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

@@ -56,7 +56,7 @@ theorem exists_sq_add_sq_add_one_eq_k (p : ℕ) [hp : Fact p.Prime] :
   hp.1.eq_two_or_odd.elim (fun hp2 => hp2.symm ▸ ⟨1, 0, 1, rfl, by decide⟩) fun hp1 =>
     let ⟨a, b, hab⟩ := ZMod.sq_add_sq p (-1)
     have hab' : (p : ℤ) ∣ a.valMinAbs ^ 2 + b.valMinAbs ^ 2 + 1 :=
-      (CharP.int_cast_eq_zero_iff (ZMod p) p _).1 <| by simpa [eq_neg_iff_add_eq_zero] using hab
+      (CharP.intCast_eq_zero_iff (ZMod p) p _).1 <| by simpa [eq_neg_iff_add_eq_zero] using hab
     let ⟨k, hk⟩ := hab'
     have hk0 : 0 ≤ k :=
       nonneg_of_mul_nonneg_right
@@ -113,10 +113,10 @@ private theorem sum_four_squares_of_two_mul_sum_four_squares {m a b c d : ℤ}
           rfl)
   let σ := swap i 0
   have h01 : 2 ∣ f (σ 0) ^ 2 + f (σ 1) ^ 2 :=
-    (CharP.int_cast_eq_zero_iff (ZMod 2) 2 _).1 <| by
+    (CharP.intCast_eq_zero_iff (ZMod 2) 2 _).1 <| by
       simpa only [Int.cast_pow, Int.cast_add, Equiv.swap_apply_right, ZMod.pow_card] using hσ.1
   have h23 : 2 ∣ f (σ 2) ^ 2 + f (σ 3) ^ 2 :=
-    (CharP.int_cast_eq_zero_iff (ZMod 2) 2 _).1 <| by
+    (CharP.intCast_eq_zero_iff (ZMod 2) 2 _).1 <| by
       simpa only [Int.cast_pow, Int.cast_add, ZMod.pow_card] using hσ.2
   let ⟨x, hx⟩ := h01
   let ⟨y, hy⟩ := h23
@@ -199,15 +199,15 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
           ((a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 : ℤ) : ZMod m) :=
         by push_cast
       have hwxyz0 : ((w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 : ℤ) : ZMod m) = 0 := by
-        rw [hwxyzabcd, habcd, Int.cast_mul, cast_coe_nat, ZMod.nat_cast_self, MulZeroClass.zero_mul]
-      let ⟨n, hn⟩ := (CharP.int_cast_eq_zero_iff _ m _).1 hwxyz0
+        rw [hwxyzabcd, habcd, Int.cast_mul, cast_coe_nat, ZMod.natCast_self, MulZeroClass.zero_mul]
+      let ⟨n, hn⟩ := (CharP.intCast_eq_zero_iff _ m _).1 hwxyz0
       have hn0 : 0 < n.natAbs :=
         Int.natAbs_pos fun hn0 =>
           have hwxyz0 : (w.natAbs ^ 2 + x.natAbs ^ 2 + y.natAbs ^ 2 + z.natAbs ^ 2 : ℕ) = 0 := by
             rw [← Int.natCast_eq_zero, ← hnat_abs]; rwa [hn0, MulZeroClass.mul_zero] at hn
           have habcd0 : (m : ℤ) ∣ a ∧ (m : ℤ) ∣ b ∧ (m : ℤ) ∣ c ∧ (m : ℤ) ∣ d := by
             simpa only [add_eq_zero_iff, Int.natAbs_eq_zero, ZMod.valMinAbs_eq_zero, and_assoc,
-              pow_eq_zero_iff two_pos, CharP.int_cast_eq_zero_iff _ m _] using hwxyz0
+              pow_eq_zero_iff two_pos, CharP.intCast_eq_zero_iff _ m _] using hwxyz0
           let ⟨ma, hma⟩ := habcd0.1
           let ⟨mb, hmb⟩ := habcd0.2.1
           let ⟨mc, hmc⟩ := habcd0.2.2.1
@@ -220,13 +220,13 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
           (hp.1.eq_one_or_self_of_dvd _ hmdvdp).elim hm1 fun hmeqp => by
             simpa [lt_irrefl, hmeqp] using hmp
       have hawbxcydz : ((m : ℕ) : ℤ) ∣ a * w + b * x + c * y + d * z :=
-        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by rw [← hwxyz0]; simp_rw [sq]; push_cast
+        (CharP.intCast_eq_zero_iff (ZMod m) m _).1 <| by rw [← hwxyz0]; simp_rw [sq]; push_cast
       have haxbwczdy : ((m : ℕ) : ℤ) ∣ a * x - b * w - c * z + d * y :=
-        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by push_cast; ring
+        (CharP.intCast_eq_zero_iff (ZMod m) m _).1 <| by push_cast; ring
       have haybzcwdx : ((m : ℕ) : ℤ) ∣ a * y + b * z - c * w - d * x :=
-        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by push_cast; ring
+        (CharP.intCast_eq_zero_iff (ZMod m) m _).1 <| by push_cast; ring
       have hazbycxdw : ((m : ℕ) : ℤ) ∣ a * z - b * y + c * x - d * w :=
-        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by push_cast; ring
+        (CharP.intCast_eq_zero_iff (ZMod m) m _).1 <| by push_cast; ring
       let ⟨s, hs⟩ := hawbxcydz
       let ⟨t, ht⟩ := haxbwczdy
       let ⟨u, hu⟩ := haybzcwdx

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

@@ -61,7 +61,7 @@ theorem exists_sq_add_sq_add_one_eq_k (p : ℕ) [hp : Fact p.Prime] :
     have hk0 : 0 ≤ k :=
       nonneg_of_mul_nonneg_right
         (by rw [← hk] <;> exact add_nonneg (add_nonneg (sq_nonneg _) (sq_nonneg _)) zero_le_one)
-        (Int.coe_nat_pos.2 hp.1.Pos)
+        (Int.natCast_pos.2 hp.1.Pos)
     ⟨a.valMinAbs, b.valMinAbs, k.natAbs, by rw [hk, Int.natAbs_of_nonneg hk0, mul_comm],
       lt_of_mul_lt_mul_left
         (calc
@@ -234,7 +234,7 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
       have hn_nonneg : 0 ≤ n :=
         nonneg_of_mul_nonneg_right
           (by erw [← hn]; repeat' try refine' add_nonneg _ _; try exact sq_nonneg _)
-          (Int.coe_nat_pos.2 <| NeZero.pos m)
+          (Int.natCast_pos.2 <| NeZero.pos m)
       have hnm : n.natAbs < m :=
         Int.ofNat_lt.1
           (lt_of_mul_lt_mul_left (by rw [Int.natAbs_of_nonneg hn_nonneg, ← hn, ← sq]; exact hwxyzlt)

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
 import Algebra.GroupPower.Identities
-import Data.Zmod.Basic
+import Data.ZMod.Basic
 import FieldTheory.Finite.Basic
 import Data.Int.Parity
 import Data.Fintype.BigOperators
@@ -46,7 +46,7 @@ theorem sq_add_sq_of_two_mul_sq_add_sq {m x y : ℤ} (h : 2 * m = x ^ 2 + y ^ 2)
         rw [even_iff_two_dvd] at hxsuby hxaddy
         rw [Int.mul_ediv_cancel' hxsuby, Int.mul_ediv_cancel' hxaddy]
       _ = 2 * 2 * (((x - y) / 2) ^ 2 + ((x + y) / 2) ^ 2) := by
-        simp [mul_add, pow_succ, mul_comm, mul_assoc, mul_left_comm]
+        simp [mul_add, pow_succ', mul_comm, mul_assoc, mul_left_comm]
 #align int.sq_add_sq_of_two_mul_sq_add_sq Int.sq_add_sq_of_two_mul_sq_add_sq
 -/
 
