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

@@ -306,7 +306,7 @@ theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
   calc
     x ^ 2 % (4 : ℕ) = 1 % (4 : ℕ) := _
     _ = 1 := by norm_num
-  rw [← ZMod.int_cast_eq_int_cast_iff'] at hx ⊢
+  rw [← ZMod.intCast_eq_intCast_iff'] at hx ⊢
   push_cast
   rw [← map_intCast (ZMod.castHom (show 2 ∣ 4 by norm_num) (ZMod 2)) x] at hx
   set y : ZMod 4 := x

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

@@ -419,14 +419,14 @@ theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n
       multiplicity 2 (x + y) + multiplicity 2 (x - y) + multiplicity 2 n :=
   by
   obtain hyx | hyx := le_total y x
-  · iterate 3 rw [← multiplicity.Int.coe_nat_multiplicity]
+  · iterate 3 rw [← multiplicity.Int.natCast_multiplicity]
     have hxyn : y ^ n ≤ x ^ n := pow_le_pow_left' hyx _
     simp only [Int.ofNat_sub hyx, Int.ofNat_sub (pow_le_pow_left' hyx _), Int.ofNat_add,
       Int.coe_nat_pow]
     rw [← Int.natCast_dvd_natCast] at hx
     rw [← Int.natCast_dvd_natCast, Int.ofNat_sub hyx] at hxy
     convert Int.two_pow_sub_pow hxy hx hn using 2
-    rw [← multiplicity.Int.coe_nat_multiplicity]
+    rw [← multiplicity.Int.natCast_multiplicity]
     rfl
   ·
     simp only [nat.sub_eq_zero_iff_le.mpr hyx, nat.sub_eq_zero_iff_le.mpr (pow_le_pow_left' hyx n),

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

@@ -5,7 +5,7 @@ Authors: Tian Chen, Mantas Bakšys
 -/
 import Algebra.GeomSum
 import Data.Int.Parity
-import Data.Zmod.Basic
+import Data.ZMod.Basic
 import NumberTheory.Padics.PadicVal
 import RingTheory.Ideal.QuotientOperations
 
@@ -204,7 +204,7 @@ theorem pow_prime_pow_sub_pow_prime_pow (a : ℕ) :
   by
   induction' a with a h_ind
   · rw [Nat.cast_zero, add_zero, pow_zero, pow_one, pow_one]
-  rw [← Nat.add_one, Nat.cast_add, Nat.cast_one, ← add_assoc, ← h_ind, pow_succ', pow_mul, pow_mul]
+  rw [← Nat.add_one, Nat.cast_add, Nat.cast_one, ← add_assoc, ← h_ind, pow_succ, pow_mul, pow_mul]
   apply pow_prime_sub_pow_prime hp hp1
   · rw [← geom_sum₂_mul]
     exact dvd_mul_of_dvd_right hxy _
@@ -233,10 +233,10 @@ theorem Int.pow_sub_pow {x y : ℤ} (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x) (
   · rw [← geom_sum₂_mul]
     exact dvd_mul_of_dvd_right hxy _
   · exact fun h => hx (hp.dvd_of_dvd_pow h)
-  · rw [Int.coe_nat_dvd]
+  · rw [Int.natCast_dvd_natCast]
     rintro ⟨c, rfl⟩
     refine' hpn ⟨c, _⟩
-    rwa [pow_succ', mul_assoc]
+    rwa [pow_succ, mul_assoc]
 #align multiplicity.int.pow_sub_pow multiplicity.Int.pow_sub_pow
 -/
 
@@ -257,7 +257,7 @@ theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : 
   obtain hyx | hyx := le_total y x
   · iterate 2 rw [← int.coe_nat_multiplicity]
     rw [Int.ofNat_sub (Nat.pow_le_pow_left hyx n)]
-    rw [← Int.coe_nat_dvd] at hxy hx
+    rw [← Int.natCast_dvd_natCast] at hxy hx
     push_cast at *
     exact int.pow_sub_pow hp hp1 hxy hx n
   ·
@@ -271,7 +271,7 @@ theorem Nat.pow_add_pow {x y : ℕ} (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : 
     multiplicity p (x ^ n + y ^ n) = multiplicity p (x + y) + multiplicity p n :=
   by
   iterate 2 rw [← int.coe_nat_multiplicity]
-  rw [← Int.coe_nat_dvd] at hxy hx
+  rw [← Int.natCast_dvd_natCast] at hxy hx
   push_cast at *
   exact int.pow_add_pow hp hp1 hxy hx hn
 #align multiplicity.nat.pow_add_pow multiplicity.Nat.pow_add_pow
@@ -340,7 +340,7 @@ theorem Int.two_pow_two_pow_add_two_pow_two_pow {x y : ℤ} (hx : ¬2 ∣ x) (hx
       this _ hx_odd, this _ hy_odd]
     norm_num
   intro x hx
-  rw [pow_succ, mul_comm, pow_mul, Int.sq_mod_four_eq_one_of_odd hx.pow]
+  rw [pow_succ', mul_comm, pow_mul, Int.sq_mod_four_eq_one_of_odd hx.pow]
 #align int.two_pow_two_pow_add_two_pow_two_pow Int.two_pow_two_pow_add_two_pow_two_pow
 -/
 
@@ -370,10 +370,10 @@ theorem Int.two_pow_sub_pow' {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2
   · exact Int.prime_two
   · simpa only [even_iff_two_dvd] using hx_odd.pow.sub_odd hy_odd.pow
   · simpa only [even_iff_two_dvd, Int.odd_iff_not_even] using hx_odd.pow
-  erw [Int.coe_nat_dvd]
+  erw [Int.natCast_dvd_natCast]
   -- `erw` to deal with `2 : ℤ` vs `(2 : ℕ) : ℤ`
   contrapose! hpn
-  rw [pow_succ']
+  rw [pow_succ]
   conv_rhs => rw [hk]
   exact mul_dvd_mul_left _ hpn
 #align int.two_pow_sub_pow' Int.two_pow_sub_pow'
@@ -423,8 +423,8 @@ theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n
     have hxyn : y ^ n ≤ x ^ n := pow_le_pow_left' hyx _
     simp only [Int.ofNat_sub hyx, Int.ofNat_sub (pow_le_pow_left' hyx _), Int.ofNat_add,
       Int.coe_nat_pow]
-    rw [← Int.coe_nat_dvd] at hx
-    rw [← Int.coe_nat_dvd, Int.ofNat_sub hyx] at hxy
+    rw [← Int.natCast_dvd_natCast] at hx
+    rw [← Int.natCast_dvd_natCast, Int.ofNat_sub hyx] at hxy
     convert Int.two_pow_sub_pow hxy hx hn using 2
     rw [← multiplicity.Int.coe_nat_multiplicity]
     rfl

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

@@ -45,7 +45,7 @@ variable [CommRing R] {a b x y : R}
 theorem dvd_geom_sum₂_iff_of_dvd_sub {x y p : R} (h : p ∣ x - y) :
     p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i) ↔ p ∣ n * y ^ (n - 1) :=
   by
-  rw [← mem_span_singleton, ← Ideal.Quotient.eq] at h 
+  rw [← mem_span_singleton, ← Ideal.Quotient.eq] at h
   simp only [← mem_span_singleton, ← eq_zero_iff_mem, RingHom.map_geom_sum₂, h, geom_sum₂_self,
     _root_.map_mul, map_pow, map_natCast]
 #align dvd_geom_sum₂_iff_of_dvd_sub dvd_geom_sum₂_iff_of_dvd_sub
@@ -182,7 +182,7 @@ theorem geom_sum₂_eq_one : multiplicity (↑p) (∑ i in range p, x ^ i * y ^
   refine' multiplicity.eq_coe_iff.2 ⟨_, _⟩
   · rw [pow_one]
     exact dvd_geom_sum₂_self hxy
-  rw [dvd_iff_dvd_of_dvd_sub hxy] at hx 
+  rw [dvd_iff_dvd_of_dvd_sub hxy] at hx
   cases' hxy with k hk
   rw [one_add_one_eq_two, eq_add_of_sub_eq' hk]
   refine' mt (dvd_iff_dvd_of_dvd_sub (@odd_sq_dvd_geom_sum₂_sub _ _ y k _ hp1)).mp _
@@ -228,7 +228,7 @@ theorem Int.pow_sub_pow {x y : ℤ} (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x) (
   have h : (multiplicity _ _).Dom := finite_nat_iff.mpr ⟨hp.ne_one, n.succ_pos⟩
   rcases eq_coe_iff.mp (PartENat.natCast_get h).symm with ⟨⟨k, hk⟩, hpn⟩
   conv_lhs => rw [hk, pow_mul, pow_mul]
-  rw [Nat.prime_iff_prime_int] at hp 
+  rw [Nat.prime_iff_prime_int] at hp
   rw [pow_sub_pow_of_prime hp, pow_prime_pow_sub_pow_prime_pow hp hp1 hxy hx, PartENat.natCast_get]
   · rw [← geom_sum₂_mul]
     exact dvd_mul_of_dvd_right hxy _
@@ -244,7 +244,7 @@ theorem Int.pow_sub_pow {x y : ℤ} (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x) (
 theorem Int.pow_add_pow {x y : ℤ} (hxy : ↑p ∣ x + y) (hx : ¬↑p ∣ x) {n : ℕ} (hn : Odd n) :
     multiplicity (↑p) (x ^ n + y ^ n) = multiplicity (↑p) (x + y) + multiplicity p n :=
   by
-  rw [← sub_neg_eq_add] at hxy 
+  rw [← sub_neg_eq_add] at hxy
   rw [← sub_neg_eq_add, ← sub_neg_eq_add, ← Odd.neg_pow hn]
   exact int.pow_sub_pow hp hp1 hxy hx n
 #align multiplicity.int.pow_add_pow multiplicity.Int.pow_add_pow
@@ -257,7 +257,7 @@ theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : 
   obtain hyx | hyx := le_total y x
   · iterate 2 rw [← int.coe_nat_multiplicity]
     rw [Int.ofNat_sub (Nat.pow_le_pow_left hyx n)]
-    rw [← Int.coe_nat_dvd] at hxy hx 
+    rw [← Int.coe_nat_dvd] at hxy hx
     push_cast at *
     exact int.pow_sub_pow hp hp1 hxy hx n
   ·
@@ -271,7 +271,7 @@ theorem Nat.pow_add_pow {x y : ℕ} (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : 
     multiplicity p (x ^ n + y ^ n) = multiplicity p (x + y) + multiplicity p n :=
   by
   iterate 2 rw [← int.coe_nat_multiplicity]
-  rw [← Int.coe_nat_dvd] at hxy hx 
+  rw [← Int.coe_nat_dvd] at hxy hx
   push_cast at *
   exact int.pow_add_pow hp hp1 hxy hx hn
 #align multiplicity.nat.pow_add_pow multiplicity.Nat.pow_add_pow
@@ -302,15 +302,15 @@ theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
   intro hx
   -- Replace `x : ℤ` with `y : zmod 4`
   replace hx : x % (2 : ℕ) = 1 % (2 : ℕ);
-  · rw [Int.odd_iff] at hx ; norm_num [hx]
+  · rw [Int.odd_iff] at hx; norm_num [hx]
   calc
     x ^ 2 % (4 : ℕ) = 1 % (4 : ℕ) := _
     _ = 1 := by norm_num
   rw [← ZMod.int_cast_eq_int_cast_iff'] at hx ⊢
   push_cast
-  rw [← map_intCast (ZMod.castHom (show 2 ∣ 4 by norm_num) (ZMod 2)) x] at hx 
+  rw [← map_intCast (ZMod.castHom (show 2 ∣ 4 by norm_num) (ZMod 2)) x] at hx
   set y : ZMod 4 := x
-  change ZMod.castHom _ (ZMod 2) y = _ at hx 
+  change ZMod.castHom _ (ZMod 2) y = _ at hx
   -- Now we can just consider each of the 4 possible values for y
         fin_cases y <;>
         rw [hy] at hx ⊢ <;>
@@ -386,7 +386,7 @@ theorem Int.two_pow_sub_pow {x y : ℤ} {n : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2
       multiplicity 2 (x + y) + multiplicity 2 (x - y) + multiplicity (2 : ℤ) n :=
   by
   have hy : Odd y := by
-    rw [← even_iff_two_dvd, ← Int.odd_iff_not_even] at hx 
+    rw [← even_iff_two_dvd, ← Int.odd_iff_not_even] at hx
     replace hxy := (@even_neg _ _ (x - y)).mpr (even_iff_two_dvd.mpr hxy)
     convert Even.add_odd hxy hx
     abel
@@ -423,8 +423,8 @@ theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n
     have hxyn : y ^ n ≤ x ^ n := pow_le_pow_left' hyx _
     simp only [Int.ofNat_sub hyx, Int.ofNat_sub (pow_le_pow_left' hyx _), Int.ofNat_add,
       Int.coe_nat_pow]
-    rw [← Int.coe_nat_dvd] at hx 
-    rw [← Int.coe_nat_dvd, Int.ofNat_sub hyx] at hxy 
+    rw [← Int.coe_nat_dvd] at hx
+    rw [← Int.coe_nat_dvd, Int.ofNat_sub hyx] at hxy
     convert Int.two_pow_sub_pow hxy hx hn using 2
     rw [← multiplicity.Int.coe_nat_multiplicity]
     rfl

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

@@ -295,7 +295,7 @@ theorem pow_two_pow_sub_pow_two_pow [CommRing R] {x y : R} (n : ℕ) :
 #align pow_two_pow_sub_pow_two_pow pow_two_pow_sub_pow_two_pow
 -/
 
-/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:80:4: warning: unsupported fin_cases 'using hy' clause -/
+/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:76:4: warning: unsupported fin_cases 'using hy' clause -/
 #print Int.sq_mod_four_eq_one_of_odd /-
 theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
   by

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

@@ -256,14 +256,13 @@ theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : 
   by
   obtain hyx | hyx := le_total y x
   · iterate 2 rw [← int.coe_nat_multiplicity]
-    rw [Int.ofNat_sub (Nat.pow_le_pow_of_le_left hyx n)]
+    rw [Int.ofNat_sub (Nat.pow_le_pow_left hyx n)]
     rw [← Int.coe_nat_dvd] at hxy hx 
     push_cast at *
     exact int.pow_sub_pow hp hp1 hxy hx n
   ·
     simp only [nat.sub_eq_zero_iff_le.mpr hyx,
-      nat.sub_eq_zero_iff_le.mpr (Nat.pow_le_pow_of_le_left hyx n), multiplicity.zero,
-      PartENat.top_add]
+      nat.sub_eq_zero_iff_le.mpr (Nat.pow_le_pow_left hyx n), multiplicity.zero, PartENat.top_add]
 #align multiplicity.nat.pow_sub_pow multiplicity.Nat.pow_sub_pow
 -/
 
@@ -421,8 +420,8 @@ theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n
   by
   obtain hyx | hyx := le_total y x
   · iterate 3 rw [← multiplicity.Int.coe_nat_multiplicity]
-    have hxyn : y ^ n ≤ x ^ n := pow_le_pow_of_le_left' hyx _
-    simp only [Int.ofNat_sub hyx, Int.ofNat_sub (pow_le_pow_of_le_left' hyx _), Int.ofNat_add,
+    have hxyn : y ^ n ≤ x ^ n := pow_le_pow_left' hyx _
+    simp only [Int.ofNat_sub hyx, Int.ofNat_sub (pow_le_pow_left' hyx _), Int.ofNat_add,
       Int.coe_nat_pow]
     rw [← Int.coe_nat_dvd] at hx 
     rw [← Int.coe_nat_dvd, Int.ofNat_sub hyx] at hxy 
@@ -430,9 +429,8 @@ theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n
     rw [← multiplicity.Int.coe_nat_multiplicity]
     rfl
   ·
-    simp only [nat.sub_eq_zero_iff_le.mpr hyx,
-      nat.sub_eq_zero_iff_le.mpr (pow_le_pow_of_le_left' hyx n), multiplicity.zero,
-      PartENat.top_add, PartENat.add_top]
+    simp only [nat.sub_eq_zero_iff_le.mpr hyx, nat.sub_eq_zero_iff_le.mpr (pow_le_pow_left' hyx n),
+      multiplicity.zero, PartENat.top_add, PartENat.add_top]
 #align nat.two_pow_sub_pow Nat.two_pow_sub_pow
 -/
 
