cast_eq_int_cast CharP.intCast_eq_intCast
+
+theorem CharP.natCast_eq_natCast [AddGroupWithOne R] (p : ℕ) [CharP R p] {a b : ℕ} :
+    (a : R) = b ↔ a ≡ b [MOD p] := by
+  rw [← Int.cast_ofNat, ← Int.cast_ofNat b]
+  exact (CharP.intCast_eq_intCast _ _).trans Int.coe_nat_modEq_iff
+#align char_p.nat_cast_eq_nat_cast CharP.natCast_eq_natCast
 
 theorem CharP.eq [AddMonoidWithOne R] {p q : ℕ} (_c1 : CharP R p) (_c2 : CharP R q) : p = q :=
   Nat.dvd_antisymm ((CharP.cast_eq_zero_iff R p q).1 (CharP.cast_eq_zero _ _))
@@ -286,10 +292,6 @@ theorem sub_pow_char_pow [CommRing R] {p : ℕ} [Fact p.Prime] [CharP R p] {n :
   sub_pow_char_pow_of_commute _ _ _ (Commute.all _ _)
 #align sub_pow_char_pow sub_pow_char_pow
 
-theorem eq_iff_modEq_int [Ring R] (p : ℕ) [CharP R p] (a b : ℤ) : (a : R) = b ↔ a ≡ b [ZMOD p] := by
-  rw [eq_comm, ← sub_eq_zero, ← Int.cast_sub, CharP.int_cast_eq_zero_iff R p, Int.modEq_iff_dvd]
-#align eq_iff_modeq_int eq_iff_modEq_int
-
 theorem CharP.neg_one_ne_one [Ring R] (p : ℕ) [CharP R p] [Fact (2 < p)] : (-1 : R) ≠ (1 : R) := by
   suffices (2 : R) ≠ 0 by
     intro h

ceb887dd

chore: re-port Algebra.CharP.Basic (#3191)

This forward-ports changes from leanprover-community/mathlib#11364

One unrelated downstream file times out, presumably due to the import graph subtly changing.

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

b38baa7d

Diff

@@ -4,14 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Joey van Langen, Casper Putz
 
 ! This file was ported from Lean 3 source module algebra.char_p.basic
-! leanprover-community/mathlib commit 05a78c9451101108e638a0f213fb1bed82483545
+! leanprover-community/mathlib commit ceb887ddf3344dab425292e497fa2af91498437c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathlib.Algebra.Hom.Iterate
 import Mathlib.Data.Int.ModEq
-import Mathlib.Data.Nat.Choose.Dvd
-import Mathlib.Data.Nat.Choose.Sum
+import Mathlib.Data.Nat.Multiplicity
 import Mathlib.GroupTheory.OrderOfElement
 import Mathlib.RingTheory.Nilpotent
 