@@ -66,7 +66,7 @@ theorem exists_sq_add_sq_add_one_eq_k (p : ℕ) [hp : Fact p.Prime] :
       lt_of_mul_lt_mul_left
         (calc
           p * k.natAbs = a.valMinAbs.natAbs ^ 2 + b.valMinAbs.natAbs ^ 2 + 1 := by
-            rw [← Int.coe_nat_inj', Int.ofNat_add, Int.ofNat_add, Int.coe_nat_pow, Int.coe_nat_pow,
+            rw [← Int.natCast_inj, Int.ofNat_add, Int.ofNat_add, Int.coe_nat_pow, Int.coe_nat_pow,
               Int.natAbs_sq, Int.natAbs_sq, Int.ofNat_one, hk, Int.ofNat_mul,
               Int.natAbs_of_nonneg hk0]
           _ ≤ (p / 2) ^ 2 + (p / 2) ^ 2 + 1 :=
@@ -189,7 +189,7 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
             ((lt_add_iff_pos_right _).2
               (by
                 rw [hm2, Int.ofNat_one, one_pow, mul_one]
-                exact add_pos_of_nonneg_of_pos (Int.coe_nat_nonneg _) zero_lt_one))
+                exact add_pos_of_nonneg_of_pos (Int.natCast_nonneg _) zero_lt_one))
           _ = m ^ 2 := by
             conv_rhs => rw [← Nat.mod_add_div m 2]
             simp [-Nat.mod_add_div, mul_add, add_mul, bit0, bit1, mul_comm, mul_assoc,
@@ -202,9 +202,9 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
         rw [hwxyzabcd, habcd, Int.cast_mul, cast_coe_nat, ZMod.nat_cast_self, MulZeroClass.zero_mul]
       let ⟨n, hn⟩ := (CharP.int_cast_eq_zero_iff _ m _).1 hwxyz0
       have hn0 : 0 < n.natAbs :=
-        Int.natAbs_pos_of_ne_zero fun hn0 =>
+        Int.natAbs_pos fun hn0 =>
           have hwxyz0 : (w.natAbs ^ 2 + x.natAbs ^ 2 + y.natAbs ^ 2 + z.natAbs ^ 2 : ℕ) = 0 := by
-            rw [← Int.coe_nat_eq_zero, ← hnat_abs]; rwa [hn0, MulZeroClass.mul_zero] at hn
+            rw [← Int.natCast_eq_zero, ← hnat_abs]; rwa [hn0, MulZeroClass.mul_zero] at hn
           have habcd0 : (m : ℤ) ∣ a ∧ (m : ℤ) ∣ b ∧ (m : ℤ) ∣ c ∧ (m : ℤ) ∣ d := by
             simpa only [add_eq_zero_iff, Int.natAbs_eq_zero, ZMod.valMinAbs_eq_zero, and_assoc,
               pow_eq_zero_iff two_pos, CharP.int_cast_eq_zero_iff _ m _] using hwxyz0
@@ -213,9 +213,9 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
           let ⟨mc, hmc⟩ := habcd0.2.2.1
           let ⟨md, hmd⟩ := habcd0.2.2.2
           have hmdvdp : m ∣ p :=
-            Int.coe_nat_dvd.1
+            Int.natCast_dvd_natCast.1
               ⟨ma ^ 2 + mb ^ 2 + mc ^ 2 + md ^ 2,
-                (mul_right_inj' (show (m : ℤ) ≠ 0 from Int.coe_nat_ne_zero.2 hm0.1)).1 <| by
+                (mul_right_inj' (show (m : ℤ) ≠ 0 from Int.natCast_ne_zero.2 hm0.1)).1 <| by
                   rw [← habcd, hma, hmb, hmc, hmd]; ring⟩
           (hp.1.eq_one_or_self_of_dvd _ hmdvdp).elim hm1 fun hmeqp => by
             simpa [lt_irrefl, hmeqp] using hmp
@@ -238,10 +238,10 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
       have hnm : n.natAbs < m :=
         Int.ofNat_lt.1
           (lt_of_mul_lt_mul_left (by rw [Int.natAbs_of_nonneg hn_nonneg, ← hn, ← sq]; exact hwxyzlt)
-            (Int.coe_nat_nonneg m))
+            (Int.natCast_nonneg m))
       have hstuv : s ^ 2 + t ^ 2 + u ^ 2 + v ^ 2 = n.natAbs * p :=
         (mul_right_inj'
-              (show (m ^ 2 : ℤ) ≠ 0 from pow_ne_zero 2 (Int.coe_nat_ne_zero.2 hm0.1))).1 <|
+              (show (m ^ 2 : ℤ) ≠ 0 from pow_ne_zero 2 (Int.natCast_ne_zero.2 hm0.1))).1 <|
           calc
             (m : ℤ) ^ 2 * (s ^ 2 + t ^ 2 + u ^ 2 + v ^ 2) =
                 ((m : ℕ) * s) ^ 2 + ((m : ℕ) * t) ^ 2 + ((m : ℕ) * u) ^ 2 + ((m : ℕ) * v) ^ 2 :=
@@ -266,8 +266,7 @@ theorem sum_four_squares : ∀ n : ℕ, ∃ a b c d : ℕ, a ^ 2 + b ^ 2 + c ^ 2
     ⟨(a * w - b * x - c * y - d * z).natAbs, (a * x + b * w + c * z - d * y).natAbs,
       (a * y - b * z + c * w + d * x).natAbs, (a * z + b * y - c * x + d * w).natAbs,
       by
-      rw [← Int.coe_nat_inj', ← Nat.mul_div_cancel' (min_fac_dvd (k + 2)), Int.ofNat_mul, ← h₁, ←
-        h₂]
+      rw [← Int.natCast_inj, ← Nat.mul_div_cancel' (min_fac_dvd (k + 2)), Int.ofNat_mul, ← h₁, ← h₂]
       simp [sum_four_sq_mul_sum_four_sq]⟩
 #align nat.sum_four_squares Nat.sum_four_squares
 -/

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

@@ -43,7 +43,7 @@ theorem sq_add_sq_of_two_mul_sq_add_sq {m x y : ℤ} (h : 2 * m = x ^ 2 + y ^ 2)
       2 * 2 * m = (x - y) ^ 2 + (x + y) ^ 2 := by rw [mul_assoc, h] <;> ring
       _ = (2 * ((x - y) / 2)) ^ 2 + (2 * ((x + y) / 2)) ^ 2 :=
         by
-        rw [even_iff_two_dvd] at hxsuby hxaddy 
+        rw [even_iff_two_dvd] at hxsuby hxaddy
         rw [Int.mul_ediv_cancel' hxsuby, Int.mul_ediv_cancel' hxaddy]
       _ = 2 * 2 * (((x - y) / 2) ^ 2 + ((x + y) / 2) ^ 2) := by
         simp [mul_add, pow_succ, mul_comm, mul_assoc, mul_left_comm]
@@ -136,7 +136,7 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
     ⟨k, hk.2,
       Nat.pos_of_ne_zero fun hk0 =>
         by
-        rw [hk0, Int.ofNat_zero, MulZeroClass.zero_mul] at hk 
+        rw [hk0, Int.ofNat_zero, MulZeroClass.zero_mul] at hk
         exact
           ne_of_gt
             (show a ^ 2 + b ^ 2 + 1 > 0 from
@@ -151,7 +151,7 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
     (fun hm2 : m % 2 = 0 =>
       let ⟨k, hk⟩ := Nat.dvd_iff_mod_eq_zero.2 hm2
       have hk0 : 0 < k :=
-        Nat.pos_of_ne_zero <| by rintro rfl; rw [MulZeroClass.mul_zero] at hk ; exact NeZero.ne m hk
+        Nat.pos_of_ne_zero <| by rintro rfl; rw [MulZeroClass.mul_zero] at hk; exact NeZero.ne m hk
       have hkm : k < m := by rw [hk, two_mul]; exact (lt_add_iff_pos_left _).2 hk0
       False.elim <|
         Nat.find_min hm hkm
@@ -204,7 +204,7 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
       have hn0 : 0 < n.natAbs :=
         Int.natAbs_pos_of_ne_zero fun hn0 =>
           have hwxyz0 : (w.natAbs ^ 2 + x.natAbs ^ 2 + y.natAbs ^ 2 + z.natAbs ^ 2 : ℕ) = 0 := by
-            rw [← Int.coe_nat_eq_zero, ← hnat_abs]; rwa [hn0, MulZeroClass.mul_zero] at hn 
+            rw [← Int.coe_nat_eq_zero, ← hnat_abs]; rwa [hn0, MulZeroClass.mul_zero] at hn
           have habcd0 : (m : ℤ) ∣ a ∧ (m : ℤ) ∣ b ∧ (m : ℤ) ∣ c ∧ (m : ℤ) ∣ d := by
             simpa only [add_eq_zero_iff, Int.natAbs_eq_zero, ZMod.valMinAbs_eq_zero, and_assoc,
               pow_eq_zero_iff two_pos, CharP.int_cast_eq_zero_iff _ m _] using hwxyz0

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

@@ -71,8 +71,8 @@ theorem exists_sq_add_sq_add_one_eq_k (p : ℕ) [hp : Fact p.Prime] :
               Int.natAbs_of_nonneg hk0]
           _ ≤ (p / 2) ^ 2 + (p / 2) ^ 2 + 1 :=
             (add_le_add
-              (add_le_add (Nat.pow_le_pow_of_le_left (ZMod.natAbs_valMinAbs_le _) _)
-                (Nat.pow_le_pow_of_le_left (ZMod.natAbs_valMinAbs_le _) _))
+              (add_le_add (Nat.pow_le_pow_left (ZMod.natAbs_valMinAbs_le _) _)
+                (Nat.pow_le_pow_left (ZMod.natAbs_valMinAbs_le _) _))
               le_rfl)
           _ < (p / 2) ^ 2 + (p / 2) ^ 2 + (p % 2) ^ 2 + (2 * (p / 2) ^ 2 + 4 * (p / 2) * (p % 2)) :=
             by
@@ -179,10 +179,10 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
             (Int.ofNat_le.2 <|
               add_le_add
                 (add_le_add
-                  (add_le_add (Nat.pow_le_pow_of_le_left (ZMod.natAbs_valMinAbs_le _) _)
-                    (Nat.pow_le_pow_of_le_left (ZMod.natAbs_valMinAbs_le _) _))
-                  (Nat.pow_le_pow_of_le_left (ZMod.natAbs_valMinAbs_le _) _))
-                (Nat.pow_le_pow_of_le_left (ZMod.natAbs_valMinAbs_le _) _))
+                  (add_le_add (Nat.pow_le_pow_left (ZMod.natAbs_valMinAbs_le _) _)
+                    (Nat.pow_le_pow_left (ZMod.natAbs_valMinAbs_le _) _))
+                  (Nat.pow_le_pow_left (ZMod.natAbs_valMinAbs_le _) _))
+                (Nat.pow_le_pow_left (ZMod.natAbs_valMinAbs_le _) _))
           _ = 4 * (m / 2 : ℕ) ^ 2 := by
             simp only [bit0_mul, one_mul, two_smul, Nat.cast_add, Nat.cast_pow, add_assoc]
           _ < 4 * (m / 2 : ℕ) ^ 2 + ((4 * (m / 2) : ℕ) * (m % 2 : ℕ) + (m % 2 : ℕ) ^ 2) :=

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

@@ -169,7 +169,7 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
       have hnat_abs :
         w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 =
           (w.natAbs ^ 2 + x.natAbs ^ 2 + y.natAbs ^ 2 + z.natAbs ^ 2 : ℕ) :=
-        by push_cast ; simp_rw [sq_abs]
+        by push_cast; simp_rw [sq_abs]
       have hwxyzlt : w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 < m ^ 2 :=
         calc
           w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 =
@@ -222,11 +222,11 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
       have hawbxcydz : ((m : ℕ) : ℤ) ∣ a * w + b * x + c * y + d * z :=
         (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by rw [← hwxyz0]; simp_rw [sq]; push_cast
       have haxbwczdy : ((m : ℕ) : ℤ) ∣ a * x - b * w - c * z + d * y :=
-        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by push_cast ; ring
+        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by push_cast; ring
       have haybzcwdx : ((m : ℕ) : ℤ) ∣ a * y + b * z - c * w - d * x :=
-        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by push_cast ; ring
+        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by push_cast; ring
       have hazbycxdw : ((m : ℕ) : ℤ) ∣ a * z - b * y + c * x - d * w :=
-        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by push_cast ; ring
+        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by push_cast; ring
       let ⟨s, hs⟩ := hawbxcydz
       let ⟨t, ht⟩ := haxbwczdy
       let ⟨u, hu⟩ := haybzcwdx