@@ -452,7 +450,7 @@ theorem pow_two_sub_pow (hyx : y < x) (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n :
   · exact hn
   · exact Nat.sub_pos_of_lt hyx
   · linarith
-  · simp only [tsub_pos_iff_lt, pow_lt_pow_of_lt_left hyx (@zero_le' _ y _) hn]
+  · simp only [tsub_pos_iff_lt, pow_lt_pow_left hyx (@zero_le' _ y _) hn]
 #align padic_val_nat.pow_two_sub_pow padicValNat.pow_two_sub_pow
 -/
 
@@ -467,7 +465,7 @@ theorem pow_sub_pow (hyx : y < x) (hxy : p ∣ x - y) (hx : ¬p ∣ x) {n : ℕ}
   · exact multiplicity.Nat.pow_sub_pow hp.out hp1 hxy hx n
   · exact hn
   · exact Nat.sub_pos_of_lt hyx
-  · exact Nat.sub_pos_of_lt (Nat.pow_lt_pow_of_lt_left hyx hn)
+  · exact Nat.sub_pos_of_lt (Nat.pow_lt_pow_left hyx hn)
 #align padic_val_nat.pow_sub_pow padicValNat.pow_sub_pow
 -/
 

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

@@ -3,11 +3,11 @@ Copyright (c) 2022 Tian Chen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tian Chen, Mantas Bakšys
 -/
-import Mathbin.Algebra.GeomSum
-import Mathbin.Data.Int.Parity
-import Mathbin.Data.Zmod.Basic
-import Mathbin.NumberTheory.Padics.PadicVal
-import Mathbin.RingTheory.Ideal.QuotientOperations
+import Algebra.GeomSum
+import Data.Int.Parity
+import Data.Zmod.Basic
+import NumberTheory.Padics.PadicVal
+import RingTheory.Ideal.QuotientOperations
 
 #align_import number_theory.multiplicity from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Tian Chen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tian Chen, Mantas Bakšys
-
-! This file was ported from Lean 3 source module number_theory.multiplicity
-! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.GeomSum
 import Mathbin.Data.Int.Parity
@@ -14,6 +9,8 @@ import Mathbin.Data.Zmod.Basic
 import Mathbin.NumberTheory.Padics.PadicVal
 import Mathbin.RingTheory.Ideal.QuotientOperations
 
+#align_import number_theory.multiplicity from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
+
 /-!
 # Multiplicity in Number Theory
 

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

@@ -44,6 +44,7 @@ section CommRing
 
 variable [CommRing R] {a b x y : R}
 
+#print dvd_geom_sum₂_iff_of_dvd_sub /-
 theorem dvd_geom_sum₂_iff_of_dvd_sub {x y p : R} (h : p ∣ x - y) :
     p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i) ↔ p ∣ n * y ^ (n - 1) :=
   by
@@ -51,17 +52,23 @@ theorem dvd_geom_sum₂_iff_of_dvd_sub {x y p : R} (h : p ∣ x - y) :
   simp only [← mem_span_singleton, ← eq_zero_iff_mem, RingHom.map_geom_sum₂, h, geom_sum₂_self,
     _root_.map_mul, map_pow, map_natCast]
 #align dvd_geom_sum₂_iff_of_dvd_sub dvd_geom_sum₂_iff_of_dvd_sub
+-/
 
+#print dvd_geom_sum₂_iff_of_dvd_sub' /-
 theorem dvd_geom_sum₂_iff_of_dvd_sub' {x y p : R} (h : p ∣ x - y) :
     p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i) ↔ p ∣ n * x ^ (n - 1) := by
   rw [geom_sum₂_comm, dvd_geom_sum₂_iff_of_dvd_sub] <;> simpa using h.neg_right
 #align dvd_geom_sum₂_iff_of_dvd_sub' dvd_geom_sum₂_iff_of_dvd_sub'
+-/
 
+#print dvd_geom_sum₂_self /-
 theorem dvd_geom_sum₂_self {x y : R} (h : ↑n ∣ x - y) :
     ↑n ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i) :=
   (dvd_geom_sum₂_iff_of_dvd_sub h).mpr (dvd_mul_right _ _)
 #align dvd_geom_sum₂_self dvd_geom_sum₂_self
+-/
 
+#print sq_dvd_add_pow_sub_sub /-
 theorem sq_dvd_add_pow_sub_sub (p x : R) (n : ℕ) :
     p ^ 2 ∣ (x + p) ^ n - x ^ (n - 1) * p * n - x ^ n :=
   by
@@ -80,15 +87,19 @@ theorem sq_dvd_add_pow_sub_sub (p x : R) (n : ℕ) :
         _ ∣ x ^ y * p ^ (n + 1 - y) * ↑((n + 1).choose y) :=
           dvd_mul_of_dvd_left (dvd_mul_left _ _) ((n + 1).choose y)
 #align sq_dvd_add_pow_sub_sub sq_dvd_add_pow_sub_sub
+-/
 
+#print not_dvd_geom_sum₂ /-
 theorem not_dvd_geom_sum₂ {p : R} (hp : Prime p) (hxy : p ∣ x - y) (hx : ¬p ∣ x) (hn : ¬p ∣ n) :
     ¬p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i) := fun h =>
   hx <|
     hp.dvd_of_dvd_pow <| (hp.dvd_or_dvd <| (dvd_geom_sum₂_iff_of_dvd_sub' hxy).mp h).resolve_left hn
 #align not_dvd_geom_sum₂ not_dvd_geom_sum₂
+-/
 
 variable {p : ℕ} (a b)
 
+#print odd_sq_dvd_geom_sum₂_sub /-
 theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
     ↑p ^ 2 ∣ ∑ i in range p, (a + p * b) ^ i * a ^ (p - 1 - i) - p * a ^ (p - 1) :=
   by
@@ -149,6 +160,7 @@ theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
       ring
       simp only [← map_pow, mul_eq_zero_of_left, Ideal.Quotient.eq_zero_iff_mem, mem_span_singleton]
 #align odd_sq_dvd_geom_sum₂_sub odd_sq_dvd_geom_sum₂_sub
+-/
 
 namespace multiplicity
 
@@ -156,16 +168,17 @@ section IntegralDomain
 
 variable [IsDomain R] [@DecidableRel R (· ∣ ·)]
 
+#print multiplicity.pow_sub_pow_of_prime /-
 theorem pow_sub_pow_of_prime {p : R} (hp : Prime p) {x y : R} (hxy : p ∣ x - y) (hx : ¬p ∣ x)
     {n : ℕ} (hn : ¬p ∣ n) : multiplicity p (x ^ n - y ^ n) = multiplicity p (x - y) := by
   rw [← geom_sum₂_mul, multiplicity.mul hp, multiplicity_eq_zero.2 (not_dvd_geom_sum₂ hp hxy hx hn),
     zero_add]
 #align multiplicity.pow_sub_pow_of_prime multiplicity.pow_sub_pow_of_prime
+-/
 
 variable (hp : Prime (p : R)) (hp1 : Odd p) (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x)
 
-include hp hp1 hxy hx
-
+#print multiplicity.geom_sum₂_eq_one /-
 theorem geom_sum₂_eq_one : multiplicity (↑p) (∑ i in range p, x ^ i * y ^ (p - 1 - i)) = 1 :=
   by
   rw [← Nat.cast_one]
@@ -179,12 +192,16 @@ theorem geom_sum₂_eq_one : multiplicity (↑p) (∑ i in range p, x ^ i * y ^
   rw [pow_two, mul_dvd_mul_iff_left hp.ne_zero]
   exact mt hp.dvd_of_dvd_pow hx
 #align multiplicity.geom_sum₂_eq_one multiplicity.geom_sum₂_eq_one
+-/
 
+#print multiplicity.pow_prime_sub_pow_prime /-
 theorem pow_prime_sub_pow_prime :
     multiplicity (↑p) (x ^ p - y ^ p) = multiplicity (↑p) (x - y) + 1 := by
   rw [← geom_sum₂_mul, multiplicity.mul hp, geom_sum₂_eq_one hp hp1 hxy hx, add_comm]
 #align multiplicity.pow_prime_sub_pow_prime multiplicity.pow_prime_sub_pow_prime
+-/
 
+#print multiplicity.pow_prime_pow_sub_pow_prime_pow /-
 theorem pow_prime_pow_sub_pow_prime_pow (a : ℕ) :
     multiplicity (↑p) (x ^ p ^ a - y ^ p ^ a) = multiplicity (↑p) (x - y) + a :=
   by
@@ -196,6 +213,7 @@ theorem pow_prime_pow_sub_pow_prime_pow (a : ℕ) :
     exact dvd_mul_of_dvd_right hxy _
   · exact fun h => hx (hp.dvd_of_dvd_pow h)
 #align multiplicity.pow_prime_pow_sub_pow_prime_pow multiplicity.pow_prime_pow_sub_pow_prime_pow
+-/
 
 end IntegralDomain
 
@@ -203,8 +221,7 @@ section LiftingTheExponent
 
 variable (hp : Nat.Prime p) (hp1 : Odd p)
 
-include hp hp1
-
+#print multiplicity.Int.pow_sub_pow /-
 /-- **Lifting the exponent lemma** for odd primes. -/
 theorem Int.pow_sub_pow {x y : ℤ} (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x) (n : ℕ) :
     multiplicity (↑p) (x ^ n - y ^ n) = multiplicity (↑p) (x - y) + multiplicity p n :=
@@ -224,7 +241,9 @@ theorem Int.pow_sub_pow {x y : ℤ} (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x) (
     refine' hpn ⟨c, _⟩
     rwa [pow_succ', mul_assoc]
 #align multiplicity.int.pow_sub_pow multiplicity.Int.pow_sub_pow
+-/
 
+#print multiplicity.Int.pow_add_pow /-
 theorem Int.pow_add_pow {x y : ℤ} (hxy : ↑p ∣ x + y) (hx : ¬↑p ∣ x) {n : ℕ} (hn : Odd n) :
     multiplicity (↑p) (x ^ n + y ^ n) = multiplicity (↑p) (x + y) + multiplicity p n :=
   by
@@ -232,7 +251,9 @@ theorem Int.pow_add_pow {x y : ℤ} (hxy : ↑p ∣ x + y) (hx : ¬↑p ∣ x) {
   rw [← sub_neg_eq_add, ← sub_neg_eq_add, ← Odd.neg_pow hn]
   exact int.pow_sub_pow hp hp1 hxy hx n
 #align multiplicity.int.pow_add_pow multiplicity.Int.pow_add_pow
+-/
 
+#print multiplicity.Nat.pow_sub_pow /-
 theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : ℕ) :
     multiplicity p (x ^ n - y ^ n) = multiplicity p (x - y) + multiplicity p n :=
   by
@@ -247,7 +268,9 @@ theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : 
       nat.sub_eq_zero_iff_le.mpr (Nat.pow_le_pow_of_le_left hyx n), multiplicity.zero,
       PartENat.top_add]
 #align multiplicity.nat.pow_sub_pow multiplicity.Nat.pow_sub_pow
+-/
 
+#print multiplicity.Nat.pow_add_pow /-
 theorem Nat.pow_add_pow {x y : ℕ} (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : ℕ} (hn : Odd n) :
     multiplicity p (x ^ n + y ^ n) = multiplicity p (x + y) + multiplicity p n :=
   by
@@ -256,6 +279,7 @@ theorem Nat.pow_add_pow {x y : ℕ} (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : 
   push_cast at *
   exact int.pow_add_pow hp hp1 hxy hx hn
 #align multiplicity.nat.pow_add_pow multiplicity.Nat.pow_add_pow
+-/
 
 end LiftingTheExponent
 
@@ -263,6 +287,7 @@ end multiplicity
 
 end CommRing
 
+#print pow_two_pow_sub_pow_two_pow /-
 theorem pow_two_pow_sub_pow_two_pow [CommRing R] {x y : R} (n : ℕ) :
     x ^ 2 ^ n - y ^ 2 ^ n = (∏ i in Finset.range n, (x ^ 2 ^ i + y ^ 2 ^ i)) * (x - y) :=
   by
@@ -272,8 +297,10 @@ theorem pow_two_pow_sub_pow_two_pow [CommRing R] {x y : R} (n : ℕ) :
       rw [this, hd, Finset.prod_range_succ, ← mul_assoc, mul_comm (x ^ 2 ^ d + y ^ 2 ^ d)]
     · ring1
 #align pow_two_pow_sub_pow_two_pow pow_two_pow_sub_pow_two_pow
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:80:4: warning: unsupported fin_cases 'using hy' clause -/
+#print Int.sq_mod_four_eq_one_of_odd /-
 theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
   by
   intro hx
@@ -294,7 +321,9 @@ theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
       revert hx <;>
     decide
 #align int.sq_mod_four_eq_one_of_odd Int.sq_mod_four_eq_one_of_odd
+-/
 
+#print Int.two_pow_two_pow_add_two_pow_two_pow /-
 theorem Int.two_pow_two_pow_add_two_pow_two_pow {x y : ℤ} (hx : ¬2 ∣ x) (hxy : 4 ∣ x - y) (i : ℕ) :
     multiplicity 2 (x ^ 2 ^ i + y ^ 2 ^ i) = ↑(1 : ℕ) :=
   by
@@ -317,14 +346,18 @@ theorem Int.two_pow_two_pow_add_two_pow_two_pow {x y : ℤ} (hx : ¬2 ∣ x) (hx
   intro x hx
   rw [pow_succ, mul_comm, pow_mul, Int.sq_mod_four_eq_one_of_odd hx.pow]
 #align int.two_pow_two_pow_add_two_pow_two_pow Int.two_pow_two_pow_add_two_pow_two_pow
+-/
 
+#print Int.two_pow_two_pow_sub_pow_two_pow /-
 theorem Int.two_pow_two_pow_sub_pow_two_pow {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2 ∣ x) :
     multiplicity 2 (x ^ 2 ^ n - y ^ 2 ^ n) = multiplicity 2 (x - y) + n := by
   simp only [pow_two_pow_sub_pow_two_pow n, multiplicity.mul Int.prime_two,
     multiplicity.Finset.prod Int.prime_two, add_comm, Nat.cast_one, Finset.sum_const,
     Finset.card_range, nsmul_one, Int.two_pow_two_pow_add_two_pow_two_pow hx hxy]
 #align int.two_pow_two_pow_sub_pow_two_pow Int.two_pow_two_pow_sub_pow_two_pow
+-/
 
+#print Int.two_pow_sub_pow' /-
 theorem Int.two_pow_sub_pow' {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2 ∣ x) :
     multiplicity 2 (x ^ n - y ^ n) = multiplicity 2 (x - y) + multiplicity (2 : ℤ) n :=
   by
@@ -348,7 +381,9 @@ theorem Int.two_pow_sub_pow' {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2
   conv_rhs => rw [hk]
   exact mul_dvd_mul_left _ hpn
 #align int.two_pow_sub_pow' Int.two_pow_sub_pow'
+-/
 
+#print Int.two_pow_sub_pow /-
 /-- **Lifting the exponent lemma** for `p = 2` -/
 theorem Int.two_pow_sub_pow {x y : ℤ} {n : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) (hn : Even n) :
     multiplicity 2 (x ^ n - y ^ n) + 1 =
@@ -380,7 +415,9 @@ theorem Int.two_pow_sub_pow {x y : ℤ} {n : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2
     apply Odd.pow
     simp only [Int.odd_iff_not_even, even_iff_two_dvd, hx, not_false_iff]
 #align int.two_pow_sub_pow Int.two_pow_sub_pow
+-/
 
+#print Nat.two_pow_sub_pow /-
 theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n : ℕ} (hn : Even n) :
     multiplicity 2 (x ^ n - y ^ n) + 1 =
       multiplicity 2 (x + y) + multiplicity 2 (x - y) + multiplicity 2 n :=
@@ -400,6 +437,7 @@ theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n
       nat.sub_eq_zero_iff_le.mpr (pow_le_pow_of_le_left' hyx n), multiplicity.zero,
       PartENat.top_add, PartENat.add_top]
 #align nat.two_pow_sub_pow Nat.two_pow_sub_pow
+-/
 
 namespace padicValNat
 
@@ -423,8 +461,6 @@ theorem pow_two_sub_pow (hyx : y < x) (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n :
 
 variable {p : ℕ} [hp : Fact p.Prime] (hp1 : Odd p)
 