@@ -22,7 +20,79 @@ import Mathlib.RingTheory.Nilpotent
 
 universe u v
 
-variable (R : Type u)
+open Finset
+
+open BigOperators
+
+variable {R : Type _}
+
+namespace Commute
+
+variable [Semiring R] {p : ℕ} {x y : R}
+
+protected theorem add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ) :
+    (x + y) ^ p ^ n =
+      x ^ p ^ n + y ^ p ^ n +
+        p * ∑ k in Ioo 0 (p ^ n), x ^ k * y ^ (p ^ n - k) * ↑((p ^ n).choose k / p) := by
+  trans x ^ p ^ n + y ^ p ^ n + ∑ k in Ioo 0 (p ^ n), x ^ k * y ^ (p ^ n - k) * (p ^ n).choose k
+  · simp_rw [h.add_pow, ← Nat.Ico_zero_eq_range, Nat.Ico_succ_right, Icc_eq_cons_Ico (zero_le _),
+      Finset.sum_cons, Ico_eq_cons_Ioo (pow_pos hp.pos _), Finset.sum_cons, tsub_self, tsub_zero,
+      pow_zero, Nat.choose_zero_right, Nat.choose_self, Nat.cast_one, mul_one, one_mul, ← add_assoc]
+  · congr 1
+    simp_rw [Finset.mul_sum, Nat.cast_comm, mul_assoc _ _ (p : R), ← Nat.cast_mul]
+    refine' Finset.sum_congr rfl fun i hi => _
+    rw [mem_Ioo] at hi
+    rw [Nat.div_mul_cancel (hp.dvd_choose_pow hi.1.ne' hi.2.ne)]
+#align commute.add_pow_prime_pow_eq Commute.add_pow_prime_pow_eq
+
+protected theorem add_pow_prime_eq (hp : p.Prime) (h : Commute x y) :
+    (x + y) ^ p =
+      x ^ p + y ^ p + p * ∑ k in Finset.Ioo 0 p, x ^ k * y ^ (p - k) * ↑(p.choose k / p) :=
+  by simpa using h.add_pow_prime_pow_eq hp 1
+#align commute.add_pow_prime_eq Commute.add_pow_prime_eq
+
+protected theorem exists_add_pow_prime_pow_eq (hp : p.Prime) (h : Commute x y) (n : ℕ) :
+    ∃ r, (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n + p * r :=
+  ⟨_, h.add_pow_prime_pow_eq hp n⟩
+#align commute.exists_add_pow_prime_pow_eq Commute.exists_add_pow_prime_pow_eq
+
+protected theorem exists_add_pow_prime_eq (hp : p.Prime) (h : Commute x y) :
+    ∃ r, (x + y) ^ p = x ^ p + y ^ p + p * r :=
+  ⟨_, h.add_pow_prime_eq hp⟩
+#align commute.exists_add_pow_prime_eq Commute.exists_add_pow_prime_eq
+
+end Commute
+
+section CommSemiring
+
+variable [CommSemiring R] {p : ℕ} {x y : R}
+
+theorem add_pow_prime_pow_eq (hp : p.Prime) (x y : R) (n : ℕ) :
+    (x + y) ^ p ^ n =
+      x ^ p ^ n + y ^ p ^ n +
+        p * ∑ k in Finset.Ioo 0 (p ^ n), x ^ k * y ^ (p ^ n - k) * ↑((p ^ n).choose k / p) :=
+  (Commute.all x y).add_pow_prime_pow_eq hp n
+#align add_pow_prime_pow_eq add_pow_prime_pow_eq
+
+theorem add_pow_prime_eq (hp : p.Prime) (x y : R) :
+    (x + y) ^ p =
+      x ^ p + y ^ p + p * ∑ k in Finset.Ioo 0 p, x ^ k * y ^ (p - k) * ↑(p.choose k / p) :=
+  (Commute.all x y).add_pow_prime_eq hp
+#align add_pow_prime_eq add_pow_prime_eq
+
+theorem exists_add_pow_prime_pow_eq (hp : p.Prime) (x y : R) (n : ℕ) :
+    ∃ r, (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n + p * r :=
+  (Commute.all x y).exists_add_pow_prime_pow_eq hp n
+#align exists_add_pow_prime_pow_eq exists_add_pow_prime_pow_eq
+
+theorem exists_add_pow_prime_eq (hp : p.Prime) (x y : R) :
+    ∃ r, (x + y) ^ p = x ^ p + y ^ p + p * r :=
+  (Commute.all x y).exists_add_pow_prime_eq hp
+#align exists_add_pow_prime_eq exists_add_pow_prime_eq
+
+end CommSemiring
+
+variable (R)
 
 /-- The generator of the kernel of the unique homomorphism ℕ → R for a semiring R.
 
@@ -46,6 +116,7 @@ theorem CharP.cast_eq_zero_iff (R : Type u) [AddMonoidWithOne R] (p : ℕ) [Char
   (x : R) = 0 ↔ p ∣ x :=
 CharP.cast_eq_zero_iff' (R := R) (p := p) x
 
+@[simp]
 theorem CharP.cast_eq_zero [AddMonoidWithOne R] (p : ℕ) [CharP R p] : (p : R) = 0 :=
   (CharP.cast_eq_zero_iff R p p).2 (dvd_refl p)
 #align char_p.cast_eq_zero CharP.cast_eq_zero
@@ -162,39 +233,22 @@ theorem eq_zero [CharZero R] : ringChar R = 0 :=
   eq R 0
 #align ring_char.eq_zero ringChar.eq_zero
 