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

@@ -3,11 +3,11 @@ Copyright (c) 2019 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathbin.Algebra.GroupPower.Identities
-import Mathbin.Data.Zmod.Basic
-import Mathbin.FieldTheory.Finite.Basic
-import Mathbin.Data.Int.Parity
-import Mathbin.Data.Fintype.BigOperators
+import Algebra.GroupPower.Identities
+import Data.Zmod.Basic
+import FieldTheory.Finite.Basic
+import Data.Int.Parity
+import Data.Fintype.BigOperators
 
 #align_import number_theory.sum_four_squares from "leanprover-community/mathlib"@"575b4ea3738b017e30fb205cb9b4a8742e5e82b6"
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module number_theory.sum_four_squares
-! leanprover-community/mathlib commit 575b4ea3738b017e30fb205cb9b4a8742e5e82b6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.GroupPower.Identities
 import Mathbin.Data.Zmod.Basic
@@ -14,6 +9,8 @@ import Mathbin.FieldTheory.Finite.Basic
 import Mathbin.Data.Int.Parity
 import Mathbin.Data.Fintype.BigOperators
 
+#align_import number_theory.sum_four_squares from "leanprover-community/mathlib"@"575b4ea3738b017e30fb205cb9b4a8742e5e82b6"
+
 /-!
 # Lagrange's four square theorem
 

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

@@ -35,6 +35,7 @@ open scoped BigOperators
 
 namespace Int
 
+#print Int.sq_add_sq_of_two_mul_sq_add_sq /-
 theorem sq_add_sq_of_two_mul_sq_add_sq {m x y : ℤ} (h : 2 * m = x ^ 2 + y ^ 2) :
     m = ((x - y) / 2) ^ 2 + ((x + y) / 2) ^ 2 :=
   have : Even (x ^ 2 + y ^ 2) := by simp [← h, even_mul]
@@ -50,7 +51,9 @@ theorem sq_add_sq_of_two_mul_sq_add_sq {m x y : ℤ} (h : 2 * m = x ^ 2 + y ^ 2)
       _ = 2 * 2 * (((x - y) / 2) ^ 2 + ((x + y) / 2) ^ 2) := by
         simp [mul_add, pow_succ, mul_comm, mul_assoc, mul_left_comm]
 #align int.sq_add_sq_of_two_mul_sq_add_sq Int.sq_add_sq_of_two_mul_sq_add_sq
+-/
 
+#print Int.exists_sq_add_sq_add_one_eq_k /-
 theorem exists_sq_add_sq_add_one_eq_k (p : ℕ) [hp : Fact p.Prime] :
     ∃ (a b : ℤ) (k : ℕ), a ^ 2 + b ^ 2 + 1 = k * p ∧ k < p :=
   hp.1.eq_two_or_odd.elim (fun hp2 => hp2.symm ▸ ⟨1, 0, 1, rfl, by decide⟩) fun hp1 =>
@@ -84,6 +87,7 @@ theorem exists_sq_add_sq_add_one_eq_k (p : ℕ) [hp : Fact p.Prime] :
           _ = p * p := by conv_rhs => rw [← Nat.mod_add_div p 2]; ring)
         (show 0 ≤ p from Nat.zero_le _)⟩
 #align int.exists_sq_add_sq_add_one_eq_k Int.exists_sq_add_sq_add_one_eq_k
+-/
 
 end Int
 

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

@@ -125,7 +125,7 @@ private theorem sum_four_squares_of_two_mul_sum_four_squares {m a b c d : ℤ}
     rw [← Int.sq_add_sq_of_two_mul_sq_add_sq hx.symm, add_assoc, ←
       Int.sq_add_sq_of_two_mul_sq_add_sq hy.symm, ← mul_right_inj' (show (2 : ℤ) ≠ 0 by decide), ←
       h, mul_add, ← hx, ← hy]
-    have : (∑ x, f (σ x) ^ 2) = ∑ x, f x ^ 2 := by conv_rhs => rw [← Equiv.sum_comp σ]
+    have : ∑ x, f (σ x) ^ 2 = ∑ x, f x ^ 2 := by conv_rhs => rw [← Equiv.sum_comp σ]
     simpa only [Fin.sum_univ_four, add_assoc] using this⟩
 
 private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :

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

@@ -49,7 +49,6 @@ theorem sq_add_sq_of_two_mul_sq_add_sq {m x y : ℤ} (h : 2 * m = x ^ 2 + y ^ 2)
         rw [Int.mul_ediv_cancel' hxsuby, Int.mul_ediv_cancel' hxaddy]
       _ = 2 * 2 * (((x - y) / 2) ^ 2 + ((x + y) / 2) ^ 2) := by
         simp [mul_add, pow_succ, mul_comm, mul_assoc, mul_left_comm]
-      
 #align int.sq_add_sq_of_two_mul_sq_add_sq Int.sq_add_sq_of_two_mul_sq_add_sq
 
 theorem exists_sq_add_sq_add_one_eq_k (p : ℕ) [hp : Fact p.Prime] :
@@ -82,8 +81,7 @@ theorem exists_sq_add_sq_add_one_eq_k (p : ℕ) [hp : Fact p.Prime] :
                 (lt_add_iff_pos_right _).2
                   (add_pos_of_nonneg_of_pos (Nat.zero_le _)
                     (mul_pos (by decide) (Nat.div_pos hp.1.two_le (by decide))))
-          _ = p * p := by conv_rhs => rw [← Nat.mod_add_div p 2]; ring
-          )
+          _ = p * p := by conv_rhs => rw [← Nat.mod_add_div p 2]; ring)
         (show 0 ≤ p from Nat.zero_le _)⟩
 #align int.exists_sq_add_sq_add_one_eq_k Int.exists_sq_add_sq_add_one_eq_k
 
@@ -195,7 +193,6 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
             conv_rhs => rw [← Nat.mod_add_div m 2]
             simp [-Nat.mod_add_div, mul_add, add_mul, bit0, bit1, mul_comm, mul_assoc,
               mul_left_comm, pow_add, add_comm, add_left_comm]
-          
       have hwxyzabcd :
         ((w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 : ℤ) : ZMod m) =
           ((a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 : ℤ) : ZMod m) :=
@@ -251,7 +248,6 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
             _ = (w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2) * (a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2) := by
               simp only [hs.symm, ht.symm, hu.symm, hv.symm]; ring
             _ = _ := by rw [hn, habcd, Int.natAbs_of_nonneg hn_nonneg]; dsimp [m]; ring
-            
       False.elim <| Nat.find_min hm hnm ⟨lt_trans hnm hmp, hn0, s, t, u, v, hstuv⟩
 
 #print Nat.sum_four_squares /-

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 
 ! This file was ported from Lean 3 source module number_theory.sum_four_squares
-! leanprover-community/mathlib commit bd9851ca476957ea4549eb19b40e7b5ade9428cc
+! leanprover-community/mathlib commit 575b4ea3738b017e30fb205cb9b4a8742e5e82b6
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Data.Fintype.BigOperators
 /-!
 # Lagrange's four square theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The main result in this file is `sum_four_squares`,
 a proof that every natural number is the sum of four square numbers.
 

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

@@ -251,6 +251,7 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
             
       False.elim <| Nat.find_min hm hnm ⟨lt_trans hnm hmp, hn0, s, t, u, v, hstuv⟩
 
+#print Nat.sum_four_squares /-
 /-- **Four squares theorem** -/
 theorem sum_four_squares : ∀ n : ℕ, ∃ a b c d : ℕ, a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = n
   | 0 => ⟨0, 0, 0, 0, rfl⟩
@@ -269,6 +270,7 @@ theorem sum_four_squares : ∀ n : ℕ, ∃ a b c d : ℕ, a ^ 2 + b ^ 2 + c ^ 2
         h₂]
       simp [sum_four_sq_mul_sum_four_sq]⟩
 #align nat.sum_four_squares Nat.sum_four_squares
+-/
 
 end Nat
 

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

@@ -42,7 +42,7 @@ theorem sq_add_sq_of_two_mul_sq_add_sq {m x y : ℤ} (h : 2 * m = x ^ 2 + y ^ 2)
       2 * 2 * m = (x - y) ^ 2 + (x + y) ^ 2 := by rw [mul_assoc, h] <;> ring
       _ = (2 * ((x - y) / 2)) ^ 2 + (2 * ((x + y) / 2)) ^ 2 :=
         by
-        rw [even_iff_two_dvd] at hxsuby hxaddy
+        rw [even_iff_two_dvd] at hxsuby hxaddy 
         rw [Int.mul_ediv_cancel' hxsuby, Int.mul_ediv_cancel' hxaddy]
       _ = 2 * 2 * (((x - y) / 2) ^ 2 + ((x + y) / 2) ^ 2) := by
         simp [mul_add, pow_succ, mul_comm, mul_assoc, mul_left_comm]
@@ -50,7 +50,7 @@ theorem sq_add_sq_of_two_mul_sq_add_sq {m x y : ℤ} (h : 2 * m = x ^ 2 + y ^ 2)
 #align int.sq_add_sq_of_two_mul_sq_add_sq Int.sq_add_sq_of_two_mul_sq_add_sq
 