-include hp hp1
-
 #print padicValNat.pow_sub_pow /-
 theorem pow_sub_pow (hyx : y < x) (hxy : p ∣ x - y) (hx : ¬p ∣ x) {n : ℕ} (hn : 0 < n) :
     padicValNat p (x ^ n - y ^ n) = padicValNat p (x - y) + padicValNat p n :=

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

@@ -45,7 +45,7 @@ section CommRing
 variable [CommRing R] {a b x y : R}
 
 theorem dvd_geom_sum₂_iff_of_dvd_sub {x y p : R} (h : p ∣ x - y) :
-    (p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i)) ↔ p ∣ n * y ^ (n - 1) :=
+    p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i) ↔ p ∣ n * y ^ (n - 1) :=
   by
   rw [← mem_span_singleton, ← Ideal.Quotient.eq] at h 
   simp only [← mem_span_singleton, ← eq_zero_iff_mem, RingHom.map_geom_sum₂, h, geom_sum₂_self,
@@ -53,7 +53,7 @@ theorem dvd_geom_sum₂_iff_of_dvd_sub {x y p : R} (h : p ∣ x - y) :
 #align dvd_geom_sum₂_iff_of_dvd_sub dvd_geom_sum₂_iff_of_dvd_sub
 
 theorem dvd_geom_sum₂_iff_of_dvd_sub' {x y p : R} (h : p ∣ x - y) :
-    (p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i)) ↔ p ∣ n * x ^ (n - 1) := by
+    p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i) ↔ p ∣ n * x ^ (n - 1) := by
   rw [geom_sum₂_comm, dvd_geom_sum₂_iff_of_dvd_sub] <;> simpa using h.neg_right
 #align dvd_geom_sum₂_iff_of_dvd_sub' dvd_geom_sum₂_iff_of_dvd_sub'
 
@@ -90,7 +90,7 @@ theorem not_dvd_geom_sum₂ {p : R} (hp : Prime p) (hxy : p ∣ x - y) (hx : ¬p
 variable {p : ℕ} (a b)
 
 theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
-    ↑p ^ 2 ∣ (∑ i in range p, (a + p * b) ^ i * a ^ (p - 1 - i)) - p * a ^ (p - 1) :=
+    ↑p ^ 2 ∣ ∑ i in range p, (a + p * b) ^ i * a ^ (p - 1 - i) - p * a ^ (p - 1) :=
   by
   have h1 : ∀ i, ↑p ^ 2 ∣ (a + ↑p * b) ^ i - (a ^ (i - 1) * (↑p * b) * ↑i + a ^ i) :=
     by
@@ -264,7 +264,7 @@ end multiplicity
 end CommRing
 
 theorem pow_two_pow_sub_pow_two_pow [CommRing R] {x y : R} (n : ℕ) :
-    x ^ 2 ^ n - y ^ 2 ^ n = (∏ i in Finset.range n, x ^ 2 ^ i + y ^ 2 ^ i) * (x - y) :=
+    x ^ 2 ^ n - y ^ 2 ^ n = (∏ i in Finset.range n, (x ^ 2 ^ i + y ^ 2 ^ i)) * (x - y) :=
   by
   induction' n with d hd
   · simp only [pow_zero, pow_one, Finset.range_zero, Finset.prod_empty, one_mul]

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

@@ -79,7 +79,6 @@ theorem sq_dvd_add_pow_sub_sub (p x : R) (n : ℕ) :
           pow_dvd_pow p (le_tsub_of_add_le_left (by linarith [finset.mem_range.mp hy]))
         _ ∣ x ^ y * p ^ (n + 1 - y) * ↑((n + 1).choose y) :=
           dvd_mul_of_dvd_left (dvd_mul_left _ _) ((n + 1).choose y)
-        
 #align sq_dvd_add_pow_sub_sub sq_dvd_add_pow_sub_sub
 
 theorem not_dvd_geom_sum₂ {p : R} (hp : Prime p) (hxy : p ∣ x - y) (hx : ¬p ∣ x) (hn : ¬p ∣ n) :
@@ -100,7 +99,6 @@ theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
       ↑p ^ 2 ∣ (↑p * b) ^ 2 := by simp only [mul_pow, dvd_mul_right]
       _ ∣ (a + ↑p * b) ^ i - (a ^ (i - 1) * (↑p * b) * ↑i + a ^ i) := by
         simp only [sq_dvd_add_pow_sub_sub (↑p * b) a i, ← sub_sub]
-      
   simp_rw [← mem_span_singleton, ← Ideal.Quotient.eq] at *
   calc
     Ideal.Quotient.mk (span {↑p ^ 2}) (∑ i in range p, (a + ↑p * b) ^ i * a ^ (p - 1 - i)) =
@@ -150,7 +148,6 @@ theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
         Nat.mul_div_assoc _ (even_iff_two_dvd.mp (Nat.Odd.sub_odd hp odd_one))]
       ring
       simp only [← map_pow, mul_eq_zero_of_left, Ideal.Quotient.eq_zero_iff_mem, mem_span_singleton]
-    
 #align odd_sq_dvd_geom_sum₂_sub odd_sq_dvd_geom_sum₂_sub
 
 namespace multiplicity
@@ -286,7 +283,6 @@ theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
   calc
     x ^ 2 % (4 : ℕ) = 1 % (4 : ℕ) := _
     _ = 1 := by norm_num
-    
   rw [← ZMod.int_cast_eq_int_cast_iff'] at hx ⊢
   push_cast
   rw [← map_intCast (ZMod.castHom (show 2 ∣ 4 by norm_num) (ZMod 2)) x] at hx 

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

@@ -47,7 +47,7 @@ variable [CommRing R] {a b x y : R}
 theorem dvd_geom_sum₂_iff_of_dvd_sub {x y p : R} (h : p ∣ x - y) :
     (p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i)) ↔ p ∣ n * y ^ (n - 1) :=
   by
-  rw [← mem_span_singleton, ← Ideal.Quotient.eq] at h
+  rw [← mem_span_singleton, ← Ideal.Quotient.eq] at h 
   simp only [← mem_span_singleton, ← eq_zero_iff_mem, RingHom.map_geom_sum₂, h, geom_sum₂_self,
     _root_.map_mul, map_pow, map_natCast]
 #align dvd_geom_sum₂_iff_of_dvd_sub dvd_geom_sum₂_iff_of_dvd_sub
@@ -175,7 +175,7 @@ theorem geom_sum₂_eq_one : multiplicity (↑p) (∑ i in range p, x ^ i * y ^
   refine' multiplicity.eq_coe_iff.2 ⟨_, _⟩
   · rw [pow_one]
     exact dvd_geom_sum₂_self hxy
-  rw [dvd_iff_dvd_of_dvd_sub hxy] at hx
+  rw [dvd_iff_dvd_of_dvd_sub hxy] at hx 
   cases' hxy with k hk
   rw [one_add_one_eq_two, eq_add_of_sub_eq' hk]
   refine' mt (dvd_iff_dvd_of_dvd_sub (@odd_sq_dvd_geom_sum₂_sub _ _ y k _ hp1)).mp _
@@ -217,7 +217,7 @@ theorem Int.pow_sub_pow {x y : ℤ} (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x) (
   have h : (multiplicity _ _).Dom := finite_nat_iff.mpr ⟨hp.ne_one, n.succ_pos⟩
   rcases eq_coe_iff.mp (PartENat.natCast_get h).symm with ⟨⟨k, hk⟩, hpn⟩
   conv_lhs => rw [hk, pow_mul, pow_mul]
-  rw [Nat.prime_iff_prime_int] at hp
+  rw [Nat.prime_iff_prime_int] at hp 
   rw [pow_sub_pow_of_prime hp, pow_prime_pow_sub_pow_prime_pow hp hp1 hxy hx, PartENat.natCast_get]
   · rw [← geom_sum₂_mul]
     exact dvd_mul_of_dvd_right hxy _
@@ -231,7 +231,7 @@ theorem Int.pow_sub_pow {x y : ℤ} (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x) (
 theorem Int.pow_add_pow {x y : ℤ} (hxy : ↑p ∣ x + y) (hx : ¬↑p ∣ x) {n : ℕ} (hn : Odd n) :
     multiplicity (↑p) (x ^ n + y ^ n) = multiplicity (↑p) (x + y) + multiplicity p n :=
   by
-  rw [← sub_neg_eq_add] at hxy
+  rw [← sub_neg_eq_add] at hxy 
   rw [← sub_neg_eq_add, ← sub_neg_eq_add, ← Odd.neg_pow hn]
   exact int.pow_sub_pow hp hp1 hxy hx n
 #align multiplicity.int.pow_add_pow multiplicity.Int.pow_add_pow
@@ -242,7 +242,7 @@ theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : 
   obtain hyx | hyx := le_total y x
   · iterate 2 rw [← int.coe_nat_multiplicity]
     rw [Int.ofNat_sub (Nat.pow_le_pow_of_le_left hyx n)]
-    rw [← Int.coe_nat_dvd] at hxy hx
+    rw [← Int.coe_nat_dvd] at hxy hx 
     push_cast at *
     exact int.pow_sub_pow hp hp1 hxy hx n
   ·
@@ -255,7 +255,7 @@ theorem Nat.pow_add_pow {x y : ℕ} (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : 
     multiplicity p (x ^ n + y ^ n) = multiplicity p (x + y) + multiplicity p n :=
   by
   iterate 2 rw [← int.coe_nat_multiplicity]
-  rw [← Int.coe_nat_dvd] at hxy hx
+  rw [← Int.coe_nat_dvd] at hxy hx 
   push_cast at *
   exact int.pow_add_pow hp hp1 hxy hx hn
 #align multiplicity.nat.pow_add_pow multiplicity.Nat.pow_add_pow
@@ -282,19 +282,19 @@ theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
   intro hx
   -- Replace `x : ℤ` with `y : zmod 4`
   replace hx : x % (2 : ℕ) = 1 % (2 : ℕ);
-  · rw [Int.odd_iff] at hx; norm_num [hx]
+  · rw [Int.odd_iff] at hx ; norm_num [hx]
   calc
     x ^ 2 % (4 : ℕ) = 1 % (4 : ℕ) := _
     _ = 1 := by norm_num
     
-  rw [← ZMod.int_cast_eq_int_cast_iff'] at hx⊢
+  rw [← ZMod.int_cast_eq_int_cast_iff'] at hx ⊢
   push_cast
-  rw [← map_intCast (ZMod.castHom (show 2 ∣ 4 by norm_num) (ZMod 2)) x] at hx
+  rw [← map_intCast (ZMod.castHom (show 2 ∣ 4 by norm_num) (ZMod 2)) x] at hx 
   set y : ZMod 4 := x
-  change ZMod.castHom _ (ZMod 2) y = _ at hx
+  change ZMod.castHom _ (ZMod 2) y = _ at hx 
   -- Now we can just consider each of the 4 possible values for y
         fin_cases y <;>
-        rw [hy] at hx⊢ <;>
+        rw [hy] at hx ⊢ <;>
       revert hx <;>
     decide
 #align int.sq_mod_four_eq_one_of_odd Int.sq_mod_four_eq_one_of_odd
@@ -359,7 +359,7 @@ theorem Int.two_pow_sub_pow {x y : ℤ} {n : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2
       multiplicity 2 (x + y) + multiplicity 2 (x - y) + multiplicity (2 : ℤ) n :=
   by
   have hy : Odd y := by
-    rw [← even_iff_two_dvd, ← Int.odd_iff_not_even] at hx
+    rw [← even_iff_two_dvd, ← Int.odd_iff_not_even] at hx 
     replace hxy := (@even_neg _ _ (x - y)).mpr (even_iff_two_dvd.mpr hxy)
     convert Even.add_odd hxy hx
     abel
@@ -394,8 +394,8 @@ theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n
     have hxyn : y ^ n ≤ x ^ n := pow_le_pow_of_le_left' hyx _
     simp only [Int.ofNat_sub hyx, Int.ofNat_sub (pow_le_pow_of_le_left' hyx _), Int.ofNat_add,
       Int.coe_nat_pow]
-    rw [← Int.coe_nat_dvd] at hx
-    rw [← Int.coe_nat_dvd, Int.ofNat_sub hyx] at hxy
+    rw [← Int.coe_nat_dvd] at hx 
+    rw [← Int.coe_nat_dvd, Int.ofNat_sub hyx] at hxy 
     convert Int.two_pow_sub_pow hxy hx hn using 2
     rw [← multiplicity.Int.coe_nat_multiplicity]
     rfl

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

@@ -36,7 +36,7 @@ This file contains results in number theory relating to multiplicity.
 
 open Ideal Ideal.Quotient Finset
 
-open BigOperators
+open scoped BigOperators
 
 variable {R : Type _} {n : ℕ}
 

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

@@ -44,12 +44,6 @@ section CommRing
 
 variable [CommRing R] {a b x y : R}
 
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-Case conversion may be inaccurate. Consider using '#align dvd_geom_sum₂_iff_of_dvd_sub dvd_geom_sum₂_iff_of_dvd_subₓ'. -/
 theorem dvd_geom_sum₂_iff_of_dvd_sub {x y p : R} (h : p ∣ x - y) :
     (p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i)) ↔ p ∣ n * y ^ (n - 1) :=
   by
@@ -58,34 +52,16 @@ theorem dvd_geom_sum₂_iff_of_dvd_sub {x y p : R} (h : p ∣ x - y) :
     _root_.map_mul, map_pow, map_natCast]
 #align dvd_geom_sum₂_iff_of_dvd_sub dvd_geom_sum₂_iff_of_dvd_sub
 
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 theorem dvd_geom_sum₂_iff_of_dvd_sub' {x y p : R} (h : p ∣ x - y) :
     (p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i)) ↔ p ∣ n * x ^ (n - 1) := by
   rw [geom_sum₂_comm, dvd_geom_sum₂_iff_of_dvd_sub] <;> simpa using h.neg_right
 #align dvd_geom_sum₂_iff_of_dvd_sub' dvd_geom_sum₂_iff_of_dvd_sub'
 
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 theorem dvd_geom_sum₂_self {x y : R} (h : ↑n ∣ x - y) :
     ↑n ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i) :=
   (dvd_geom_sum₂_iff_of_dvd_sub h).mpr (dvd_mul_right _ _)
 #align dvd_geom_sum₂_self dvd_geom_sum₂_self
 
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-Case conversion may be inaccurate. Consider using '#align sq_dvd_add_pow_sub_sub sq_dvd_add_pow_sub_subₓ'. -/
 theorem sq_dvd_add_pow_sub_sub (p x : R) (n : ℕ) :
     p ^ 2 ∣ (x + p) ^ n - x ^ (n - 1) * p * n - x ^ n :=
   by
@@ -106,12 +82,6 @@ theorem sq_dvd_add_pow_sub_sub (p x : R) (n : ℕ) :
         
 #align sq_dvd_add_pow_sub_sub sq_dvd_add_pow_sub_sub
 
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 theorem not_dvd_geom_sum₂ {p : R} (hp : Prime p) (hxy : p ∣ x - y) (hx : ¬p ∣ x) (hn : ¬p ∣ n) :
     ¬p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i) := fun h =>
   hx <|
@@ -120,12 +90,6 @@ theorem not_dvd_geom_sum₂ {p : R} (hp : Prime p) (hxy : p ∣ x - y) (hx : ¬p
 
 variable {p : ℕ} (a b)
 
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-Case conversion may be inaccurate. Consider using '#align odd_sq_dvd_geom_sum₂_sub odd_sq_dvd_geom_sum₂_subₓ'. -/
 theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
     ↑p ^ 2 ∣ (∑ i in range p, (a + p * b) ^ i * a ^ (p - 1 - i)) - p * a ^ (p - 1) :=
   by
@@ -195,12 +159,6 @@ section IntegralDomain
 
 variable [IsDomain R] [@DecidableRel R (· ∣ ·)]
 