-@[simp]
+-- @[simp] -- Porting note: simp can prove this
 theorem Nat.cast_ringChar : (ringChar R : R) = 0 := by rw [ringChar.spec]
 #align ring_char.nat.cast_ring_char ringChar.Nat.cast_ringChar
 
 end ringChar
 
-theorem add_pow_char_of_commute [Semiring R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R)
+theorem add_pow_char_of_commute [Semiring R] {p : ℕ} [hp : Fact p.Prime] [CharP R p] (x y : R)
     (h : Commute x y) : (x + y) ^ p = x ^ p + y ^ p := by
-  rw [Commute.add_pow h, Finset.sum_range_succ_comm, tsub_self, pow_zero, Nat.choose_self]
-  rw [Nat.cast_one, mul_one, mul_one]; congr 1
-  convert Finset.sum_eq_single (f := fun (x_1 : ℕ) => x ^ x_1 * y ^ (p - x_1) * (Nat.choose p x_1))
-    (s := Finset.range p) 0
-    (by
-      intro b h1 h2
-      suffices (p.choose b : R) = 0 by
-        simp [this]
-      rw [CharP.cast_eq_zero_iff R p]
-      exact Nat.Prime.dvd_choose_self Fact.out h2 (Finset.mem_range.1 h1))
-    (by
-      intro h1
-      contrapose! h1
-      rw [Finset.mem_range]
-      exact Nat.Prime.pos Fact.out)
-  simp only [mul_one, one_mul, Nat.choose_zero_right, tsub_zero, Nat.cast_one, pow_zero]
+  let ⟨r, hr⟩ := h.exists_add_pow_prime_eq hp.out
+  simp [hr]
 #align add_pow_char_of_commute add_pow_char_of_commute
 
-theorem add_pow_char_pow_of_commute [Semiring R] {p : ℕ} [Fact p.Prime] [CharP R p] {n : ℕ}
+theorem add_pow_char_pow_of_commute [Semiring R] {p n : ℕ} [hp : Fact p.Prime] [CharP R p]
     (x y : R) (h : Commute x y) : (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n := by
-  induction n with
-  | zero => simp
-  | succ n n_ih =>
-      rw [pow_succ', pow_mul, pow_mul, pow_mul, n_ih]
-      apply add_pow_char_of_commute; apply Commute.pow_pow h
+  let ⟨r, hr⟩ := h.exists_add_pow_prime_pow_eq hp.out n
+  simp [hr]
 #align add_pow_char_pow_of_commute add_pow_char_pow_of_commute
 
 theorem sub_pow_char_of_commute [Ring R] {p : ℕ} [Fact p.Prime] [CharP R p] (x y : R)
@@ -509,7 +563,7 @@ end Semiring
 section Ring
 
 variable [Ring R] [NoZeroDivisors R] [Nontrivial R] [Finite R]
--- porting note: redundant binder annotation update
+-- porting note: removed redundant binder annotation update `(R)`
 
 theorem char_is_prime (p : ℕ) [CharP R p] : p.Prime :=
   Or.resolve_right (char_is_prime_or_zero R p) (char_ne_zero_of_finite R p)
@@ -589,12 +643,11 @@ end
 section
 
 variable [NonAssocRing R] [Fintype R] (n : ℕ)
--- porting note: redundant binder annotation update
+-- porting note: removed redundant binder annotation update `(R)`
 
 theorem charP_of_ne_zero (hn : Fintype.card R = n) (hR : ∀ i < n, (i : R) = 0 → i = 0) :
     CharP R n :=
-  { cast_eq_zero_iff' :=
-      by
+  { cast_eq_zero_iff' := by
       have H : (n : R) = 0 := by rw [← hn, CharP.cast_card_eq_zero]
       intro k
       constructor
@@ -660,8 +713,7 @@ theorem Int.cast_injOn_of_ringChar_ne_two {R : Type _} [NonAssocRing R] [Nontriv
   by_contra hf
   replace ha : a = 0 ∨ a = 1 ∨ a = -1 := ha
   replace hb : b = 0 ∨ b = 1 ∨ b = -1 := hb
-  have hh : a - b = 1 ∨ b - a = 1 ∨ a - b = 2 ∨ b - a = 2 :=
-    by
+  have hh : a - b = 1 ∨ b - a = 1 ∨ a - b = 2 ∨ b - a = 2 := by
     rcases ha with (ha | ha | ha) <;> rcases hb with (hb | hb | hb)
     pick_goal 5
     pick_goal 9
@@ -687,7 +739,7 @@ end
 namespace NeZero
 
 variable [AddMonoidWithOne R] {r : R} {n p : ℕ} {a : ℕ+}
--- porting note: redundant binder annotation update
+-- porting note: removed redundant binder annotation update `(R)`
 
 theorem of_not_dvd [CharP R p] (h : ¬p ∣ n) : NeZero (n : R) :=
   ⟨(CharP.cast_eq_zero_iff R p n).not.mpr h⟩