 theorem exists_sq_add_sq_add_one_eq_k (p : ℕ) [hp : Fact p.Prime] :
-    ∃ (a b : ℤ)(k : ℕ), a ^ 2 + b ^ 2 + 1 = k * p ∧ k < p :=
+    ∃ (a b : ℤ) (k : ℕ), a ^ 2 + b ^ 2 + 1 = k * p ∧ k < p :=
   hp.1.eq_two_or_odd.elim (fun hp2 => hp2.symm ▸ ⟨1, 0, 1, rfl, by decide⟩) fun hp1 =>
     let ⟨a, b, hab⟩ := ZMod.sq_add_sq p (-1)
     have hab' : (p : ℤ) ∣ a.valMinAbs ^ 2 + b.valMinAbs ^ 2 + 1 :=
@@ -134,7 +134,7 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
     ⟨k, hk.2,
       Nat.pos_of_ne_zero fun hk0 =>
         by
-        rw [hk0, Int.ofNat_zero, MulZeroClass.zero_mul] at hk
+        rw [hk0, Int.ofNat_zero, MulZeroClass.zero_mul] at hk 
         exact
           ne_of_gt
             (show a ^ 2 + b ^ 2 + 1 > 0 from
@@ -149,7 +149,7 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
     (fun hm2 : m % 2 = 0 =>
       let ⟨k, hk⟩ := Nat.dvd_iff_mod_eq_zero.2 hm2
       have hk0 : 0 < k :=
-        Nat.pos_of_ne_zero <| by rintro rfl; rw [MulZeroClass.mul_zero] at hk; exact NeZero.ne m hk
+        Nat.pos_of_ne_zero <| by rintro rfl; rw [MulZeroClass.mul_zero] at hk ; exact NeZero.ne m hk
       have hkm : k < m := by rw [hk, two_mul]; exact (lt_add_iff_pos_left _).2 hk0
       False.elim <|
         Nat.find_min hm hkm
@@ -203,7 +203,7 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
       have hn0 : 0 < n.natAbs :=
         Int.natAbs_pos_of_ne_zero fun hn0 =>
           have hwxyz0 : (w.natAbs ^ 2 + x.natAbs ^ 2 + y.natAbs ^ 2 + z.natAbs ^ 2 : ℕ) = 0 := by
-            rw [← Int.coe_nat_eq_zero, ← hnat_abs]; rwa [hn0, MulZeroClass.mul_zero] at hn
+            rw [← Int.coe_nat_eq_zero, ← hnat_abs]; rwa [hn0, MulZeroClass.mul_zero] at hn 
           have habcd0 : (m : ℤ) ∣ a ∧ (m : ℤ) ∣ b ∧ (m : ℤ) ∣ c ∧ (m : ℤ) ∣ d := by
             simpa only [add_eq_zero_iff, Int.natAbs_eq_zero, ZMod.valMinAbs_eq_zero, and_assoc,
               pow_eq_zero_iff two_pos, CharP.int_cast_eq_zero_iff _ m _] using hwxyz0

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

@@ -28,7 +28,7 @@ The proof used is close to Lagrange's original proof.
 
 open Finset Polynomial FiniteField Equiv
 
-open BigOperators
+open scoped BigOperators
 
 namespace Int
 
@@ -90,7 +90,7 @@ namespace Nat
 
 open Int
 
-open Classical
+open scoped Classical
 
 private theorem sum_four_squares_of_two_mul_sum_four_squares {m a b c d : ℤ}
     (h : a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = 2 * m) :

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

@@ -79,9 +79,7 @@ theorem exists_sq_add_sq_add_one_eq_k (p : ℕ) [hp : Fact p.Prime] :
                 (lt_add_iff_pos_right _).2
                   (add_pos_of_nonneg_of_pos (Nat.zero_le _)
                     (mul_pos (by decide) (Nat.div_pos hp.1.two_le (by decide))))
-          _ = p * p := by
-            conv_rhs => rw [← Nat.mod_add_div p 2]
-            ring
+          _ = p * p := by conv_rhs => rw [← Nat.mod_add_div p 2]; ring
           )
         (show 0 ≤ p from Nat.zero_le _)⟩
 #align int.exists_sq_add_sq_add_one_eq_k Int.exists_sq_add_sq_add_one_eq_k
@@ -151,19 +149,14 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
     (fun hm2 : m % 2 = 0 =>
       let ⟨k, hk⟩ := Nat.dvd_iff_mod_eq_zero.2 hm2
       have hk0 : 0 < k :=
-        Nat.pos_of_ne_zero <| by
-          rintro rfl
-          rw [MulZeroClass.mul_zero] at hk
-          exact NeZero.ne m hk
+        Nat.pos_of_ne_zero <| by rintro rfl; rw [MulZeroClass.mul_zero] at hk; exact NeZero.ne m hk
       have hkm : k < m := by rw [hk, two_mul]; exact (lt_add_iff_pos_left _).2 hk0
       False.elim <|
         Nat.find_min hm hkm
           ⟨lt_trans hkm hmp, hk0,
             sum_four_squares_of_two_mul_sum_four_squares
-              (show a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = 2 * (k * p)
-                by
-                rw [habcd, hk, Int.ofNat_mul, mul_assoc]
-                norm_num)⟩)
+              (show a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = 2 * (k * p) by
+                rw [habcd, hk, Int.ofNat_mul, mul_assoc]; norm_num)⟩)
     fun hm2 : m % 2 = 1 =>
     if hm1 : m = 1 then ⟨a, b, c, d, by simp only [hm1, habcd, Int.ofNat_one, one_mul]⟩
     else
@@ -174,9 +167,7 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
       have hnat_abs :
         w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 =
           (w.natAbs ^ 2 + x.natAbs ^ 2 + y.natAbs ^ 2 + z.natAbs ^ 2 : ℕ) :=
-        by
-        push_cast
-        simp_rw [sq_abs]
+        by push_cast ; simp_rw [sq_abs]
       have hwxyzlt : w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 < m ^ 2 :=
         calc
           w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 =
@@ -211,10 +202,8 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
       let ⟨n, hn⟩ := (CharP.int_cast_eq_zero_iff _ m _).1 hwxyz0
       have hn0 : 0 < n.natAbs :=
         Int.natAbs_pos_of_ne_zero fun hn0 =>
-          have hwxyz0 : (w.natAbs ^ 2 + x.natAbs ^ 2 + y.natAbs ^ 2 + z.natAbs ^ 2 : ℕ) = 0 :=
-            by
-            rw [← Int.coe_nat_eq_zero, ← hnat_abs]
-            rwa [hn0, MulZeroClass.mul_zero] at hn
+          have hwxyz0 : (w.natAbs ^ 2 + x.natAbs ^ 2 + y.natAbs ^ 2 + z.natAbs ^ 2 : ℕ) = 0 := by
+            rw [← Int.coe_nat_eq_zero, ← hnat_abs]; rwa [hn0, MulZeroClass.mul_zero] at hn
           have habcd0 : (m : ℤ) ∣ a ∧ (m : ℤ) ∣ b ∧ (m : ℤ) ∣ c ∧ (m : ℤ) ∣ d := by
             simpa only [add_eq_zero_iff, Int.natAbs_eq_zero, ZMod.valMinAbs_eq_zero, and_assoc,
               pow_eq_zero_iff two_pos, CharP.int_cast_eq_zero_iff _ m _] using hwxyz0
@@ -225,49 +214,29 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
           have hmdvdp : m ∣ p :=
             Int.coe_nat_dvd.1
               ⟨ma ^ 2 + mb ^ 2 + mc ^ 2 + md ^ 2,
-                (mul_right_inj' (show (m : ℤ) ≠ 0 from Int.coe_nat_ne_zero.2 hm0.1)).1 <|
-                  by
-                  rw [← habcd, hma, hmb, hmc, hmd]
-                  ring⟩
+                (mul_right_inj' (show (m : ℤ) ≠ 0 from Int.coe_nat_ne_zero.2 hm0.1)).1 <| by
+                  rw [← habcd, hma, hmb, hmc, hmd]; ring⟩
           (hp.1.eq_one_or_self_of_dvd _ hmdvdp).elim hm1 fun hmeqp => by
             simpa [lt_irrefl, hmeqp] using hmp
       have hawbxcydz : ((m : ℕ) : ℤ) ∣ a * w + b * x + c * y + d * z :=
-        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <|
-          by
-          rw [← hwxyz0]
-          simp_rw [sq]
-          push_cast
+        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by rw [← hwxyz0]; simp_rw [sq]; push_cast
       have haxbwczdy : ((m : ℕ) : ℤ) ∣ a * x - b * w - c * z + d * y :=
-        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <|
-          by
-          push_cast
-          ring
+        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by push_cast ; ring
       have haybzcwdx : ((m : ℕ) : ℤ) ∣ a * y + b * z - c * w - d * x :=
-        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <|
-          by
-          push_cast
-          ring
+        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by push_cast ; ring
       have hazbycxdw : ((m : ℕ) : ℤ) ∣ a * z - b * y + c * x - d * w :=
-        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <|
-          by
-          push_cast
-          ring
+        (CharP.int_cast_eq_zero_iff (ZMod m) m _).1 <| by push_cast ; ring
       let ⟨s, hs⟩ := hawbxcydz
       let ⟨t, ht⟩ := haxbwczdy
       let ⟨u, hu⟩ := haybzcwdx
       let ⟨v, hv⟩ := hazbycxdw
       have hn_nonneg : 0 ≤ n :=
         nonneg_of_mul_nonneg_right
-          (by
-            erw [← hn]
-            repeat' try refine' add_nonneg _ _; try exact sq_nonneg _)
+          (by erw [← hn]; repeat' try refine' add_nonneg _ _; try exact sq_nonneg _)
           (Int.coe_nat_pos.2 <| NeZero.pos m)
       have hnm : n.natAbs < m :=
         Int.ofNat_lt.1
-          (lt_of_mul_lt_mul_left
-            (by
-              rw [Int.natAbs_of_nonneg hn_nonneg, ← hn, ← sq]
-              exact hwxyzlt)
+          (lt_of_mul_lt_mul_left (by rw [Int.natAbs_of_nonneg hn_nonneg, ← hn, ← sq]; exact hwxyzlt)
             (Int.coe_nat_nonneg m))
       have hstuv : s ^ 2 + t ^ 2 + u ^ 2 + v ^ 2 = n.natAbs * p :=
         (mul_right_inj'
@@ -275,17 +244,10 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
           calc
             (m : ℤ) ^ 2 * (s ^ 2 + t ^ 2 + u ^ 2 + v ^ 2) =
                 ((m : ℕ) * s) ^ 2 + ((m : ℕ) * t) ^ 2 + ((m : ℕ) * u) ^ 2 + ((m : ℕ) * v) ^ 2 :=
-              by
-              simp [mul_pow]
-              ring
-            _ = (w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2) * (a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2) :=
-              by
-              simp only [hs.symm, ht.symm, hu.symm, hv.symm]
-              ring
-            _ = _ := by
-              rw [hn, habcd, Int.natAbs_of_nonneg hn_nonneg]
-              dsimp [m]
-              ring
+              by simp [mul_pow]; ring
+            _ = (w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2) * (a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2) := by
+              simp only [hs.symm, ht.symm, hu.symm, hv.symm]; ring
+            _ = _ := by rw [hn, habcd, Int.natAbs_of_nonneg hn_nonneg]; dsimp [m]; ring
             