-/- warning: multiplicity.pow_sub_pow_of_prime -> multiplicity.pow_sub_pow_of_prime is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))] {p : R}, (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) -> (forall {x : R} {y : R}, (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) 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))))))) x y)) -> (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p x)) -> (forall {n : Nat}, (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p ((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 (CommRing.toRing.{u1} R _inst_1)))))))) n))) -> (Eq.{1} PartENat (multiplicity.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (fun (a : R) (b : R) => _inst_3 a b) 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 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 n))) (multiplicity.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (fun (a : R) (b : R) => _inst_3 a b) 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))))))) x y)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (fun (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2388 : R) (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2390 : R) => Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x._@.Mathlib.NumberTheory.Multiplicity._hyg.2388 x._@.Mathlib.NumberTheory.Multiplicity._hyg.2390)] {p : R}, (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)) p) -> (forall {x : R} {y : R}, (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p x)) -> (forall {n : Nat}, (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n))) -> (Eq.{1} PartENat (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) 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 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 n))) (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) p (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)))))
-Case conversion may be inaccurate. Consider using '#align multiplicity.pow_sub_pow_of_prime multiplicity.pow_sub_pow_of_primeₓ'. -/
 theorem pow_sub_pow_of_prime {p : R} (hp : Prime p) {x y : R} (hxy : p ∣ x - y) (hx : ¬p ∣ x)
     {n : ℕ} (hn : ¬p ∣ n) : multiplicity p (x ^ n - y ^ n) = multiplicity p (x - y) := by
   rw [← geom_sum₂_mul, multiplicity.mul hp, multiplicity_eq_zero.2 (not_dvd_geom_sum₂ hp hxy hx hn),
@@ -211,12 +169,6 @@ variable (hp : Prime (p : R)) (hp1 : Odd p) (hxy : ↑p ∣ x - y) (hx : ¬↑p
 
 include hp hp1 hxy hx
 
-/- warning: multiplicity.geom_sum₂_eq_one -> multiplicity.geom_sum₂_eq_one is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align multiplicity.geom_sum₂_eq_one multiplicity.geom_sum₂_eq_oneₓ'. -/
 theorem geom_sum₂_eq_one : multiplicity (↑p) (∑ i in range p, x ^ i * y ^ (p - 1 - i)) = 1 :=
   by
   rw [← Nat.cast_one]
@@ -231,23 +183,11 @@ theorem geom_sum₂_eq_one : multiplicity (↑p) (∑ i in range p, x ^ i * y ^
   exact mt hp.dvd_of_dvd_pow hx
 #align multiplicity.geom_sum₂_eq_one multiplicity.geom_sum₂_eq_one
 
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-Case conversion may be inaccurate. Consider using '#align multiplicity.pow_prime_sub_pow_prime multiplicity.pow_prime_sub_pow_primeₓ'. -/
 theorem pow_prime_sub_pow_prime :
     multiplicity (↑p) (x ^ p - y ^ p) = multiplicity (↑p) (x - y) + 1 := by
   rw [← geom_sum₂_mul, multiplicity.mul hp, geom_sum₂_eq_one hp hp1 hxy hx, add_comm]
 #align multiplicity.pow_prime_sub_pow_prime multiplicity.pow_prime_sub_pow_prime
 
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-Case conversion may be inaccurate. Consider using '#align multiplicity.pow_prime_pow_sub_pow_prime_pow multiplicity.pow_prime_pow_sub_pow_prime_powₓ'. -/
 theorem pow_prime_pow_sub_pow_prime_pow (a : ℕ) :
     multiplicity (↑p) (x ^ p ^ a - y ^ p ^ a) = multiplicity (↑p) (x - y) + a :=
   by
@@ -268,12 +208,6 @@ variable (hp : Nat.Prime p) (hp1 : Odd p)
 
 include hp hp1
 
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-Case conversion may be inaccurate. Consider using '#align multiplicity.int.pow_sub_pow multiplicity.Int.pow_sub_powₓ'. -/
 /-- **Lifting the exponent lemma** for odd primes. -/
 theorem Int.pow_sub_pow {x y : ℤ} (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x) (n : ℕ) :
     multiplicity (↑p) (x ^ n - y ^ n) = multiplicity (↑p) (x - y) + multiplicity p n :=
@@ -294,12 +228,6 @@ theorem Int.pow_sub_pow {x y : ℤ} (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x) (
     rwa [pow_succ', mul_assoc]
 #align multiplicity.int.pow_sub_pow multiplicity.Int.pow_sub_pow
 
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-Case conversion may be inaccurate. Consider using '#align multiplicity.int.pow_add_pow multiplicity.Int.pow_add_powₓ'. -/
 theorem Int.pow_add_pow {x y : ℤ} (hxy : ↑p ∣ x + y) (hx : ¬↑p ∣ x) {n : ℕ} (hn : Odd n) :
     multiplicity (↑p) (x ^ n + y ^ n) = multiplicity (↑p) (x + y) + multiplicity p n :=
   by
@@ -308,12 +236,6 @@ theorem Int.pow_add_pow {x y : ℤ} (hxy : ↑p ∣ x + y) (hx : ¬↑p ∣ x) {
   exact int.pow_sub_pow hp hp1 hxy hx n
 #align multiplicity.int.pow_add_pow multiplicity.Int.pow_add_pow
 
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 theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : ℕ) :
     multiplicity p (x ^ n - y ^ n) = multiplicity p (x - y) + multiplicity p n :=
   by
@@ -329,12 +251,6 @@ theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : 
       PartENat.top_add]
 #align multiplicity.nat.pow_sub_pow multiplicity.Nat.pow_sub_pow
 
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 theorem Nat.pow_add_pow {x y : ℕ} (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : ℕ} (hn : Odd n) :
     multiplicity p (x ^ n + y ^ n) = multiplicity p (x + y) + multiplicity p n :=
   by
@@ -350,12 +266,6 @@ end multiplicity
 
 end CommRing
 
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 theorem pow_two_pow_sub_pow_two_pow [CommRing R] {x y : R} (n : ℕ) :
     x ^ 2 ^ n - y ^ 2 ^ n = (∏ i in Finset.range n, x ^ 2 ^ i + y ^ 2 ^ i) * (x - y) :=
   by
@@ -366,12 +276,6 @@ theorem pow_two_pow_sub_pow_two_pow [CommRing R] {x y : R} (n : ℕ) :
     · ring1
 #align pow_two_pow_sub_pow_two_pow pow_two_pow_sub_pow_two_pow
 
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 /- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:80:4: warning: unsupported fin_cases 'using hy' clause -/
 theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
   by
@@ -395,12 +299,6 @@ theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
     decide
 #align int.sq_mod_four_eq_one_of_odd Int.sq_mod_four_eq_one_of_odd
 
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 theorem Int.two_pow_two_pow_add_two_pow_two_pow {x y : ℤ} (hx : ¬2 ∣ x) (hxy : 4 ∣ x - y) (i : ℕ) :
     multiplicity 2 (x ^ 2 ^ i + y ^ 2 ^ i) = ↑(1 : ℕ) :=
   by
@@ -424,12 +322,6 @@ theorem Int.two_pow_two_pow_add_two_pow_two_pow {x y : ℤ} (hx : ¬2 ∣ x) (hx
   rw [pow_succ, mul_comm, pow_mul, Int.sq_mod_four_eq_one_of_odd hx.pow]
 #align int.two_pow_two_pow_add_two_pow_two_pow Int.two_pow_two_pow_add_two_pow_two_pow
 
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-Case conversion may be inaccurate. Consider using '#align int.two_pow_two_pow_sub_pow_two_pow Int.two_pow_two_pow_sub_pow_two_powₓ'. -/
 theorem Int.two_pow_two_pow_sub_pow_two_pow {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2 ∣ x) :
     multiplicity 2 (x ^ 2 ^ n - y ^ 2 ^ n) = multiplicity 2 (x - y) + n := by
   simp only [pow_two_pow_sub_pow_two_pow n, multiplicity.mul Int.prime_two,
@@ -437,12 +329,6 @@ theorem Int.two_pow_two_pow_sub_pow_two_pow {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x
     Finset.card_range, nsmul_one, Int.two_pow_two_pow_add_two_pow_two_pow hx hxy]
 #align int.two_pow_two_pow_sub_pow_two_pow Int.two_pow_two_pow_sub_pow_two_pow
 
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-Case conversion may be inaccurate. Consider using '#align int.two_pow_sub_pow' Int.two_pow_sub_pow'ₓ'. -/
 theorem Int.two_pow_sub_pow' {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2 ∣ x) :
     multiplicity 2 (x ^ n - y ^ n) = multiplicity 2 (x - y) + multiplicity (2 : ℤ) n :=
   by
@@ -467,12 +353,6 @@ theorem Int.two_pow_sub_pow' {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2
   exact mul_dvd_mul_left _ hpn
 #align int.two_pow_sub_pow' Int.two_pow_sub_pow'
 
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-Case conversion may be inaccurate. Consider using '#align int.two_pow_sub_pow Int.two_pow_sub_powₓ'. -/
 /-- **Lifting the exponent lemma** for `p = 2` -/
 theorem Int.two_pow_sub_pow {x y : ℤ} {n : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) (hn : Even n) :
     multiplicity 2 (x ^ n - y ^ n) + 1 =
@@ -505,12 +385,6 @@ theorem Int.two_pow_sub_pow {x y : ℤ} {n : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2
     simp only [Int.odd_iff_not_even, even_iff_two_dvd, hx, not_false_iff]
 #align int.two_pow_sub_pow Int.two_pow_sub_pow
 
-/- warning: nat.two_pow_sub_pow -> Nat.two_pow_sub_pow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nat.two_pow_sub_pow Nat.two_pow_sub_powₓ'. -/
 theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n : ℕ} (hn : Even n) :
     multiplicity 2 (x ^ n - y ^ n) + 1 =
       multiplicity 2 (x + y) + multiplicity 2 (x - y) + multiplicity 2 n :=

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

@@ -378,8 +378,7 @@ theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
   intro hx
   -- Replace `x : ℤ` with `y : zmod 4`
   replace hx : x % (2 : ℕ) = 1 % (2 : ℕ);
-  · rw [Int.odd_iff] at hx
-    norm_num [hx]
+  · rw [Int.odd_iff] at hx; norm_num [hx]
   calc
     x ^ 2 % (4 : ℕ) = 1 % (4 : ℕ) := _
     _ = 1 := by norm_num
@@ -413,9 +412,7 @@ theorem Int.two_pow_two_pow_add_two_pow_two_pow {x y : ℤ} (hx : ¬2 ∣ x) (hx
     exact hx_odd.pow.add_odd hy_odd.pow
   cases' i with i
   · intro hxy'
-    have : 2 * 2 ∣ 2 * x := by
-      convert dvd_add hxy hxy'
-      ring
+    have : 2 * 2 ∣ 2 * x := by convert dvd_add hxy hxy'; ring
     have : 2 ∣ x := (mul_dvd_mul_iff_left (by norm_num)).mp this
     contradiction
   suffices ∀ x : ℤ, Odd x → x ^ 2 ^ (i + 1) % 4 = 1
@@ -576,8 +573,7 @@ theorem pow_add_pow (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : ℕ} (hn : Odd n)
     padicValNat p (x ^ n + y ^ n) = padicValNat p (x + y) + padicValNat p n :=
   by
   cases y
-  · have := dvd_zero p
-    contradiction
+  · have := dvd_zero p; contradiction
   rw [← PartENat.natCast_inj, Nat.cast_add]
   iterate 3 rw [padicValNat_def, PartENat.natCast_get]
   · exact multiplicity.Nat.pow_add_pow hp.out hp1 hxy hx hn

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tian Chen, Mantas Bakšys
 
 ! This file was ported from Lean 3 source module number_theory.multiplicity
-! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
+! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.RingTheory.Ideal.QuotientOperations
 /-!
 # Multiplicity in Number Theory
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains results in number theory relating to multiplicity.
 
 ## Main statements

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

@@ -196,7 +196,7 @@ variable [IsDomain R] [@DecidableRel R (· ∣ ·)]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))] {p : R}, (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) -> (forall {x : R} {y : R}, (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) 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))))))) x y)) -> (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p x)) -> (forall {n : Nat}, (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p ((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 (CommRing.toRing.{u1} R _inst_1)))))))) n))) -> (Eq.{1} PartENat (multiplicity.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (fun (a : R) (b : R) => _inst_3 a b) 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 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 n))) (multiplicity.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (fun (a : R) (b : R) => _inst_3 a b) 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))))))) x y)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (fun (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2380 : R) (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2382 : R) => Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x._@.Mathlib.NumberTheory.Multiplicity._hyg.2380 x._@.Mathlib.NumberTheory.Multiplicity._hyg.2382)] {p : R}, (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)) p) -> (forall {x : R} {y : R}, (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p x)) -> (forall {n : Nat}, (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n))) -> (Eq.{1} PartENat (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) 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 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 n))) (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) p (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (fun (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2388 : R) (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2390 : R) => Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x._@.Mathlib.NumberTheory.Multiplicity._hyg.2388 x._@.Mathlib.NumberTheory.Multiplicity._hyg.2390)] {p : R}, (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)) p) -> (forall {x : R} {y : R}, (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p x)) -> (forall {n : Nat}, (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n))) -> (Eq.{1} PartENat (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) 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 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 n))) (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) p (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)))))
 Case conversion may be inaccurate. Consider using '#align multiplicity.pow_sub_pow_of_prime multiplicity.pow_sub_pow_of_primeₓ'. -/
 theorem pow_sub_pow_of_prime {p : R} (hp : Prime p) {x y : R} (hxy : p ∣ x - y) (hx : ¬p ∣ x)
     {n : ℕ} (hn : ¬p ∣ n) : multiplicity p (x ^ n - y ^ n) = multiplicity p (x - y) := by
@@ -212,7 +212,7 @@ include hp hp1 hxy hx
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} {p : Nat} [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))], (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p)) -> (Odd.{0} Nat Nat.semiring p) -> (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) 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))))))) x y)) -> (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) x)) -> (Eq.{1} PartENat (multiplicity.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (fun (a : R) (b : R) => _inst_3 a b) ((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 (CommRing.toRing.{u1} R _inst_1)))))))) p) (Finset.sum.{u1, 0} R Nat (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finset.range p) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{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 i) (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 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) p (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i))))) (OfNat.ofNat.{0} PartENat 1 (OfNat.mk.{0} PartENat 1 (One.one.{0} PartENat PartENat.hasOne))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} {p : Nat} [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (fun (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2580 : R) (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2582 : R) => Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x._@.Mathlib.NumberTheory.Multiplicity._hyg.2580 x._@.Mathlib.NumberTheory.Multiplicity._hyg.2582)], (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p)) -> (Odd.{0} Nat Nat.semiring p) -> (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) x)) -> (Eq.{1} PartENat (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (Finset.sum.{u1, 0} R Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finset.range p) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{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 (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x i) (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 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))))) (OfNat.ofNat.{0} PartENat 1 (One.toOfNat1.{0} PartENat PartENat.instOnePartENat)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} {p : Nat} [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (fun (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2588 : R) (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2590 : R) => Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x._@.Mathlib.NumberTheory.Multiplicity._hyg.2588 x._@.Mathlib.NumberTheory.Multiplicity._hyg.2590)], (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p)) -> (Odd.{0} Nat Nat.semiring p) -> (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) x)) -> (Eq.{1} PartENat (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (Finset.sum.{u1, 0} R Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finset.range p) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{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 (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x i) (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 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))))) (OfNat.ofNat.{0} PartENat 1 (One.toOfNat1.{0} PartENat PartENat.instOnePartENat)))
 Case conversion may be inaccurate. Consider using '#align multiplicity.geom_sum₂_eq_one multiplicity.geom_sum₂_eq_oneₓ'. -/
 theorem geom_sum₂_eq_one : multiplicity (↑p) (∑ i in range p, x ^ i * y ^ (p - 1 - i)) = 1 :=
   by
@@ -232,7 +232,7 @@ theorem geom_sum₂_eq_one : multiplicity (↑p) (∑ i in range p, x ^ i * y ^
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} {p : Nat} [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))], (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p)) -> (Odd.{0} Nat Nat.semiring p) -> (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) 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))))))) x y)) -> (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) x)) -> (Eq.{1} PartENat (multiplicity.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (fun (a : R) (b : R) => _inst_3 a b) ((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 (CommRing.toRing.{u1} R _inst_1)))))))) 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))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (multiplicity.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (fun (a : R) (b : R) => _inst_3 a b) ((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 (CommRing.toRing.{u1} R _inst_1)))))))) 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))))))) x y)) (OfNat.ofNat.{0} PartENat 1 (OfNat.mk.{0} PartENat 1 (One.one.{0} PartENat PartENat.hasOne)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} {p : Nat} [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (fun (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2869 : R) (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2871 : R) => Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x._@.Mathlib.NumberTheory.Multiplicity._hyg.2869 x._@.Mathlib.NumberTheory.Multiplicity._hyg.2871)], (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p)) -> (Odd.{0} Nat Nat.semiring p) -> (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) x)) -> (Eq.{1} PartENat (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (OfNat.ofNat.{0} PartENat 1 (One.toOfNat1.{0} PartENat PartENat.instOnePartENat))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} {p : Nat} [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (fun (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2877 : R) (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2879 : R) => Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x._@.Mathlib.NumberTheory.Multiplicity._hyg.2877 x._@.Mathlib.NumberTheory.Multiplicity._hyg.2879)], (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p)) -> (Odd.{0} Nat Nat.semiring p) -> (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) x)) -> (Eq.{1} PartENat (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (OfNat.ofNat.{0} PartENat 1 (One.toOfNat1.{0} PartENat PartENat.instOnePartENat))))
 Case conversion may be inaccurate. Consider using '#align multiplicity.pow_prime_sub_pow_prime multiplicity.pow_prime_sub_pow_primeₓ'. -/
 theorem pow_prime_sub_pow_prime :
     multiplicity (↑p) (x ^ p - y ^ p) = multiplicity (↑p) (x - y) + 1 := by
@@ -243,7 +243,7 @@ theorem pow_prime_sub_pow_prime :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} {p : Nat} [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))], (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p)) -> (Odd.{0} Nat Nat.semiring p) -> (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) 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))))))) x y)) -> (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) x)) -> (forall (a : Nat), Eq.{1} PartENat (multiplicity.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (fun (a : R) (b : R) => _inst_3 a b) ((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 (CommRing.toRing.{u1} R _inst_1)))))))) 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 (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p a)) (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 a)))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (multiplicity.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (fun (a : R) (b : R) => _inst_3 a b) ((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 (CommRing.toRing.{u1} R _inst_1)))))))) 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))))))) x y)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) a)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} {p : Nat} [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (fun (x._@.Mathlib.NumberTheory.Multiplicity._hyg.3009 : R) (x._@.Mathlib.NumberTheory.Multiplicity._hyg.3011 : R) => Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x._@.Mathlib.NumberTheory.Multiplicity._hyg.3009 x._@.Mathlib.NumberTheory.Multiplicity._hyg.3011)], (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p)) -> (Odd.{0} Nat Nat.semiring p) -> (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) x)) -> (forall (a : Nat), Eq.{1} PartENat (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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 (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p a)) (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 a)))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) a)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} {p : Nat} [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (fun (x._@.Mathlib.NumberTheory.Multiplicity._hyg.3017 : R) (x._@.Mathlib.NumberTheory.Multiplicity._hyg.3019 : R) => Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x._@.Mathlib.NumberTheory.Multiplicity._hyg.3017 x._@.Mathlib.NumberTheory.Multiplicity._hyg.3019)], (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p)) -> (Odd.{0} Nat Nat.semiring p) -> (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) x)) -> (forall (a : Nat), Eq.{1} PartENat (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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 (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p a)) (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 a)))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) a)))
 Case conversion may be inaccurate. Consider using '#align multiplicity.pow_prime_pow_sub_pow_prime_pow multiplicity.pow_prime_pow_sub_pow_prime_powₓ'. -/
 theorem pow_prime_pow_sub_pow_prime_pow (a : ℕ) :
     multiplicity (↑p) (x ^ p ^ a - y ^ p ^ a) = multiplicity (↑p) (x - y) + a :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -41,6 +41,12 @@ section CommRing
 
 variable [CommRing R] {a b x y : R}
 
+/- warning: dvd_geom_sum₂_iff_of_dvd_sub -> dvd_geom_sum₂_iff_of_dvd_sub 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 dvd_geom_sum₂_iff_of_dvd_sub dvd_geom_sum₂_iff_of_dvd_subₓ'. -/
 theorem dvd_geom_sum₂_iff_of_dvd_sub {x y p : R} (h : p ∣ x - y) :
     (p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i)) ↔ p ∣ n * y ^ (n - 1) :=
   by
@@ -49,16 +55,34 @@ theorem dvd_geom_sum₂_iff_of_dvd_sub {x y p : R} (h : p ∣ x - y) :
     _root_.map_mul, map_pow, map_natCast]
 #align dvd_geom_sum₂_iff_of_dvd_sub dvd_geom_sum₂_iff_of_dvd_sub
 
+/- warning: dvd_geom_sum₂_iff_of_dvd_sub' -> dvd_geom_sum₂_iff_of_dvd_sub' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align dvd_geom_sum₂_iff_of_dvd_sub' dvd_geom_sum₂_iff_of_dvd_sub'ₓ'. -/
 theorem dvd_geom_sum₂_iff_of_dvd_sub' {x y p : R} (h : p ∣ x - y) :
     (p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i)) ↔ p ∣ n * x ^ (n - 1) := by
   rw [geom_sum₂_comm, dvd_geom_sum₂_iff_of_dvd_sub] <;> simpa using h.neg_right
 #align dvd_geom_sum₂_iff_of_dvd_sub' dvd_geom_sum₂_iff_of_dvd_sub'
 
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+Case conversion may be inaccurate. Consider using '#align dvd_geom_sum₂_self dvd_geom_sum₂_selfₓ'. -/
 theorem dvd_geom_sum₂_self {x y : R} (h : ↑n ∣ x - y) :
     ↑n ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i) :=
   (dvd_geom_sum₂_iff_of_dvd_sub h).mpr (dvd_mul_right _ _)
 #align dvd_geom_sum₂_self dvd_geom_sum₂_self
 
+/- warning: sq_dvd_add_pow_sub_sub -> sq_dvd_add_pow_sub_sub is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align sq_dvd_add_pow_sub_sub sq_dvd_add_pow_sub_subₓ'. -/
 theorem sq_dvd_add_pow_sub_sub (p x : R) (n : ℕ) :
     p ^ 2 ∣ (x + p) ^ n - x ^ (n - 1) * p * n - x ^ n :=
   by
@@ -79,6 +103,12 @@ theorem sq_dvd_add_pow_sub_sub (p x : R) (n : ℕ) :
         
 #align sq_dvd_add_pow_sub_sub sq_dvd_add_pow_sub_sub
 
+/- warning: not_dvd_geom_sum₂ -> not_dvd_geom_sum₂ is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {n : Nat} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} {p : R}, (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) -> (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) 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))))))) x y)) -> (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p x)) -> (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p ((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 (CommRing.toRing.{u1} R _inst_1)))))))) n))) -> (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p (Finset.sum.{u1, 0} R Nat (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finset.range n) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{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 i) (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 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i))))))
+but is expected to have type
+  forall {R : Type.{u1}} {n : Nat} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} {p : R}, (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) -> (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p x)) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n))) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p (Finset.sum.{u1, 0} R Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finset.range n) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{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 (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x i) (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 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))))))
+Case conversion may be inaccurate. Consider using '#align not_dvd_geom_sum₂ not_dvd_geom_sum₂ₓ'. -/
 theorem not_dvd_geom_sum₂ {p : R} (hp : Prime p) (hxy : p ∣ x - y) (hx : ¬p ∣ x) (hn : ¬p ∣ n) :
     ¬p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i) := fun h =>
   hx <|
@@ -87,6 +117,12 @@ theorem not_dvd_geom_sum₂ {p : R} (hp : Prime p) (hxy : p ∣ x - y) (hx : ¬p
 
 variable {p : ℕ} (a b)
 
+/- warning: odd_sq_dvd_geom_sum₂_sub -> odd_sq_dvd_geom_sum₂_sub is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : R) (b : R) {p : Nat}, (Odd.{0} Nat Nat.semiring p) -> (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{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)))) ((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 (CommRing.toRing.{u1} R _inst_1)))))))) p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (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))))))) (Finset.sum.{u1, 0} R Nat (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finset.range p) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{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)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) a (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) b)) i) (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)))) a (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) p (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) 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)))) a (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) p (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (a : R) (b : R) {p : Nat}, (Odd.{0} Nat Nat.semiring p) -> (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{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)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Finset.sum.{u1, 0} R Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finset.range p) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{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 (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) a (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) b)) i) (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)))))) a (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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)))))) a (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+Case conversion may be inaccurate. Consider using '#align odd_sq_dvd_geom_sum₂_sub odd_sq_dvd_geom_sum₂_subₓ'. -/
 theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
     ↑p ^ 2 ∣ (∑ i in range p, (a + p * b) ^ i * a ^ (p - 1 - i)) - p * a ^ (p - 1) :=
   by
@@ -156,6 +192,12 @@ section IntegralDomain
 
 variable [IsDomain R] [@DecidableRel R (· ∣ ·)]
 
+/- warning: multiplicity.pow_sub_pow_of_prime -> multiplicity.pow_sub_pow_of_prime is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))] {p : R}, (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) -> (forall {x : R} {y : R}, (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) 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))))))) x y)) -> (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p x)) -> (forall {n : Nat}, (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p ((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 (CommRing.toRing.{u1} R _inst_1)))))))) n))) -> (Eq.{1} PartENat (multiplicity.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (fun (a : R) (b : R) => _inst_3 a b) 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 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 n))) (multiplicity.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (fun (a : R) (b : R) => _inst_3 a b) 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))))))) x y)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (fun (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2380 : R) (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2382 : R) => Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x._@.Mathlib.NumberTheory.Multiplicity._hyg.2380 x._@.Mathlib.NumberTheory.Multiplicity._hyg.2382)] {p : R}, (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)) p) -> (forall {x : R} {y : R}, (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p x)) -> (forall {n : Nat}, (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) p (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n))) -> (Eq.{1} PartENat (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) 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 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 n))) (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) p (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)))))
+Case conversion may be inaccurate. Consider using '#align multiplicity.pow_sub_pow_of_prime multiplicity.pow_sub_pow_of_primeₓ'. -/
 theorem pow_sub_pow_of_prime {p : R} (hp : Prime p) {x y : R} (hxy : p ∣ x - y) (hx : ¬p ∣ x)
     {n : ℕ} (hn : ¬p ∣ n) : multiplicity p (x ^ n - y ^ n) = multiplicity p (x - y) := by
   rw [← geom_sum₂_mul, multiplicity.mul hp, multiplicity_eq_zero.2 (not_dvd_geom_sum₂ hp hxy hx hn),
@@ -166,6 +208,12 @@ variable (hp : Prime (p : R)) (hp1 : Odd p) (hxy : ↑p ∣ x - y) (hx : ¬↑p
 
 include hp hp1 hxy hx
 
+/- warning: multiplicity.geom_sum₂_eq_one -> multiplicity.geom_sum₂_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} {p : Nat} [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))], (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p)) -> (Odd.{0} Nat Nat.semiring p) -> (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) 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))))))) x y)) -> (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{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 (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) x)) -> (Eq.{1} PartENat (multiplicity.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (fun (a : R) (b : R) => _inst_3 a b) ((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 (CommRing.toRing.{u1} R _inst_1)))))))) p) (Finset.sum.{u1, 0} R Nat (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finset.range p) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{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 i) (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 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) p (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i))))) (OfNat.ofNat.{0} PartENat 1 (OfNat.mk.{0} PartENat 1 (One.one.{0} PartENat PartENat.hasOne))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} {p : Nat} [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : DecidableRel.{succ u1} R (fun (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2580 : R) (x._@.Mathlib.NumberTheory.Multiplicity._hyg.2582 : R) => Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x._@.Mathlib.NumberTheory.Multiplicity._hyg.2580 x._@.Mathlib.NumberTheory.Multiplicity._hyg.2582)], (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p)) -> (Odd.{0} Nat Nat.semiring p) -> (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y)) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) x)) -> (Eq.{1} PartENat (multiplicity.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : R) (b : R) => _inst_3 a b) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (Finset.sum.{u1, 0} R Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finset.range p) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{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 (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x i) (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 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))))) (OfNat.ofNat.{0} PartENat 1 (One.toOfNat1.{0} PartENat PartENat.instOnePartENat)))
+Case conversion may be inaccurate. Consider using '#align multiplicity.geom_sum₂_eq_one multiplicity.geom_sum₂_eq_oneₓ'. -/
 theorem geom_sum₂_eq_one : multiplicity (↑p) (∑ i in range p, x ^ i * y ^ (p - 1 - i)) = 1 :=
   by
   rw [← Nat.cast_one]
@@ -180,11 +228,23 @@ theorem geom_sum₂_eq_one : multiplicity (↑p) (∑ i in range p, x ^ i * y ^
   exact mt hp.dvd_of_dvd_pow hx
 #align multiplicity.geom_sum₂_eq_one multiplicity.geom_sum₂_eq_one
 
+/- warning: multiplicity.pow_prime_sub_pow_prime -> multiplicity.pow_prime_sub_pow_prime 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 multiplicity.pow_prime_sub_pow_prime multiplicity.pow_prime_sub_pow_primeₓ'. -/
 theorem pow_prime_sub_pow_prime :
     multiplicity (↑p) (x ^ p - y ^ p) = multiplicity (↑p) (x - y) + 1 := by
   rw [← geom_sum₂_mul, multiplicity.mul hp, geom_sum₂_eq_one hp hp1 hxy hx, add_comm]
 #align multiplicity.pow_prime_sub_pow_prime multiplicity.pow_prime_sub_pow_prime
 
+/- warning: multiplicity.pow_prime_pow_sub_pow_prime_pow -> multiplicity.pow_prime_pow_sub_pow_prime_pow 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 multiplicity.pow_prime_pow_sub_pow_prime_pow multiplicity.pow_prime_pow_sub_pow_prime_powₓ'. -/
 theorem pow_prime_pow_sub_pow_prime_pow (a : ℕ) :
     multiplicity (↑p) (x ^ p ^ a - y ^ p ^ a) = multiplicity (↑p) (x - y) + a :=
   by
@@ -205,6 +265,12 @@ variable (hp : Nat.Prime p) (hp1 : Odd p)
 
 include hp hp1
 
+/- warning: multiplicity.int.pow_sub_pow -> multiplicity.Int.pow_sub_pow is a dubious translation:
+lean 3 declaration is
+  forall {p : Nat}, (Nat.Prime p) -> (Odd.{0} Nat Nat.semiring p) -> (forall {x : Int} {y : Int}, (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) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) x y)) -> (Not (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) x)) -> (forall (n : Nat), Eq.{1} PartENat (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) ((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) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) x n) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) y n))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) ((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) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) x y)) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidableDvd a b) p n))))
+but is expected to have type
+  forall {p : Nat}, (Nat.Prime p) -> (Odd.{0} Nat Nat.semiring p) -> (forall {x : Int} {y : Int}, (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) x y)) -> (Not (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) x)) -> (forall (n : Nat), Eq.{1} PartENat (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (Nat.cast.{0} Int instNatCastInt p) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat x n) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat y n))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (Nat.cast.{0} Int instNatCastInt p) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) x y)) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidable_dvd a b) p n))))
+Case conversion may be inaccurate. Consider using '#align multiplicity.int.pow_sub_pow multiplicity.Int.pow_sub_powₓ'. -/
 /-- **Lifting the exponent lemma** for odd primes. -/
 theorem Int.pow_sub_pow {x y : ℤ} (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x) (n : ℕ) :
     multiplicity (↑p) (x ^ n - y ^ n) = multiplicity (↑p) (x - y) + multiplicity p n :=
@@ -225,6 +291,12 @@ theorem Int.pow_sub_pow {x y : ℤ} (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x) (
     rwa [pow_succ', mul_assoc]
 #align multiplicity.int.pow_sub_pow multiplicity.Int.pow_sub_pow
 