       False.elim <| Nat.find_min hm hnm ⟨lt_trans hnm hmp, hn0, s, t, u, v, hstuv⟩
 

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

@@ -128,7 +128,6 @@ private theorem sum_four_squares_of_two_mul_sum_four_squares {m a b c d : ℤ}
       h, mul_add, ← hx, ← hy]
     have : (∑ x, f (σ x) ^ 2) = ∑ x, f x ^ 2 := by conv_rhs => rw [← Equiv.sum_comp σ]
     simpa only [Fin.sum_univ_four, add_assoc] using this⟩
-#align nat.sum_four_squares_of_two_mul_sum_four_squares nat.sum_four_squares_of_two_mul_sum_four_squares
 
 private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
     ∃ a b c d : ℤ, a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = p :=
@@ -289,7 +288,6 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
               ring
             
       False.elim <| Nat.find_min hm hnm ⟨lt_trans hnm hmp, hn0, s, t, u, v, hstuv⟩
-#align nat.prime_sum_four_squares nat.prime_sum_four_squares
 
 /-- **Four squares theorem** -/
 theorem sum_four_squares : ∀ n : ℕ, ∃ a b c d : ℕ, a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = n

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

@@ -107,8 +107,8 @@ private theorem sum_four_squares_of_two_mul_sum_four_squares {m a b c d : ℤ}
   let ⟨i, hσ⟩ :=
     this (fun x => coe (f x))
       (by
-        rw [← @zero_mul (ZMod 2) _ m, ← show ((2 : ℤ) : ZMod 2) = 0 from rfl, ← Int.cast_mul, ←
-              h] <;>
+        rw [← @MulZeroClass.zero_mul (ZMod 2) _ m, ← show ((2 : ℤ) : ZMod 2) = 0 from rfl, ←
+              Int.cast_mul, ← h] <;>
             simp only [Int.cast_add, Int.cast_pow] <;>
           rfl)
   let σ := swap i 0
@@ -137,7 +137,7 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
     ⟨k, hk.2,
       Nat.pos_of_ne_zero fun hk0 =>
         by
-        rw [hk0, Int.ofNat_zero, zero_mul] at hk
+        rw [hk0, Int.ofNat_zero, MulZeroClass.zero_mul] at hk
         exact
           ne_of_gt
             (show a ^ 2 + b ^ 2 + 1 > 0 from
@@ -154,7 +154,7 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
       have hk0 : 0 < k :=
         Nat.pos_of_ne_zero <| by
           rintro rfl
-          rw [mul_zero] at hk
+          rw [MulZeroClass.mul_zero] at hk
           exact NeZero.ne m hk
       have hkm : k < m := by rw [hk, two_mul]; exact (lt_add_iff_pos_left _).2 hk0
       False.elim <|
@@ -208,14 +208,14 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
           ((a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 : ℤ) : ZMod m) :=
         by push_cast
       have hwxyz0 : ((w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 : ℤ) : ZMod m) = 0 := by
-        rw [hwxyzabcd, habcd, Int.cast_mul, cast_coe_nat, ZMod.nat_cast_self, zero_mul]
+        rw [hwxyzabcd, habcd, Int.cast_mul, cast_coe_nat, ZMod.nat_cast_self, MulZeroClass.zero_mul]
       let ⟨n, hn⟩ := (CharP.int_cast_eq_zero_iff _ m _).1 hwxyz0
       have hn0 : 0 < n.natAbs :=
         Int.natAbs_pos_of_ne_zero fun hn0 =>
           have hwxyz0 : (w.natAbs ^ 2 + x.natAbs ^ 2 + y.natAbs ^ 2 + z.natAbs ^ 2 : ℕ) = 0 :=
             by
             rw [← Int.coe_nat_eq_zero, ← hnat_abs]
-            rwa [hn0, mul_zero] at hn
+            rwa [hn0, MulZeroClass.mul_zero] at hn
           have habcd0 : (m : ℤ) ∣ a ∧ (m : ℤ) ∣ b ∧ (m : ℤ) ∣ c ∧ (m : ℤ) ∣ d := by
             simpa only [add_eq_zero_iff, Int.natAbs_eq_zero, ZMod.valMinAbs_eq_zero, and_assoc,
               pow_eq_zero_iff two_pos, CharP.int_cast_eq_zero_iff _ m _] using hwxyz0

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

@@ -68,10 +68,10 @@ theorem exists_sq_add_sq_add_one_eq_k (p : ℕ) [hp : Fact p.Prime] :
               Int.natAbs_sq, Int.natAbs_sq, Int.ofNat_one, hk, Int.ofNat_mul,
               Int.natAbs_of_nonneg hk0]
           _ ≤ (p / 2) ^ 2 + (p / 2) ^ 2 + 1 :=
-            add_le_add
+            (add_le_add
               (add_le_add (Nat.pow_le_pow_of_le_left (ZMod.natAbs_valMinAbs_le _) _)
                 (Nat.pow_le_pow_of_le_left (ZMod.natAbs_valMinAbs_le _) _))
-              le_rfl
+              le_rfl)
           _ < (p / 2) ^ 2 + (p / 2) ^ 2 + (p % 2) ^ 2 + (2 * (p / 2) ^ 2 + 4 * (p / 2) * (p % 2)) :=
             by
             rw [hp1, one_pow, mul_one] <;>
@@ -184,20 +184,20 @@ private theorem prime_sum_four_squares (p : ℕ) [hp : Fact p.Prime] :
               (w.natAbs ^ 2 + x.natAbs ^ 2 + y.natAbs ^ 2 + z.natAbs ^ 2 : ℕ) :=
             hnat_abs
           _ ≤ ((m / 2) ^ 2 + (m / 2) ^ 2 + (m / 2) ^ 2 + (m / 2) ^ 2 : ℕ) :=
-            Int.ofNat_le.2 <|
+            (Int.ofNat_le.2 <|
               add_le_add
                 (add_le_add
                   (add_le_add (Nat.pow_le_pow_of_le_left (ZMod.natAbs_valMinAbs_le _) _)
                     (Nat.pow_le_pow_of_le_left (ZMod.natAbs_valMinAbs_le _) _))
                   (Nat.pow_le_pow_of_le_left (ZMod.natAbs_valMinAbs_le _) _))
-                (Nat.pow_le_pow_of_le_left (ZMod.natAbs_valMinAbs_le _) _)
+                (Nat.pow_le_pow_of_le_left (ZMod.natAbs_valMinAbs_le _) _))
           _ = 4 * (m / 2 : ℕ) ^ 2 := by
             simp only [bit0_mul, one_mul, two_smul, Nat.cast_add, Nat.cast_pow, add_assoc]
           _ < 4 * (m / 2 : ℕ) ^ 2 + ((4 * (m / 2) : ℕ) * (m % 2 : ℕ) + (m % 2 : ℕ) ^ 2) :=
-            (lt_add_iff_pos_right _).2
+            ((lt_add_iff_pos_right _).2
               (by
                 rw [hm2, Int.ofNat_one, one_pow, mul_one]
-                exact add_pos_of_nonneg_of_pos (Int.coe_nat_nonneg _) zero_lt_one)
+                exact add_pos_of_nonneg_of_pos (Int.coe_nat_nonneg _) zero_lt_one))
           _ = m ^ 2 := by
             conv_rhs => rw [← Nat.mod_add_div m 2]
             simp [-Nat.mod_add_div, mul_add, add_mul, bit0, bit1, mul_comm, mul_assoc,