+/- warning: multiplicity.int.pow_add_pow -> multiplicity.Int.pow_add_pow is a dubious translation:
+lean 3 declaration is
+  forall {p : Nat}, (Nat.Prime p) -> (Odd.{0} Nat Nat.semiring p) -> (forall {x : Int} {y : Int}, (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) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) x y)) -> (Not (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) x)) -> (forall {n : Nat}, (Odd.{0} Nat Nat.semiring n) -> (Eq.{1} PartENat (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) ((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) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) x n) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) y n))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) ((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) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) x y)) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidableDvd a b) p n)))))
+but is expected to have type
+  forall {p : Nat}, (Nat.Prime p) -> (Odd.{0} Nat Nat.semiring p) -> (forall {x : Int} {y : Int}, (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) x y)) -> (Not (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) x)) -> (forall {n : Nat}, (Odd.{0} Nat Nat.semiring n) -> (Eq.{1} PartENat (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (Nat.cast.{0} Int instNatCastInt p) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat x n) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat y n))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (Nat.cast.{0} Int instNatCastInt p) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) x y)) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidable_dvd a b) p n)))))
+Case conversion may be inaccurate. Consider using '#align multiplicity.int.pow_add_pow multiplicity.Int.pow_add_powₓ'. -/
 theorem Int.pow_add_pow {x y : ℤ} (hxy : ↑p ∣ x + y) (hx : ¬↑p ∣ x) {n : ℕ} (hn : Odd n) :
     multiplicity (↑p) (x ^ n + y ^ n) = multiplicity (↑p) (x + y) + multiplicity p n :=
   by
@@ -233,6 +305,12 @@ theorem Int.pow_add_pow {x y : ℤ} (hxy : ↑p ∣ x + y) (hx : ¬↑p ∣ x) {
   exact int.pow_sub_pow hp hp1 hxy hx n
 #align multiplicity.int.pow_add_pow multiplicity.Int.pow_add_pow
 
+/- warning: multiplicity.nat.pow_sub_pow -> multiplicity.Nat.pow_sub_pow is a dubious translation:
+lean 3 declaration is
+  forall {p : Nat}, (Nat.Prime p) -> (Odd.{0} Nat Nat.semiring p) -> (forall {x : Nat} {y : Nat}, (Dvd.Dvd.{0} Nat Nat.hasDvd p (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) x y)) -> (Not (Dvd.Dvd.{0} Nat Nat.hasDvd p x)) -> (forall (n : Nat), Eq.{1} PartENat (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidableDvd a b) p (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)) x n) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) y n))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidableDvd a b) p (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) x y)) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidableDvd a b) p n))))
+but is expected to have type
+  forall {p : Nat}, (Nat.Prime p) -> (Odd.{0} Nat Nat.semiring p) -> (forall {x : Nat} {y : Nat}, (Dvd.dvd.{0} Nat Nat.instDvdNat p (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) x y)) -> (Not (Dvd.dvd.{0} Nat Nat.instDvdNat p x)) -> (forall (n : Nat), Eq.{1} PartENat (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidable_dvd a b) p (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) x n) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) y n))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidable_dvd a b) p (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) x y)) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidable_dvd a b) p n))))
+Case conversion may be inaccurate. Consider using '#align multiplicity.nat.pow_sub_pow multiplicity.Nat.pow_sub_powₓ'. -/
 theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : ℕ) :
     multiplicity p (x ^ n - y ^ n) = multiplicity p (x - y) + multiplicity p n :=
   by
@@ -248,6 +326,12 @@ theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : 
       PartENat.top_add]
 #align multiplicity.nat.pow_sub_pow multiplicity.Nat.pow_sub_pow
 
+/- warning: multiplicity.nat.pow_add_pow -> multiplicity.Nat.pow_add_pow is a dubious translation:
+lean 3 declaration is
+  forall {p : Nat}, (Nat.Prime p) -> (Odd.{0} Nat Nat.semiring p) -> (forall {x : Nat} {y : Nat}, (Dvd.Dvd.{0} Nat Nat.hasDvd p (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) x y)) -> (Not (Dvd.Dvd.{0} Nat Nat.hasDvd p x)) -> (forall {n : Nat}, (Odd.{0} Nat Nat.semiring n) -> (Eq.{1} PartENat (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidableDvd a b) p (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) x n) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) y n))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidableDvd a b) p (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) x y)) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidableDvd a b) p n)))))
+but is expected to have type
+  forall {p : Nat}, (Nat.Prime p) -> (Odd.{0} Nat Nat.semiring p) -> (forall {x : Nat} {y : Nat}, (Dvd.dvd.{0} Nat Nat.instDvdNat p (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x y)) -> (Not (Dvd.dvd.{0} Nat Nat.instDvdNat p x)) -> (forall {n : Nat}, (Odd.{0} Nat Nat.semiring n) -> (Eq.{1} PartENat (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidable_dvd a b) p (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) x n) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) y n))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidable_dvd a b) p (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x y)) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidable_dvd a b) p n)))))
+Case conversion may be inaccurate. Consider using '#align multiplicity.nat.pow_add_pow multiplicity.Nat.pow_add_powₓ'. -/
 theorem Nat.pow_add_pow {x y : ℕ} (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : ℕ} (hn : Odd n) :
     multiplicity p (x ^ n + y ^ n) = multiplicity p (x + y) + multiplicity p n :=
   by
@@ -263,6 +347,12 @@ end multiplicity
 
 end CommRing
 
+/- warning: pow_two_pow_sub_pow_two_pow -> pow_two_pow_sub_pow_two_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} (n : Nat), Eq.{succ u1} R (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)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 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)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finset.prod.{u1, 0} R Nat (CommRing.toCommMonoid.{u1} R _inst_1) (Finset.range n) (fun (i : Nat) => HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{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)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) i)) (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)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) i)))) (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))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R} (n : Nat), Eq.{succ u1} R (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) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 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) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finset.prod.{u1, 0} R Nat (CommRing.toCommMonoid.{u1} R _inst_1) (Finset.range n) (fun (i : Nat) => HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{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 (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) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) i)) (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) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) i)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) x y))
+Case conversion may be inaccurate. Consider using '#align pow_two_pow_sub_pow_two_pow pow_two_pow_sub_pow_two_powₓ'. -/
 theorem pow_two_pow_sub_pow_two_pow [CommRing R] {x y : R} (n : ℕ) :
     x ^ 2 ^ n - y ^ 2 ^ n = (∏ i in Finset.range n, x ^ 2 ^ i + y ^ 2 ^ i) * (x - y) :=
   by
@@ -273,6 +363,12 @@ theorem pow_two_pow_sub_pow_two_pow [CommRing R] {x y : R} (n : ℕ) :
     · ring1
 #align pow_two_pow_sub_pow_two_pow pow_two_pow_sub_pow_two_pow
 
+/- warning: int.sq_mod_four_eq_one_of_odd -> Int.sq_mod_four_eq_one_of_odd is a dubious translation:
+lean 3 declaration is
+  forall {x : Int}, (Odd.{0} Int Int.semiring x) -> (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Int 4 (OfNat.mk.{0} Int 4 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))
+but is expected to have type
+  forall {x : Int}, (Odd.{0} Int Int.instSemiringInt x) -> (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Int 4 (instOfNatInt 4))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))
+Case conversion may be inaccurate. Consider using '#align int.sq_mod_four_eq_one_of_odd Int.sq_mod_four_eq_one_of_oddₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:80:4: warning: unsupported fin_cases 'using hy' clause -/
 theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
   by
@@ -297,6 +393,12 @@ theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
     decide
 #align int.sq_mod_four_eq_one_of_odd Int.sq_mod_four_eq_one_of_odd
 
+/- warning: int.two_pow_two_pow_add_two_pow_two_pow -> Int.two_pow_two_pow_add_two_pow_two_pow is a dubious translation:
+lean 3 declaration is
+  forall {x : Int} {y : Int}, (Not (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) x)) -> (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) (OfNat.ofNat.{0} Int 4 (OfNat.mk.{0} Int 4 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) x y)) -> (forall (i : Nat), Eq.{1} PartENat (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) i)) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) i)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))
+but is expected to have type
+  forall {x : Int} {y : Int}, (Not (Dvd.dvd.{0} Int Int.instDvdInt (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) x)) -> (Dvd.dvd.{0} Int Int.instDvdInt (OfNat.ofNat.{0} Int 4 (instOfNatInt 4)) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) x y)) -> (forall (i : Nat), Eq.{1} PartENat (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) i)) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) i)))) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
+Case conversion may be inaccurate. Consider using '#align int.two_pow_two_pow_add_two_pow_two_pow Int.two_pow_two_pow_add_two_pow_two_powₓ'. -/
 theorem Int.two_pow_two_pow_add_two_pow_two_pow {x y : ℤ} (hx : ¬2 ∣ x) (hxy : 4 ∣ x - y) (i : ℕ) :
     multiplicity 2 (x ^ 2 ^ i + y ^ 2 ^ i) = ↑(1 : ℕ) :=
   by
@@ -322,6 +424,12 @@ theorem Int.two_pow_two_pow_add_two_pow_two_pow {x y : ℤ} (hx : ¬2 ∣ x) (hx
   rw [pow_succ, mul_comm, pow_mul, Int.sq_mod_four_eq_one_of_odd hx.pow]
 #align int.two_pow_two_pow_add_two_pow_two_pow Int.two_pow_two_pow_add_two_pow_two_pow
 
+/- warning: int.two_pow_two_pow_sub_pow_two_pow -> Int.two_pow_two_pow_sub_pow_two_pow is a dubious translation:
+lean 3 declaration is
+  forall {x : Int} {y : Int} (n : Nat), (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) (OfNat.ofNat.{0} Int 4 (OfNat.mk.{0} Int 4 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) x y)) -> (Not (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) x)) -> (Eq.{1} PartENat (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n)) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n)))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) x y)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat PartENat (HasLiftT.mk.{1, 1} Nat PartENat (CoeTCₓ.coe.{1, 1} Nat PartENat (Nat.castCoe.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne))))) n)))
+but is expected to have type
+  forall {x : Int} {y : Int} (n : Nat), (Dvd.dvd.{0} Int Int.instDvdInt (OfNat.ofNat.{0} Int 4 (instOfNatInt 4)) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) x y)) -> (Not (Dvd.dvd.{0} Int Int.instDvdInt (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) x)) -> (Eq.{1} PartENat (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n)) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat y (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n)))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) x y)) (Nat.cast.{0} PartENat (AddMonoidWithOne.toNatCast.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)) n)))
+Case conversion may be inaccurate. Consider using '#align int.two_pow_two_pow_sub_pow_two_pow Int.two_pow_two_pow_sub_pow_two_powₓ'. -/
 theorem Int.two_pow_two_pow_sub_pow_two_pow {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2 ∣ x) :
     multiplicity 2 (x ^ 2 ^ n - y ^ 2 ^ n) = multiplicity 2 (x - y) + n := by
   simp only [pow_two_pow_sub_pow_two_pow n, multiplicity.mul Int.prime_two,
@@ -329,6 +437,12 @@ theorem Int.two_pow_two_pow_sub_pow_two_pow {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x
     Finset.card_range, nsmul_one, Int.two_pow_two_pow_add_two_pow_two_pow hx hxy]
 #align int.two_pow_two_pow_sub_pow_two_pow Int.two_pow_two_pow_sub_pow_two_pow
 
+/- warning: int.two_pow_sub_pow' -> Int.two_pow_sub_pow' is a dubious translation:
+lean 3 declaration is
+  forall {x : Int} {y : Int} (n : Nat), (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) (OfNat.ofNat.{0} Int 4 (OfNat.mk.{0} Int 4 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) x y)) -> (Not (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) x)) -> (Eq.{1} PartENat (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) x n) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) y n))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) x y)) (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n))))
+but is expected to have type
+  forall {x : Int} {y : Int} (n : Nat), (Dvd.dvd.{0} Int Int.instDvdInt (OfNat.ofNat.{0} Int 4 (instOfNatInt 4)) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) x y)) -> (Not (Dvd.dvd.{0} Int Int.instDvdInt (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) x)) -> (Eq.{1} PartENat (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat x n) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat y n))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) x y)) (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) (Nat.cast.{0} Int instNatCastInt n))))
+Case conversion may be inaccurate. Consider using '#align int.two_pow_sub_pow' Int.two_pow_sub_pow'ₓ'. -/
 theorem Int.two_pow_sub_pow' {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2 ∣ x) :
     multiplicity 2 (x ^ n - y ^ n) = multiplicity 2 (x - y) + multiplicity (2 : ℤ) n :=
   by
@@ -353,6 +467,12 @@ theorem Int.two_pow_sub_pow' {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2
   exact mul_dvd_mul_left _ hpn
 #align int.two_pow_sub_pow' Int.two_pow_sub_pow'
 
+/- warning: int.two_pow_sub_pow -> Int.two_pow_sub_pow is a dubious translation:
+lean 3 declaration is
+  forall {x : Int} {y : Int} {n : Nat}, (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) x y)) -> (Not (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) x)) -> (Even.{0} Nat Nat.hasAdd n) -> (Eq.{1} PartENat (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) x n) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) y n))) (OfNat.ofNat.{0} PartENat 1 (OfNat.mk.{0} PartENat 1 (One.one.{0} PartENat PartENat.hasOne)))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) x y)) (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) x y))) (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n))))
+but is expected to have type
+  forall {x : Int} {y : Int} {n : Nat}, (Dvd.dvd.{0} Int Int.instDvdInt (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) x y)) -> (Not (Dvd.dvd.{0} Int Int.instDvdInt (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) x)) -> (Even.{0} Nat instAddNat n) -> (Eq.{1} PartENat (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat x n) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat y n))) (OfNat.ofNat.{0} PartENat 1 (One.toOfNat1.{0} PartENat PartENat.instOnePartENat))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) x y)) (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) x y))) (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) (Nat.cast.{0} Int instNatCastInt n))))
+Case conversion may be inaccurate. Consider using '#align int.two_pow_sub_pow Int.two_pow_sub_powₓ'. -/
 /-- **Lifting the exponent lemma** for `p = 2` -/
 theorem Int.two_pow_sub_pow {x y : ℤ} {n : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) (hn : Even n) :
     multiplicity 2 (x ^ n - y ^ n) + 1 =
@@ -385,6 +505,12 @@ theorem Int.two_pow_sub_pow {x y : ℤ} {n : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2
     simp only [Int.odd_iff_not_even, even_iff_two_dvd, hx, not_false_iff]
 #align int.two_pow_sub_pow Int.two_pow_sub_pow
 
+/- warning: nat.two_pow_sub_pow -> Nat.two_pow_sub_pow is a dubious translation:
+lean 3 declaration is
+  forall {x : Nat} {y : Nat}, (Dvd.Dvd.{0} Nat Nat.hasDvd (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) x y)) -> (Not (Dvd.Dvd.{0} Nat Nat.hasDvd (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) x)) -> (forall {n : Nat}, (Even.{0} Nat Nat.hasAdd n) -> (Eq.{1} PartENat (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidableDvd a b) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (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)) x n) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) y n))) (OfNat.ofNat.{0} PartENat 1 (OfNat.mk.{0} PartENat 1 (One.one.{0} PartENat PartENat.hasOne)))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.hasAdd) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidableDvd a b) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) x y)) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidableDvd a b) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) x y))) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidableDvd a b) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n))))
+but is expected to have type
+  forall {x : Nat} {y : Nat}, (Dvd.dvd.{0} Nat Nat.instDvdNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) x y)) -> (Not (Dvd.dvd.{0} Nat Nat.instDvdNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) x)) -> (forall {n : Nat}, (Even.{0} Nat instAddNat n) -> (Eq.{1} PartENat (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidable_dvd a b) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) x n) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) y n))) (OfNat.ofNat.{0} PartENat 1 (One.toOfNat1.{0} PartENat PartENat.instOnePartENat))) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (HAdd.hAdd.{0, 0, 0} PartENat PartENat PartENat (instHAdd.{0} PartENat PartENat.instAddPartENat) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidable_dvd a b) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x y)) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidable_dvd a b) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) x y))) (multiplicity.{0} Nat Nat.monoid (fun (a : Nat) (b : Nat) => Nat.decidable_dvd a b) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n))))
+Case conversion may be inaccurate. Consider using '#align nat.two_pow_sub_pow Nat.two_pow_sub_powₓ'. -/
 theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n : ℕ} (hn : Even n) :
     multiplicity 2 (x ^ n - y ^ n) + 1 =
       multiplicity 2 (x + y) + multiplicity 2 (x - y) + multiplicity 2 n :=
@@ -409,6 +535,7 @@ namespace padicValNat
 
 variable {x y : ℕ}
 
+#print padicValNat.pow_two_sub_pow /-
 theorem pow_two_sub_pow (hyx : y < x) (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n : ℕ} (hn : 0 < n)
     (hneven : Even n) :
     padicValNat 2 (x ^ n - y ^ n) + 1 =
@@ -422,11 +549,13 @@ theorem pow_two_sub_pow (hyx : y < x) (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n :
   · linarith
   · simp only [tsub_pos_iff_lt, pow_lt_pow_of_lt_left hyx (@zero_le' _ y _) hn]
 #align padic_val_nat.pow_two_sub_pow padicValNat.pow_two_sub_pow
+-/
 
 variable {p : ℕ} [hp : Fact p.Prime] (hp1 : Odd p)
 
 include hp hp1
 
+#print padicValNat.pow_sub_pow /-
 theorem pow_sub_pow (hyx : y < x) (hxy : p ∣ x - y) (hx : ¬p ∣ x) {n : ℕ} (hn : 0 < n) :
     padicValNat p (x ^ n - y ^ n) = padicValNat p (x - y) + padicValNat p n :=
   by
@@ -437,7 +566,9 @@ theorem pow_sub_pow (hyx : y < x) (hxy : p ∣ x - y) (hx : ¬p ∣ x) {n : ℕ}
   · exact Nat.sub_pos_of_lt hyx
   · exact Nat.sub_pos_of_lt (Nat.pow_lt_pow_of_lt_left hyx hn)
 #align padic_val_nat.pow_sub_pow padicValNat.pow_sub_pow
+-/
 