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

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

@@ -125,10 +125,10 @@ private theorem sum_four_squares_of_two_mul_sum_four_squares {m a b c d : ℤ}
     rfl
   set σ := swap i 0
   obtain ⟨x, hx⟩ : (2 : ℤ) ∣ f (σ 0) ^ 2 + f (σ 1) ^ 2 :=
-    (CharP.int_cast_eq_zero_iff (ZMod 2) 2 _).1 <| by
+    (CharP.intCast_eq_zero_iff (ZMod 2) 2 _).1 <| by
       simpa only [σ, Int.cast_pow, Int.cast_add, Equiv.swap_apply_right, ZMod.pow_card] using hσ.1
   obtain ⟨y, hy⟩ : (2 : ℤ) ∣ f (σ 2) ^ 2 + f (σ 3) ^ 2 :=
-    (CharP.int_cast_eq_zero_iff (ZMod 2) 2 _).1 <| by
+    (CharP.intCast_eq_zero_iff (ZMod 2) 2 _).1 <| by
       simpa only [Int.cast_pow, Int.cast_add, ZMod.pow_card] using hσ.2
   refine ⟨(f (σ 0) - f (σ 1)) / 2, (f (σ 0) + f (σ 1)) / 2, (f (σ 2) - f (σ 3)) / 2,
     (f (σ 2) + f (σ 3)) / 2, ?_⟩
@@ -178,7 +178,7 @@ protected theorem Prime.sum_four_squares {p : ℕ} (hp : p.Prime) :
     -- `m ∣ |f a| ^ 2 + |f b| ^ 2 + |f c| ^ 2 + |f d| ^ 2`
     obtain ⟨r, hr⟩ :
         m ∣ (f a).natAbs ^ 2 + (f b).natAbs ^ 2 + (f c).natAbs ^ 2 + (f d).natAbs ^ 2 := by
-      simp only [← Int.natCast_dvd_natCast, ← ZMod.int_cast_zmod_eq_zero_iff_dvd]
+      simp only [← Int.natCast_dvd_natCast, ← ZMod.intCast_zmod_eq_zero_iff_dvd]
       push_cast [hf_mod, sq_abs]
       norm_cast
       simp [habcd]
@@ -187,7 +187,7 @@ protected theorem Prime.sum_four_squares {p : ℕ} (hp : p.Prime) :
     rcases (zero_le r).eq_or_gt with rfl | hr₀
     · replace hr : f a = 0 ∧ f b = 0 ∧ f c = 0 ∧ f d = 0 := by simpa [and_assoc] using hr
       obtain ⟨⟨a, rfl⟩, ⟨b, rfl⟩, ⟨c, rfl⟩, ⟨d, rfl⟩⟩ : m ∣ a ∧ m ∣ b ∧ m ∣ c ∧ m ∣ d := by
-        simp only [← ZMod.nat_cast_zmod_eq_zero_iff_dvd, ← hf_mod, hr, Int.cast_zero, and_self]
+        simp only [← ZMod.natCast_zmod_eq_zero_iff_dvd, ← hf_mod, hr, Int.cast_zero, and_self]
       have : m * m ∣ m * p := habcd ▸ ⟨a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2, by ring⟩
       rw [mul_dvd_mul_iff_left hm₀.ne'] at this
       exact (hp.eq_one_or_self_of_dvd _ this).elim hm₁.ne' hmp.ne
@@ -213,14 +213,14 @@ protected theorem Prime.sum_four_squares {p : ℕ} (hp : p.Prime) :
     have := congr_arg₂ (· * Nat.cast ·) hr habcd
     simp only [← _root_.euler_four_squares, Nat.cast_add, Nat.cast_pow] at this
     refine ⟨_, _, _, _, ?_, ?_, ?_, ?_, this⟩
-    · simp [← ZMod.int_cast_zmod_eq_zero_iff_dvd, hf_mod, mul_comm]
+    · simp [← ZMod.intCast_zmod_eq_zero_iff_dvd, hf_mod, mul_comm]
     · suffices ((a : ZMod m) ^ 2 + (b : ZMod m) ^ 2 + (c : ZMod m) ^ 2 + (d : ZMod m) ^ 2) = 0 by
-        simpa [← ZMod.int_cast_zmod_eq_zero_iff_dvd, hf_mod, sq, add_comm, add_assoc,
+        simpa [← ZMod.intCast_zmod_eq_zero_iff_dvd, hf_mod, sq, add_comm, add_assoc,
           add_left_comm] using this
       norm_cast
       simp [habcd]
-    · simp [← ZMod.int_cast_zmod_eq_zero_iff_dvd, hf_mod, mul_comm]
-    · simp [← ZMod.int_cast_zmod_eq_zero_iff_dvd, hf_mod, mul_comm]
+    · simp [← ZMod.intCast_zmod_eq_zero_iff_dvd, hf_mod, mul_comm]
+    · simp [← ZMod.intCast_zmod_eq_zero_iff_dvd, hf_mod, mul_comm]
 
 /-- **Four squares theorem** -/
 theorem sum_four_squares (n : ℕ) : ∃ a b c d : ℕ, a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = n := by

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

@@ -39,7 +39,7 @@ theorem Nat.euler_four_squares (a b c d x y z w : ℕ) :
       ((a : ℤ) * z - b * w + c * x + d * y).natAbs ^ 2 +
       ((a : ℤ) * w + b * z - c * y + d * x).natAbs ^ 2 =
       (a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2) * (x ^ 2 + y ^ 2 + z ^ 2 + w ^ 2) := by
-  rw [← Int.coe_nat_inj']
+  rw [← Int.natCast_inj]
   push_cast
   simp only [sq_abs, _root_.euler_four_squares]
 
@@ -178,7 +178,7 @@ protected theorem Prime.sum_four_squares {p : ℕ} (hp : p.Prime) :
     -- `m ∣ |f a| ^ 2 + |f b| ^ 2 + |f c| ^ 2 + |f d| ^ 2`
     obtain ⟨r, hr⟩ :
         m ∣ (f a).natAbs ^ 2 + (f b).natAbs ^ 2 + (f c).natAbs ^ 2 + (f d).natAbs ^ 2 := by
-      simp only [← Int.coe_nat_dvd, ← ZMod.int_cast_zmod_eq_zero_iff_dvd]
+      simp only [← Int.natCast_dvd_natCast, ← ZMod.int_cast_zmod_eq_zero_iff_dvd]
       push_cast [hf_mod, sq_abs]
       norm_cast
       simp [habcd]

Classifies by adding issue number #10756 to porting notes claiming anything equivalent to:

• "added theorem"
• "added theorems"
• "new theorem"
• "new theorems"
• "added lemma"
• "new lemma"
• "new lemmas"

@@ -61,7 +61,7 @@ theorem sq_add_sq_of_two_mul_sq_add_sq {m x y : ℤ} (h : 2 * m = x ^ 2 + y ^ 2)
         simp [mul_add, pow_succ, mul_comm, mul_assoc, mul_left_comm]
 #align int.sq_add_sq_of_two_mul_sq_add_sq Int.sq_add_sq_of_two_mul_sq_add_sq
 
--- Porting note: new theorem
+-- Porting note (#10756): new theorem
 theorem lt_of_sum_four_squares_eq_mul {a b c d k m : ℕ}
     (h : a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = k * m)
     (ha : 2 * a < m) (hb : 2 * b < m) (hc : 2 * c < m) (hd : 2 * d < m) :
@@ -76,7 +76,7 @@ theorem lt_of_sum_four_squares_eq_mul {a b c d k m : ℕ}
       fin_cases i <;> assumption
     _ = 2 ^ 2 * (m * m) := by simp; ring
 
--- Porting note: new theorem
+-- Porting note (#10756): new theorem
 theorem exists_sq_add_sq_add_one_eq_mul (p : ℕ) [hp : Fact p.Prime] :
     ∃ (a b k : ℕ), 0 < k ∧ k < p ∧ a ^ 2 + b ^ 2 + 1 = k * p := by
   rcases hp.1.eq_two_or_odd' with (rfl | hodd)

@@ -234,7 +234,6 @@ theorem sum_four_squares (n : ℕ) : ∃ a b c d : ℕ, a ^ 2 + b ^ 2 + c ^ 2 +
     rcases hm with ⟨a, b, c, d, rfl⟩
     rcases hn with ⟨w, x, y, z, rfl⟩
     exact ⟨_, _, _, _, euler_four_squares _ _ _ _ _ _ _ _⟩
-
 #align nat.sum_four_squares Nat.sum_four_squares
 
 end Nat

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".

@@ -61,7 +61,7 @@ theorem sq_add_sq_of_two_mul_sq_add_sq {m x y : ℤ} (h : 2 * m = x ^ 2 + y ^ 2)
         simp [mul_add, pow_succ, mul_comm, mul_assoc, mul_left_comm]
 #align int.sq_add_sq_of_two_mul_sq_add_sq Int.sq_add_sq_of_two_mul_sq_add_sq
 
--- porting note: new theorem
+-- Porting note: new theorem
 theorem lt_of_sum_four_squares_eq_mul {a b c d k m : ℕ}
     (h : a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = k * m)
     (ha : 2 * a < m) (hb : 2 * b < m) (hc : 2 * c < m) (hd : 2 * d < m) :
@@ -76,7 +76,7 @@ theorem lt_of_sum_four_squares_eq_mul {a b c d k m : ℕ}
       fin_cases i <;> assumption
     _ = 2 ^ 2 * (m * m) := by simp; ring
 
--- porting note: new theorem
+-- Porting note: new theorem
 theorem exists_sq_add_sq_add_one_eq_mul (p : ℕ) [hp : Fact p.Prime] :
     ∃ (a b k : ℕ), 0 < k ∧ k < p ∧ a ^ 2 + b ^ 2 + 1 = k * p := by
   rcases hp.1.eq_two_or_odd' with (rfl | hodd)

This covers many instances, but is not exhaustive.

Independently of whether that syntax should be avoided (similar to #10534), I think all these changes are small improvements.

@@ -169,14 +169,16 @@ protected theorem Prime.sum_four_squares {p : ℕ} (hp : p.Prime) :
     exact hmin m hm₂ ⟨hm₂.trans hmp, hm₀, _, _, _, _, natAbs_iff.2 h⟩
   · -- For each `x` in `a`, `b`, `c`, `d`, take a number `f x ≡ x [ZMOD m]` with least possible
     -- absolute value
-    obtain ⟨f, hf_lt, hf_mod⟩ : ∃ f : ℕ → ℤ, (∀ x, 2 * (f x).natAbs < m) ∧ ∀ x, (f x : ZMod m) = x
-    · refine ⟨fun x ↦ (x : ZMod m).valMinAbs, fun x ↦ ?_, fun x ↦ (x : ZMod m).coe_valMinAbs⟩
+    obtain ⟨f, hf_lt, hf_mod⟩ :
+        ∃ f : ℕ → ℤ, (∀ x, 2 * (f x).natAbs < m) ∧ ∀ x, (f x : ZMod m) = x := by
+      refine ⟨fun x ↦ (x : ZMod m).valMinAbs, fun x ↦ ?_, fun x ↦ (x : ZMod m).coe_valMinAbs⟩
       exact (mul_le_mul' le_rfl (x : ZMod m).natAbs_valMinAbs_le).trans_lt
         (Nat.mul_div_lt_iff_not_dvd.2 hm)
     -- Since `|f x| ^ 2 = (f x) ^ 2 ≡ x ^ 2 [ZMOD m]`, we have
     -- `m ∣ |f a| ^ 2 + |f b| ^ 2 + |f c| ^ 2 + |f d| ^ 2`
-    obtain ⟨r, hr⟩ : m ∣ (f a).natAbs ^ 2 + (f b).natAbs ^ 2 + (f c).natAbs ^ 2 + (f d).natAbs ^ 2
-    · simp only [← Int.coe_nat_dvd, ← ZMod.int_cast_zmod_eq_zero_iff_dvd]
+    obtain ⟨r, hr⟩ :
+        m ∣ (f a).natAbs ^ 2 + (f b).natAbs ^ 2 + (f c).natAbs ^ 2 + (f d).natAbs ^ 2 := by
+      simp only [← Int.coe_nat_dvd, ← ZMod.int_cast_zmod_eq_zero_iff_dvd]
       push_cast [hf_mod, sq_abs]
       norm_cast
       simp [habcd]
@@ -184,8 +186,8 @@ protected theorem Prime.sum_four_squares {p : ℕ} (hp : p.Prime) :
     -- `m` divides each `a`, `b`, `c`, `d`, thus `m ∣ p` which is impossible.
     rcases (zero_le r).eq_or_gt with rfl | hr₀
     · replace hr : f a = 0 ∧ f b = 0 ∧ f c = 0 ∧ f d = 0 := by simpa [and_assoc] using hr
-      obtain ⟨⟨a, rfl⟩, ⟨b, rfl⟩, ⟨c, rfl⟩, ⟨d, rfl⟩⟩ : m ∣ a ∧ m ∣ b ∧ m ∣ c ∧ m ∣ d
-      · simp only [← ZMod.nat_cast_zmod_eq_zero_iff_dvd, ← hf_mod, hr, Int.cast_zero, and_self]
+      obtain ⟨⟨a, rfl⟩, ⟨b, rfl⟩, ⟨c, rfl⟩, ⟨d, rfl⟩⟩ : m ∣ a ∧ m ∣ b ∧ m ∣ c ∧ m ∣ d := by
+        simp only [← ZMod.nat_cast_zmod_eq_zero_iff_dvd, ← hf_mod, hr, Int.cast_zero, and_self]
       have : m * m ∣ m * p := habcd ▸ ⟨a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2, by ring⟩
       rw [mul_dvd_mul_iff_left hm₀.ne'] at this
       exact (hp.eq_one_or_self_of_dvd _ this).elim hm₁.ne' hmp.ne

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -126,7 +126,7 @@ private theorem sum_four_squares_of_two_mul_sum_four_squares {m a b c d : ℤ}
   set σ := swap i 0
   obtain ⟨x, hx⟩ : (2 : ℤ) ∣ f (σ 0) ^ 2 + f (σ 1) ^ 2 :=
     (CharP.int_cast_eq_zero_iff (ZMod 2) 2 _).1 <| by
-      simpa only [Int.cast_pow, Int.cast_add, Equiv.swap_apply_right, ZMod.pow_card] using hσ.1
+      simpa only [σ, Int.cast_pow, Int.cast_add, Equiv.swap_apply_right, ZMod.pow_card] using hσ.1
   obtain ⟨y, hy⟩ : (2 : ℤ) ∣ f (σ 2) ^ 2 + f (σ 3) ^ 2 :=
     (CharP.int_cast_eq_zero_iff (ZMod 2) 2 _).1 <| by
       simpa only [Int.cast_pow, Int.cast_add, ZMod.pow_card] using hσ.2

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com>

@@ -66,7 +66,8 @@ theorem lt_of_sum_four_squares_eq_mul {a b c d k m : ℕ}
     (h : a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = k * m)
     (ha : 2 * a < m) (hb : 2 * b < m) (hc : 2 * c < m) (hd : 2 * d < m) :
     k < m := by
-  refine lt_of_mul_lt_mul_right (lt_of_mul_lt_mul_left ?_ (zero_le (2 ^ 2))) (zero_le m)
+  refine _root_.lt_of_mul_lt_mul_right
+    (_root_.lt_of_mul_lt_mul_left ?_ (zero_le (2 ^ 2))) (zero_le m)
   calc
     2 ^ 2 * (k * ↑m) = ∑ i : Fin 4, (2 * ![a, b, c, d] i) ^ 2 := by
       simp [← h, Fin.sum_univ_succ, mul_add, mul_pow, add_assoc]

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -83,14 +83,13 @@ theorem exists_sq_add_sq_add_one_eq_mul (p : ℕ) [hp : Fact p.Prime] :
   rcases Nat.sq_add_sq_zmodEq p (-1) with ⟨a, b, ha, hb, hab⟩
   rcases Int.modEq_iff_dvd.1 hab.symm with ⟨k, hk⟩
   rw [sub_neg_eq_add, mul_comm] at hk
-  have hk₀ : 0 < k
-  · refine pos_of_mul_pos_left ?_ (Nat.cast_nonneg p)
+  have hk₀ : 0 < k := by
+    refine pos_of_mul_pos_left ?_ (Nat.cast_nonneg p)
     rw [← hk]
     positivity
   lift k to ℕ using hk₀.le
   refine ⟨a, b, k, Nat.cast_pos.1 hk₀, ?_, mod_cast hk⟩
-  replace hk : a ^ 2 + b ^ 2 + 1 ^ 2 + 0 ^ 2 = k * p
-  · exact mod_cast hk
+  replace hk : a ^ 2 + b ^ 2 + 1 ^ 2 + 0 ^ 2 = k * p := mod_cast hk
   refine lt_of_sum_four_squares_eq_mul hk ?_ ?_ ?_ ?_
   · exact (mul_le_mul' le_rfl ha).trans_lt (Nat.mul_div_lt_iff_not_dvd.2 hodd.not_two_dvd_nat)
   · exact (mul_le_mul' le_rfl hb).trans_lt (Nat.mul_div_lt_iff_not_dvd.2 hodd.not_two_dvd_nat)
@@ -146,8 +145,8 @@ protected theorem Prime.sum_four_squares {p : ℕ} (hp : p.Prime) :
       a.natAbs ^ 2 + b.natAbs ^ 2 + c.natAbs ^ 2 + d.natAbs ^ 2 = k ↔
         a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = k := by
     rw [← @Nat.cast_inj ℤ]; push_cast [sq_abs]; rfl
-  have hm : ∃ m < p, 0 < m ∧ ∃ a b c d : ℕ, a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = m * p
-  · obtain ⟨a, b, k, hk₀, hkp, hk⟩ := exists_sq_add_sq_add_one_eq_mul p
+  have hm : ∃ m < p, 0 < m ∧ ∃ a b c d : ℕ, a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = m * p := by
+    obtain ⟨a, b, k, hk₀, hkp, hk⟩ := exists_sq_add_sq_add_one_eq_mul p
     refine ⟨k, hkp, hk₀, a, b, 1, 0, ?_⟩
     simpa
   -- Take the minimal possible `m`
@@ -183,37 +182,37 @@ protected theorem Prime.sum_four_squares {p : ℕ} (hp : p.Prime) :
     -- The quotient `r` is not zero, because otherwise `f a = f b = f c = f d = 0`, hence
     -- `m` divides each `a`, `b`, `c`, `d`, thus `m ∣ p` which is impossible.
     rcases (zero_le r).eq_or_gt with rfl | hr₀
-    · replace hr : f a = 0 ∧ f b = 0 ∧ f c = 0 ∧ f d = 0; · simpa [and_assoc] using hr
+    · replace hr : f a = 0 ∧ f b = 0 ∧ f c = 0 ∧ f d = 0 := by simpa [and_assoc] using hr
       obtain ⟨⟨a, rfl⟩, ⟨b, rfl⟩, ⟨c, rfl⟩, ⟨d, rfl⟩⟩ : m ∣ a ∧ m ∣ b ∧ m ∣ c ∧ m ∣ d
       · simp only [← ZMod.nat_cast_zmod_eq_zero_iff_dvd, ← hf_mod, hr, Int.cast_zero, and_self]
       have : m * m ∣ m * p := habcd ▸ ⟨a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2, by ring⟩
       rw [mul_dvd_mul_iff_left hm₀.ne'] at this
       exact (hp.eq_one_or_self_of_dvd _ this).elim hm₁.ne' hmp.ne
     -- Since `2 * |f x| < m` for each `x ∈ {a, b, c, d}`, we have `r < m`
-    have hrm : r < m
-    · rw [mul_comm] at hr
+    have hrm : r < m := by
+      rw [mul_comm] at hr
       apply lt_of_sum_four_squares_eq_mul hr <;> apply hf_lt
     -- Now it suffices to represent `r * p` as a sum of four squares
     -- More precisely, we will represent `(m * r) * (m * p)` as a sum of squares of four numbers,
     -- each of them is divisible by `m`
     rsuffices ⟨w, x, y, z, hw, hx, hy, hz, h⟩ : ∃ w x y z : ℤ, ↑m ∣ w ∧ ↑m ∣ x ∧ ↑m ∣ y ∧ ↑m ∣ z ∧
       w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 = ↑(m * r) * ↑(m * p)
-    · have : (w / m) ^ 2 + (x / m) ^ 2 + (y / m) ^ 2 + (z / m) ^ 2 = ↑(r * p)
-      · refine mul_left_cancel₀ (pow_ne_zero 2 (Nat.cast_ne_zero.2 hm₀.ne')) ?_
+    · have : (w / m) ^ 2 + (x / m) ^ 2 + (y / m) ^ 2 + (z / m) ^ 2 = ↑(r * p) := by
+        refine mul_left_cancel₀ (pow_ne_zero 2 (Nat.cast_ne_zero.2 hm₀.ne')) ?_
         conv_rhs => rw [← Nat.cast_pow, ← Nat.cast_mul, sq m, mul_mul_mul_comm, Nat.cast_mul, ← h]
         simp only [mul_add, ← mul_pow, Int.mul_ediv_cancel', *]
       rw [← natAbs_iff] at this
       exact hmin r hrm ⟨hrm.trans hmp, hr₀, _, _, _, _, this⟩
     -- To do the last step, we apply the Euler's four square identity once more
-    replace hr : (f b) ^ 2 + (f a) ^ 2 + (f d) ^ 2 + (-f c) ^ 2 = ↑(m * r)
-    · rw [← natAbs_iff, natAbs_neg, ← hr]
+    replace hr : (f b) ^ 2 + (f a) ^ 2 + (f d) ^ 2 + (-f c) ^ 2 = ↑(m * r) := by
+      rw [← natAbs_iff, natAbs_neg, ← hr]
       ac_rfl
     have := congr_arg₂ (· * Nat.cast ·) hr habcd
     simp only [← _root_.euler_four_squares, Nat.cast_add, Nat.cast_pow] at this
     refine ⟨_, _, _, _, ?_, ?_, ?_, ?_, this⟩
     · simp [← ZMod.int_cast_zmod_eq_zero_iff_dvd, hf_mod, mul_comm]
-    · suffices : ((a : ZMod m) ^ 2 + (b : ZMod m) ^ 2 + (c : ZMod m) ^ 2 + (d : ZMod m) ^ 2) = 0
-      · simpa [← ZMod.int_cast_zmod_eq_zero_iff_dvd, hf_mod, sq, add_comm, add_assoc,
+    · suffices ((a : ZMod m) ^ 2 + (b : ZMod m) ^ 2 + (c : ZMod m) ^ 2 + (d : ZMod m) ^ 2) = 0 by
+        simpa [← ZMod.int_cast_zmod_eq_zero_iff_dvd, hf_mod, sq, add_comm, add_assoc,
           add_left_comm] using this
       norm_cast
       simp [habcd]