+#print padicValNat.pow_add_pow /-
 theorem pow_add_pow (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : ℕ} (hn : Odd n) :
     padicValNat p (x ^ n + y ^ n) = padicValNat p (x + y) + padicValNat p n :=
   by
@@ -451,6 +582,7 @@ theorem pow_add_pow (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : ℕ} (hn : Odd n)
   · simp only [add_pos_iff, Nat.succ_pos', or_true_iff]
   · exact Nat.lt_add_left _ _ _ (pow_pos y.succ_pos _)
 #align padic_val_nat.pow_add_pow padicValNat.pow_add_pow
+-/
 
 end padicValNat
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tian Chen, Mantas Bakšys
 
 ! This file was ported from Lean 3 source module number_theory.multiplicity
-! leanprover-community/mathlib commit 76de8ae01554c3b37d66544866659ff174e66e1f
+! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -51,7 +51,7 @@ theorem dvd_geom_sum₂_iff_of_dvd_sub {x y p : R} (h : p ∣ x - y) :
 
 theorem dvd_geom_sum₂_iff_of_dvd_sub' {x y p : R} (h : p ∣ x - y) :
     (p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i)) ↔ p ∣ n * x ^ (n - 1) := by
-  rw [geom_sum₂_comm, dvd_geom_sum₂_iff_of_dvd_sub] <;> simpa using (dvd_neg _ _).mpr h
+  rw [geom_sum₂_comm, dvd_geom_sum₂_iff_of_dvd_sub] <;> simpa using h.neg_right
 #align dvd_geom_sum₂_iff_of_dvd_sub' dvd_geom_sum₂_iff_of_dvd_sub'
 
 theorem dvd_geom_sum₂_self {x y : R} (h : ↑n ∣ x - y) :

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tian Chen, Mantas Bakšys
 
 ! This file was ported from Lean 3 source module number_theory.multiplicity
-! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
+! leanprover-community/mathlib commit 76de8ae01554c3b37d66544866659ff174e66e1f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -289,6 +289,7 @@ theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
   push_cast
   rw [← map_intCast (ZMod.castHom (show 2 ∣ 4 by norm_num) (ZMod 2)) x] at hx
   set y : ZMod 4 := x
+  change ZMod.castHom _ (ZMod 2) y = _ at hx
   -- Now we can just consider each of the 4 possible values for y
         fin_cases y <;>
         rw [hy] at hx⊢ <;>

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

@@ -285,7 +285,7 @@ theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 :=
     x ^ 2 % (4 : ℕ) = 1 % (4 : ℕ) := _
     _ = 1 := by norm_num
     
-  rw [← ZMod.int_coe_eq_int_coe_iff'] at hx⊢
+  rw [← ZMod.int_cast_eq_int_cast_iff'] at hx⊢
   push_cast
   rw [← map_intCast (ZMod.castHom (show 2 ∣ 4 by norm_num) (ZMod 2)) x] at hx
   set y : ZMod 4 := x

mathlib commit https://github.com/leanprover-community/mathlib/commit/f24cc2891c0e328f0ee8c57387103aa462c44b5e

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tian Chen, Mantas Bakšys
 
 ! This file was ported from Lean 3 source module number_theory.multiplicity
-! leanprover-community/mathlib commit 3d32bf9cef95940e3fe1ca0dd2412e0f21579f46
+! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -12,6 +12,7 @@ import Mathbin.Algebra.GeomSum
 import Mathbin.Data.Int.Parity
 import Mathbin.Data.Zmod.Basic
 import Mathbin.NumberTheory.Padics.PadicVal
+import Mathbin.RingTheory.Ideal.QuotientOperations
 
 /-!
 # Multiplicity in Number Theory

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

@@ -62,7 +62,7 @@ theorem sq_dvd_add_pow_sub_sub (p x : R) (n : ℕ) :
     p ^ 2 ∣ (x + p) ^ n - x ^ (n - 1) * p * n - x ^ n :=
   by
   cases n
-  · simp only [pow_zero, Nat.cast_zero, mul_zero, sub_zero, sub_self, dvd_zero]
+  · simp only [pow_zero, Nat.cast_zero, MulZeroClass.mul_zero, sub_zero, sub_self, dvd_zero]
   · simp only [Nat.succ_sub_succ_eq_sub, tsub_zero, Nat.cast_succ, add_pow, Finset.sum_range_succ,
       Nat.choose_self, Nat.succ_sub _, tsub_self, pow_one, Nat.choose_succ_self_right, pow_zero,
       mul_one, Nat.cast_zero, zero_add, Nat.succ_eq_add_one]
@@ -131,7 +131,7 @@ theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
       simp only [Finset.mul_sum, ← mul_assoc, ← pow_add]
       rw [Finset.sum_congr rfl]
       rintro (⟨⟩ | ⟨x⟩) hx
-      · rw [Nat.cast_zero, mul_zero, mul_zero]
+      · rw [Nat.cast_zero, MulZeroClass.mul_zero, MulZeroClass.mul_zero]
       · have : x.succ - 1 + (p - 1 - x.succ) = p - 2 :=
           by
           rw [← Nat.add_sub_assoc (Nat.le_pred_of_lt (finset.mem_range.mp hx))]

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

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

@@ -345,8 +345,8 @@ theorem Int.two_pow_sub_pow {x y : ℤ} {n : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2
     · simp only [Int.odd_iff_not_even, even_iff_two_dvd, hx, not_false_iff]
   rw [Int.two_pow_sub_pow' d hxy4 _, sq_sub_sq, ← Int.ofNat_mul_out, multiplicity.mul Int.prime_two,
     multiplicity.mul Int.prime_two]
-  suffices multiplicity (2 : ℤ) ↑(2 : ℕ) = 1 by rw [this, add_comm (1 : PartENat), ← add_assoc]
-  · norm_cast
+  · suffices multiplicity (2 : ℤ) ↑(2 : ℕ) = 1 by rw [this, add_comm (1 : PartENat), ← add_assoc]
+    norm_cast
     rw [multiplicity.multiplicity_self _ _]
     · apply Prime.not_unit
       simp only [← Nat.prime_iff, Nat.prime_two]

This is less exhaustive than its sibling #11486 because edge cases are harder to classify. No fundamental difficulty, just me being a bit fast and lazy.

Reduce the diff of #11203

@@ -226,7 +226,7 @@ theorem Int.pow_add_pow {x y : ℤ} (hxy : ↑p ∣ x + y) (hx : ¬↑p ∣ x) {
 theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : ℕ) :
     multiplicity p (x ^ n - y ^ n) = multiplicity p (x - y) + multiplicity p n := by
   obtain hyx | hyx := le_total y x
-  · iterate 2 rw [← Int.coe_nat_multiplicity]
+  · iterate 2 rw [← Int.natCast_multiplicity]
     rw [Int.ofNat_sub (Nat.pow_le_pow_left hyx n)]
     rw [← Int.natCast_dvd_natCast] at hxy hx
     rw [Int.natCast_sub hyx] at *
@@ -239,7 +239,7 @@ theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : 
 
 theorem Nat.pow_add_pow {x y : ℕ} (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : ℕ} (hn : Odd n) :
     multiplicity p (x ^ n + y ^ n) = multiplicity p (x + y) + multiplicity p n := by
-  iterate 2 rw [← Int.coe_nat_multiplicity]
+  iterate 2 rw [← Int.natCast_multiplicity]
   rw [← Int.natCast_dvd_natCast] at hxy hx
   push_cast at *
   exact Int.pow_add_pow hp hp1 hxy hx hn
@@ -360,13 +360,13 @@ theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n
     multiplicity 2 (x ^ n - y ^ n) + 1 =
       multiplicity 2 (x + y) + multiplicity 2 (x - y) + multiplicity 2 n := by
   obtain hyx | hyx := le_total y x
-  · iterate 3 rw [← multiplicity.Int.coe_nat_multiplicity]
+  · iterate 3 rw [← multiplicity.Int.natCast_multiplicity]
     simp only [Int.ofNat_sub hyx, Int.ofNat_sub (pow_le_pow_left' hyx _), Int.ofNat_add,
       Int.coe_nat_pow]
     rw [← Int.natCast_dvd_natCast] at hx
     rw [← Int.natCast_dvd_natCast, Int.ofNat_sub hyx] at hxy
     convert Int.two_pow_sub_pow hxy hx hn using 2
-    rw [← multiplicity.Int.coe_nat_multiplicity]
+    rw [← multiplicity.Int.natCast_multiplicity]
     rfl
   · simp only [Nat.sub_eq_zero_iff_le.mpr hyx,
       Nat.sub_eq_zero_iff_le.mpr (pow_le_pow_left' hyx n), multiplicity.zero,

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

@@ -210,7 +210,7 @@ theorem Int.pow_sub_pow {x y : ℤ} (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x) (
   · rw [← geom_sum₂_mul]
     exact dvd_mul_of_dvd_right hxy _
   · exact fun h => hx (hp.dvd_of_dvd_pow h)
-  · rw [Int.coe_nat_dvd]
+  · rw [Int.natCast_dvd_natCast]
     rintro ⟨c, rfl⟩
     refine' hpn ⟨c, _⟩
     rwa [pow_succ, mul_assoc]
@@ -228,8 +228,8 @@ theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : 
   obtain hyx | hyx := le_total y x
   · iterate 2 rw [← Int.coe_nat_multiplicity]
     rw [Int.ofNat_sub (Nat.pow_le_pow_left hyx n)]
-    rw [← Int.coe_nat_dvd] at hxy hx
-    rw [Int.coe_nat_sub hyx] at *
+    rw [← Int.natCast_dvd_natCast] at hxy hx
+    rw [Int.natCast_sub hyx] at *
     push_cast at *
     exact Int.pow_sub_pow hp hp1 hxy hx n
   · simp only [Nat.sub_eq_zero_iff_le.mpr hyx,
@@ -240,7 +240,7 @@ theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : 
 theorem Nat.pow_add_pow {x y : ℕ} (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : ℕ} (hn : Odd n) :
     multiplicity p (x ^ n + y ^ n) = multiplicity p (x + y) + multiplicity p n := by
   iterate 2 rw [← Int.coe_nat_multiplicity]
-  rw [← Int.coe_nat_dvd] at hxy hx
+  rw [← Int.natCast_dvd_natCast] at hxy hx
   push_cast at *
   exact Int.pow_add_pow hp hp1 hxy hx hn
 #align multiplicity.nat.pow_add_pow multiplicity.Nat.pow_add_pow
@@ -318,7 +318,7 @@ theorem Int.two_pow_sub_pow' {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2
   · exact Int.prime_two
   · simpa only [even_iff_two_dvd] using hx_odd.pow.sub_odd hy_odd.pow
   · simpa only [even_iff_two_dvd, Int.odd_iff_not_even] using hx_odd.pow
-  erw [Int.coe_nat_dvd]
+  erw [Int.natCast_dvd_natCast]
   -- `erw` to deal with `2 : ℤ` vs `(2 : ℕ) : ℤ`
   contrapose! hpn
   rw [pow_succ]
@@ -363,8 +363,8 @@ theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n
   · iterate 3 rw [← multiplicity.Int.coe_nat_multiplicity]
     simp only [Int.ofNat_sub hyx, Int.ofNat_sub (pow_le_pow_left' hyx _), Int.ofNat_add,
       Int.coe_nat_pow]
-    rw [← Int.coe_nat_dvd] at hx
-    rw [← Int.coe_nat_dvd, Int.ofNat_sub hyx] at hxy
+    rw [← Int.natCast_dvd_natCast] at hx
+    rw [← Int.natCast_dvd_natCast, Int.ofNat_sub hyx] at hxy
     convert Int.two_pow_sub_pow hxy hx hn using 2
     rw [← multiplicity.Int.coe_nat_multiplicity]
     rfl

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.

@@ -184,7 +184,7 @@ theorem pow_prime_pow_sub_pow_prime_pow (a : ℕ) :
     multiplicity (↑p) (x ^ p ^ a - y ^ p ^ a) = multiplicity (↑p) (x - y) + a := by
   induction' a with a h_ind
   · rw [Nat.cast_zero, add_zero, pow_zero, pow_one, pow_one]
-  rw [← Nat.add_one, Nat.cast_add, Nat.cast_one, ← add_assoc, ← h_ind, pow_succ', pow_mul, pow_mul]
+  rw [← Nat.add_one, Nat.cast_add, Nat.cast_one, ← add_assoc, ← h_ind, pow_succ, pow_mul, pow_mul]
   apply pow_prime_sub_pow_prime hp hp1
   · rw [← geom_sum₂_mul]
     exact dvd_mul_of_dvd_right hxy _
@@ -213,7 +213,7 @@ theorem Int.pow_sub_pow {x y : ℤ} (hxy : ↑p ∣ x - y) (hx : ¬↑p ∣ x) (
   · rw [Int.coe_nat_dvd]
     rintro ⟨c, rfl⟩
     refine' hpn ⟨c, _⟩
-    rwa [pow_succ', mul_assoc]
+    rwa [pow_succ, mul_assoc]
 #align multiplicity.int.pow_sub_pow multiplicity.Int.pow_sub_pow
 
 theorem Int.pow_add_pow {x y : ℤ} (hxy : ↑p ∣ x + y) (hx : ¬↑p ∣ x) {n : ℕ} (hn : Odd n) :
@@ -293,7 +293,7 @@ theorem Int.two_pow_two_pow_add_two_pow_two_pow {x y : ℤ} (hx : ¬2 ∣ x) (hx
       this _ hx_odd, this _ hy_odd]
     decide
   intro x hx
-  rw [pow_succ, mul_comm, pow_mul, Int.sq_mod_four_eq_one_of_odd hx.pow]
+  rw [pow_succ', mul_comm, pow_mul, Int.sq_mod_four_eq_one_of_odd hx.pow]
 #align int.two_pow_two_pow_add_two_pow_two_pow Int.two_pow_two_pow_add_two_pow_two_pow
 
 theorem Int.two_pow_two_pow_sub_pow_two_pow {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2 ∣ x) :
@@ -321,7 +321,7 @@ theorem Int.two_pow_sub_pow' {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2
   erw [Int.coe_nat_dvd]
   -- `erw` to deal with `2 : ℤ` vs `(2 : ℕ) : ℤ`
   contrapose! hpn
-  rw [pow_succ']
+  rw [pow_succ]
   conv_rhs => rw [hk]
   exact mul_dvd_mul_left _ hpn
 #align int.two_pow_sub_pow' Int.two_pow_sub_pow'

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".

@@ -261,7 +261,7 @@ theorem pow_two_pow_sub_pow_two_pow [CommRing R] {x y : R} (n : ℕ) :
       ring
 #align pow_two_pow_sub_pow_two_pow pow_two_pow_sub_pow_two_pow
 
--- porting note: simplified proof because `fin_cases` was not available in that case
+-- Porting note: simplified proof because `fin_cases` was not available in that case
 theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 := by
   intro hx
   unfold Odd at hx

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.

@@ -386,7 +386,7 @@ theorem pow_two_sub_pow (hyx : y < x) (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n :
   · convert Nat.two_pow_sub_pow hxy hx hneven using 2
   · exact hn.bot_lt
   · exact Nat.sub_pos_of_lt hyx
-  · linarith
+  · omega
   · simp only [tsub_pos_iff_lt, pow_lt_pow_left hyx zero_le' hn]
 #align padic_val_nat.pow_two_sub_pow padicValNat.pow_two_sub_pow
 

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -5,11 +5,9 @@ Authors: Tian Chen, Mantas Bakšys
 -/
 import Mathlib.Algebra.GeomSum
 import Mathlib.Data.Int.Parity
-import Mathlib.Data.ZMod.Basic
 import Mathlib.NumberTheory.Padics.PadicVal
-import Mathlib.RingTheory.Ideal.QuotientOperations
-import Mathlib.Init.Meta.WellFoundedTactics
 import Mathlib.Algebra.GroupPower.Order
+import Mathlib.RingTheory.Ideal.Quotient
 
 #align_import number_theory.multiplicity from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"
 

cherry-picked from #9347

Co-Authored-By: @digama0

@@ -9,6 +9,7 @@ import Mathlib.Data.ZMod.Basic
 import Mathlib.NumberTheory.Padics.PadicVal
 import Mathlib.RingTheory.Ideal.QuotientOperations
 import Mathlib.Init.Meta.WellFoundedTactics
+import Mathlib.Algebra.GroupPower.Order
 
 #align_import number_theory.multiplicity from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"
 

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

Renames

Algebra.GroupPower.Order

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

Algebra.GroupPower.CovariantClass

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

Data.Nat.Pow

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

Lemmas added

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

Lemmas removed

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

Other changes

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

@@ -228,13 +228,13 @@ theorem Nat.pow_sub_pow {x y : ℕ} (hxy : p ∣ x - y) (hx : ¬p ∣ x) (n : 
     multiplicity p (x ^ n - y ^ n) = multiplicity p (x - y) + multiplicity p n := by
   obtain hyx | hyx := le_total y x
   · iterate 2 rw [← Int.coe_nat_multiplicity]
-    rw [Int.ofNat_sub (Nat.pow_le_pow_of_le_left hyx n)]
+    rw [Int.ofNat_sub (Nat.pow_le_pow_left hyx n)]
     rw [← Int.coe_nat_dvd] at hxy hx
     rw [Int.coe_nat_sub hyx] at *
     push_cast at *
     exact Int.pow_sub_pow hp hp1 hxy hx n
   · simp only [Nat.sub_eq_zero_iff_le.mpr hyx,
-      Nat.sub_eq_zero_iff_le.mpr (Nat.pow_le_pow_of_le_left hyx n), multiplicity.zero,
+      Nat.sub_eq_zero_iff_le.mpr (Nat.pow_le_pow_left hyx n), multiplicity.zero,
       PartENat.top_add]
 #align multiplicity.nat.pow_sub_pow multiplicity.Nat.pow_sub_pow
 
@@ -362,7 +362,7 @@ theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n
       multiplicity 2 (x + y) + multiplicity 2 (x - y) + multiplicity 2 n := by
   obtain hyx | hyx := le_total y x
   · iterate 3 rw [← multiplicity.Int.coe_nat_multiplicity]
-    simp only [Int.ofNat_sub hyx, Int.ofNat_sub (pow_le_pow_of_le_left' hyx _), Int.ofNat_add,
+    simp only [Int.ofNat_sub hyx, Int.ofNat_sub (pow_le_pow_left' hyx _), Int.ofNat_add,
       Int.coe_nat_pow]
     rw [← Int.coe_nat_dvd] at hx
     rw [← Int.coe_nat_dvd, Int.ofNat_sub hyx] at hxy
@@ -370,7 +370,7 @@ theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n
     rw [← multiplicity.Int.coe_nat_multiplicity]
     rfl
   · simp only [Nat.sub_eq_zero_iff_le.mpr hyx,
-      Nat.sub_eq_zero_iff_le.mpr (pow_le_pow_of_le_left' hyx n), multiplicity.zero,
+      Nat.sub_eq_zero_iff_le.mpr (pow_le_pow_left' hyx n), multiplicity.zero,
       PartENat.top_add, PartENat.add_top]
 #align nat.two_pow_sub_pow Nat.two_pow_sub_pow
 
@@ -378,29 +378,29 @@ namespace padicValNat
 
 variable {x y : ℕ}
 
-theorem pow_two_sub_pow (hyx : y < x) (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n : ℕ} (hn : 0 < n)
+theorem pow_two_sub_pow (hyx : y < x) (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n : ℕ} (hn : n ≠ 0)
     (hneven : Even n) :
     padicValNat 2 (x ^ n - y ^ n) + 1 =
       padicValNat 2 (x + y) + padicValNat 2 (x - y) + padicValNat 2 n := by
   simp only [← PartENat.natCast_inj, Nat.cast_add]
   iterate 4 rw [padicValNat_def, PartENat.natCast_get]
   · convert Nat.two_pow_sub_pow hxy hx hneven using 2
-  · exact hn
+  · exact hn.bot_lt
   · exact Nat.sub_pos_of_lt hyx
   · linarith
-  · simp only [tsub_pos_iff_lt, pow_lt_pow_of_lt_left hyx (@zero_le' _ y _) hn]
+  · simp only [tsub_pos_iff_lt, pow_lt_pow_left hyx zero_le' hn]
 #align padic_val_nat.pow_two_sub_pow padicValNat.pow_two_sub_pow
 
 variable {p : ℕ} [hp : Fact p.Prime] (hp1 : Odd p)
 
-theorem pow_sub_pow (hyx : y < x) (hxy : p ∣ x - y) (hx : ¬p ∣ x) {n : ℕ} (hn : 0 < n) :
+theorem pow_sub_pow (hyx : y < x) (hxy : p ∣ x - y) (hx : ¬p ∣ x) {n : ℕ} (hn : n ≠ 0) :
     padicValNat p (x ^ n - y ^ n) = padicValNat p (x - y) + padicValNat p n := by
   rw [← PartENat.natCast_inj, Nat.cast_add]
   iterate 3 rw [padicValNat_def, PartENat.natCast_get]
   · exact multiplicity.Nat.pow_sub_pow hp.out hp1 hxy hx n
-  · exact hn
+  · exact hn.bot_lt
   · exact Nat.sub_pos_of_lt hyx
-  · exact Nat.sub_pos_of_lt (Nat.pow_lt_pow_of_lt_left hyx hn)
+  · exact Nat.sub_pos_of_lt (Nat.pow_lt_pow_left hyx hn)
 #align padic_val_nat.pow_sub_pow padicValNat.pow_sub_pow
 
 theorem pow_add_pow (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : ℕ} (hn : Odd n) :

@@ -412,7 +412,7 @@ theorem pow_add_pow (hxy : p ∣ x + y) (hx : ¬p ∣ x) {n : ℕ} (hn : Odd n)
   · exact multiplicity.Nat.pow_add_pow hp.out hp1 hxy hx hn
   · exact Odd.pos hn
   · simp only [add_pos_iff, Nat.succ_pos', or_true_iff]
-  · exact Nat.lt_add_left _ _ _ (pow_pos y.succ_pos _)
+  · exact Nat.lt_add_left _ (pow_pos y.succ_pos _)
 #align padic_val_nat.pow_add_pow padicValNat.pow_add_pow
 
 end padicValNat

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
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

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>

@@ -109,7 +109,7 @@ theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
     _ =
         mk (span {s})
             (∑ x : ℕ in Finset.range p, a ^ (x - 1) * (a ^ (p - 1 - x) * (↑p * (b * ↑x)))) +
-          mk (span {s}) (∑ x : ℕ in Finset.range p, a ^ (p - 1)) := by
+          mk (span {s}) (∑ _x : ℕ in Finset.range p, a ^ (p - 1)) := by
       rw [add_right_inj]
       have : ∀ (x : ℕ), (hx : x ∈ range p) → a ^ (x + (p - 1 - x)) = a ^ (p - 1) := by
         intro x hx
@@ -269,13 +269,13 @@ theorem Int.sq_mod_four_eq_one_of_odd {x : ℤ} : Odd x → x ^ 2 % 4 = 1 := by
   rcases hx with ⟨_, rfl⟩
   ring_nf
   rw [add_assoc, ← add_mul, Int.add_mul_emod_self]
-  norm_num
+  decide
 #align int.sq_mod_four_eq_one_of_odd Int.sq_mod_four_eq_one_of_odd
 
 theorem Int.two_pow_two_pow_add_two_pow_two_pow {x y : ℤ} (hx : ¬2 ∣ x) (hxy : 4 ∣ x - y) (i : ℕ) :
     multiplicity 2 (x ^ 2 ^ i + y ^ 2 ^ i) = ↑(1 : ℕ) := by
   have hx_odd : Odd x := by rwa [Int.odd_iff_not_even, even_iff_two_dvd]
-  have hxy_even : Even (x - y) := even_iff_two_dvd.mpr (dvd_trans (by norm_num) hxy)
+  have hxy_even : Even (x - y) := even_iff_two_dvd.mpr (dvd_trans (by decide) hxy)
   have hy_odd : Odd y := by simpa using hx_odd.sub_even hxy_even
   refine' multiplicity.eq_coe_iff.mpr ⟨_, _⟩
   · rw [pow_one, ← even_iff_two_dvd]
@@ -292,7 +292,7 @@ theorem Int.two_pow_two_pow_add_two_pow_two_pow {x y : ℤ} (hx : ¬2 ∣ x) (hx
   suffices ∀ x : ℤ, Odd x → x ^ 2 ^ (i + 1) % 4 = 1 by
     rw [show (2 ^ (1 + 1) : ℤ) = 4 by norm_num, Int.dvd_iff_emod_eq_zero, Int.add_emod,
       this _ hx_odd, this _ hy_odd]
-    norm_num
+    decide
   intro x hx
   rw [pow_succ, mul_comm, pow_mul, Int.sq_mod_four_eq_one_of_odd hx.pow]
 #align int.two_pow_two_pow_add_two_pow_two_pow Int.two_pow_two_pow_add_two_pow_two_pow
@@ -307,7 +307,7 @@ theorem Int.two_pow_two_pow_sub_pow_two_pow {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x
 theorem Int.two_pow_sub_pow' {x y : ℤ} (n : ℕ) (hxy : 4 ∣ x - y) (hx : ¬2 ∣ x) :
     multiplicity 2 (x ^ n - y ^ n) = multiplicity 2 (x - y) + multiplicity (2 : ℤ) n := by
   have hx_odd : Odd x := by rwa [Int.odd_iff_not_even, even_iff_two_dvd]
-  have hxy_even : Even (x - y) := even_iff_two_dvd.mpr (dvd_trans (by norm_num) hxy)
+  have hxy_even : Even (x - y) := even_iff_two_dvd.mpr (dvd_trans (by decide) hxy)
   have hy_odd : Odd y := by simpa using hx_odd.sub_even hxy_even
   cases' n with n
   · simp only [pow_zero, sub_self, multiplicity.zero, Int.ofNat_zero, Nat.zero_eq, add_top]

@@ -114,7 +114,7 @@ theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
       have : ∀ (x : ℕ), (hx : x ∈ range p) → a ^ (x + (p - 1 - x)) = a ^ (p - 1) := by
         intro x hx
         rw [← Nat.add_sub_assoc _ x, Nat.add_sub_cancel_left]
-        exact Nat.le_pred_of_lt (Finset.mem_range.mp hx)
+        exact Nat.le_sub_one_of_lt (Finset.mem_range.mp hx)
       rw [Finset.sum_congr rfl this]
     _ =
         mk (span {s})
@@ -129,7 +129,7 @@ theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
       rintro (⟨⟩ | ⟨x⟩) hx
       · rw [Nat.cast_zero, mul_zero, mul_zero]
       · have : x.succ - 1 + (p - 1 - x.succ) = p - 2 := by
-          rw [← Nat.add_sub_assoc (Nat.le_pred_of_lt (Finset.mem_range.mp hx))]
+          rw [← Nat.add_sub_assoc (Nat.le_sub_one_of_lt (Finset.mem_range.mp hx))]
           exact congr_arg Nat.pred (Nat.add_sub_cancel_left _ _)
         rw [this]
         ring1

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).

@@ -127,7 +127,7 @@ theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
       simp only [Finset.mul_sum, ← mul_assoc, ← pow_add]
       rw [Finset.sum_congr rfl]
       rintro (⟨⟩ | ⟨x⟩) hx
-      · rw [Nat.cast_zero, MulZeroClass.mul_zero, MulZeroClass.mul_zero]
+      · rw [Nat.cast_zero, mul_zero, mul_zero]
       · have : x.succ - 1 + (p - 1 - x.succ) = p - 2 := by
           rw [← Nat.add_sub_assoc (Nat.le_pred_of_lt (Finset.mem_range.mp hx))]
           exact congr_arg Nat.pred (Nat.add_sub_cancel_left _ _)

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

This has nice performance benefits.

@@ -33,7 +33,7 @@ open Ideal Ideal.Quotient Finset
 
 open BigOperators
 
-variable {R : Type _} {n : ℕ}
+variable {R : Type*} {n : ℕ}
 
 section CommRing
 

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Tian Chen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tian Chen, Mantas Bakšys
-
-! This file was ported from Lean 3 source module number_theory.multiplicity
-! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.GeomSum
 import Mathlib.Data.Int.Parity
@@ -15,6 +10,8 @@ import Mathlib.NumberTheory.Padics.PadicVal
 import Mathlib.RingTheory.Ideal.QuotientOperations
 import Mathlib.Init.Meta.WellFoundedTactics
 
+#align_import number_theory.multiplicity from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"
+
 /-!
 # Multiplicity in Number Theory
 

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

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

@@ -114,7 +114,7 @@ theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
             (∑ x : ℕ in Finset.range p, a ^ (x - 1) * (a ^ (p - 1 - x) * (↑p * (b * ↑x)))) +
           mk (span {s}) (∑ x : ℕ in Finset.range p, a ^ (p - 1)) := by
       rw [add_right_inj]
-      have : ∀ (x : ℕ), (hx : x ∈ range p) →  a ^ (x + (p - 1 - x)) = a ^ (p - 1) := by
+      have : ∀ (x : ℕ), (hx : x ∈ range p) → a ^ (x + (p - 1 - x)) = a ^ (p - 1) := by
         intro x hx
         rw [← Nat.add_sub_assoc _ x, Nat.add_sub_cancel_left]
         exact Nat.le_pred_of_lt (Finset.mem_range.mp hx)
@@ -138,7 +138,7 @@ theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
         ring1
     _ = mk (span {s}) (↑p * a ^ (p - 1)) := by
       have : Finset.sum (range p) (fun (x : ℕ) ↦ (x : R)) =
-          ((Finset.sum (range p) (fun (x : ℕ)  ↦ (x : ℕ)))) := by simp only [Nat.cast_sum]
+          ((Finset.sum (range p) (fun (x : ℕ) ↦ (x : ℕ)))) := by simp only [Nat.cast_sum]
       simp only [add_left_eq_self, ← Finset.mul_sum, this]
       norm_cast
       simp only [Finset.sum_range_id]

https://github.com/leanprover-community/mathlib4/actions/runs/5349279420/jobs/9700275999 shows this working successfully (i.e. the action failing as there were ring's that should be ring_nf's

We then clean up the noisy lines in mathlib

@@ -105,7 +105,7 @@ theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
         mk (span {s})
             (∑ x : ℕ in Finset.range p, a ^ (x - 1) * (a ^ (p - 1 - x) * (↑p * (b * ↑x)))) +
           mk (span {s}) (∑ x : ℕ in Finset.range p, a ^ (x + (p - 1 - x))) := by
-      ring
+      ring_nf
       simp only [← pow_add, map_add, Finset.sum_add_distrib, ← map_sum]
       congr
       simp [pow_add a, mul_assoc]
@@ -145,7 +145,7 @@ theorem odd_sq_dvd_geom_sum₂_sub (hp : Odd p) :
       norm_cast
       simp only [Nat.cast_mul, _root_.map_mul,
           Nat.mul_div_assoc p (even_iff_two_dvd.mp (Nat.Odd.sub_odd hp odd_one))]
-      ring
+      ring_nf
       rw [mul_assoc, mul_assoc]
       refine' mul_eq_zero_of_left _ _
       refine' Ideal.Quotient.eq_zero_iff_mem.mpr _

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>