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

@@ -57,6 +57,7 @@ theorem sq_add_sq_of_two_mul_sq_add_sq {m x y : ℤ} (h : 2 * m = x ^ 2 + y ^ 2)
         rw [even_iff_two_dvd] at hxsuby hxaddy
         rw [Int.mul_ediv_cancel' hxsuby, Int.mul_ediv_cancel' hxaddy]
       _ = 2 * 2 * (((x - y) / 2) ^ 2 + ((x + y) / 2) ^ 2) := by
+        set_option simprocs false in
         simp [mul_add, pow_succ, mul_comm, mul_assoc, mul_left_comm]
 #align int.sq_add_sq_of_two_mul_sq_add_sq Int.sq_add_sq_of_two_mul_sq_add_sq
 

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>

@@ -3,7 +3,6 @@ Copyright (c) 2019 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathlib.Algebra.GroupPower.Identities
 import Mathlib.Data.ZMod.Basic
 import Mathlib.FieldTheory.Finite.Basic
 import Mathlib.Data.Int.Parity

I had a slightly logic-heavy argument that was nicely simplified by stating this lemma. Also fix a few lemma names.

From LeanAPAP and LeanCamCombi

@@ -161,7 +161,7 @@ protected theorem Prime.sum_four_squares {p : ℕ} (hp : p.Prime) :
   by_cases hm : 2 ∣ m
   · -- If `m` is an even number, then `(m / 2) * p` can be represented as a sum of four squares
     rcases hm with ⟨m, rfl⟩
-    rw [zero_lt_mul_left two_pos] at hm₀
+    rw [mul_pos_iff_of_pos_left two_pos] at hm₀
     have hm₂ : m < 2 * m := by simpa [two_mul]
     apply_fun (Nat.cast : ℕ → ℤ) at habcd
     push_cast [mul_assoc] at habcd

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.

@@ -71,7 +71,7 @@ theorem lt_of_sum_four_squares_eq_mul {a b c d k m : ℕ}
     2 ^ 2 * (k * ↑m) = ∑ i : Fin 4, (2 * ![a, b, c, d] i) ^ 2 := by
       simp [← h, Fin.sum_univ_succ, mul_add, mul_pow, add_assoc]
     _ < ∑ _i : Fin 4, m ^ 2 := Finset.sum_lt_sum_of_nonempty Finset.univ_nonempty fun i _ ↦ by
-      refine pow_lt_pow_of_lt_left ?_ (zero_le _) two_pos
+      refine pow_lt_pow_left ?_ (zero_le _) two_ne_zero
       fin_cases i <;> assumption
     _ = 2 ^ 2 * (m * m) := by simp; ring
 

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

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

@@ -88,9 +88,9 @@ theorem exists_sq_add_sq_add_one_eq_mul (p : ℕ) [hp : Fact p.Prime] :
     rw [← hk]
     positivity
   lift k to ℕ using hk₀.le
-  refine ⟨a, b, k, Nat.cast_pos.1 hk₀, ?_, by exact_mod_cast hk⟩
+  refine ⟨a, b, k, Nat.cast_pos.1 hk₀, ?_, mod_cast hk⟩
   replace hk : a ^ 2 + b ^ 2 + 1 ^ 2 + 0 ^ 2 = k * p
-  · exact_mod_cast hk
+  · exact mod_cast hk
   refine lt_of_sum_four_squares_eq_mul hk ?_ ?_ ?_ ?_
   · exact (mul_le_mul' le_rfl ha).trans_lt (Nat.mul_div_lt_iff_not_dvd.2 hodd.not_two_dvd_nat)
   · exact (mul_le_mul' le_rfl hb).trans_lt (Nat.mul_div_lt_iff_not_dvd.2 hodd.not_two_dvd_nat)
@@ -101,7 +101,7 @@ theorem exists_sq_add_sq_add_one_eq_mul (p : ℕ) [hp : Fact p.Prime] :
 theorem exists_sq_add_sq_add_one_eq_k (p : ℕ) [Fact p.Prime] :
     ∃ (a b : ℤ) (k : ℕ), a ^ 2 + b ^ 2 + 1 = k * p ∧ k < p :=
   let ⟨a, b, k, _, hkp, hk⟩ := exists_sq_add_sq_add_one_eq_mul p
-  ⟨a, b, k, by exact_mod_cast hk, hkp⟩
+  ⟨a, b, k, mod_cast hk, hkp⟩
 #align int.exists_sq_add_sq_add_one_eq_k Int.exists_sq_add_sq_add_one_eq_k
 
 end Int

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>

@@ -27,8 +27,6 @@ open Finset Polynomial FiniteField Equiv
 
 open scoped BigOperators
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 /-- **Euler's four-square identity**. -/
 theorem euler_four_squares {R : Type*} [CommRing R] (a b c d x y z w : R) :
     (a * x - b * y - c * z - d * w) ^ 2 + (a * y + b * x + c * w - d * z) ^ 2 +
@@ -187,7 +185,7 @@ protected theorem Prime.sum_four_squares {p : ℕ} (hp : p.Prime) :
     rcases (zero_le r).eq_or_gt with rfl | hr₀
     · replace hr : f a = 0 ∧ f b = 0 ∧ f c = 0 ∧ f d = 0; · simpa [and_assoc] using hr
       obtain ⟨⟨a, rfl⟩, ⟨b, rfl⟩, ⟨c, rfl⟩, ⟨d, rfl⟩⟩ : m ∣ a ∧ m ∣ b ∧ m ∣ c ∧ m ∣ d
-      · simp only [← ZMod.nat_cast_zmod_eq_zero_iff_dvd, ← hf_mod, hr, Int.cast_zero]
+      · simp only [← ZMod.nat_cast_zmod_eq_zero_iff_dvd, ← hf_mod, hr, Int.cast_zero, and_self]
       have : m * m ∣ m * p := habcd ▸ ⟨a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2, by ring⟩
       rw [mul_dvd_mul_iff_left hm₀.ne'] at this
       exact (hp.eq_one_or_self_of_dvd _ this).elim hm₁.ne' hmp.ne

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

This has nice performance benefits.

@@ -30,7 +30,7 @@ open scoped BigOperators
 local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 /-- **Euler's four-square identity**. -/
-theorem euler_four_squares {R : Type _} [CommRing R] (a b c d x y z w : R) :
+theorem euler_four_squares {R : Type*} [CommRing R] (a b c d x y z w : R) :
     (a * x - b * y - c * z - d * w) ^ 2 + (a * y + b * x + c * w - d * z) ^ 2 +
       (a * z - b * w + c * x + d * y) ^ 2 + (a * w + b * z - c * y + d * x) ^ 2 =
       (a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2) * (x ^ 2 + y ^ 2 + z ^ 2 + w ^ 2) := by ring

@@ -27,7 +27,7 @@ open Finset Polynomial FiniteField Equiv
 
 open scoped BigOperators
 
-local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y) -- Porting note: See Lean 4 issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 /-- **Euler's four-square identity**. -/
 theorem euler_four_squares {R : Type _} [CommRing R] (a b c d x y z w : R) :

• 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) 2019 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module number_theory.sum_four_squares
-! leanprover-community/mathlib commit bd9851ca476957ea4549eb19b40e7b5ade9428cc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.GroupPower.Identities
 import Mathlib.Data.ZMod.Basic
@@ -14,6 +9,8 @@ import Mathlib.FieldTheory.Finite.Basic
 import Mathlib.Data.Int.Parity
 import Mathlib.Data.Fintype.BigOperators
 
+#align_import number_theory.sum_four_squares from "leanprover-community/mathlib"@"bd9851ca476957ea4549eb19b40e7b5ade9428cc"
+
 /-!
 # Lagrange's four square theorem
 

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

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

@@ -60,7 +60,7 @@ theorem sq_add_sq_of_two_mul_sq_add_sq {m x y : ℤ} (h : 2 * m = x ^ 2 + y ^ 2)
     calc
       2 * 2 * m = (x - y) ^ 2 + (x + y) ^ 2 := by rw [mul_assoc, h]; ring
       _ = (2 * ((x - y) / 2)) ^ 2 + (2 * ((x + y) / 2)) ^ 2 := by
-        rw [even_iff_two_dvd] at hxsuby hxaddy 
+        rw [even_iff_two_dvd] at hxsuby hxaddy
         rw [Int.mul_ediv_cancel' hxsuby, Int.mul_ediv_cancel' hxaddy]
       _ = 2 * 2 * (((x - y) / 2) ^ 2 + ((x + y) / 2) ^ 2) := by
         simp [mul_add, pow_succ, mul_comm, mul_assoc, mul_left_comm]
@@ -89,7 +89,7 @@ theorem exists_sq_add_sq_add_one_eq_mul (p : ℕ) [hp : Fact p.Prime] :
   rcases Int.modEq_iff_dvd.1 hab.symm with ⟨k, hk⟩
   rw [sub_neg_eq_add, mul_comm] at hk
   have hk₀ : 0 < k
-  · refine pos_of_mul_pos_left  ?_ (Nat.cast_nonneg p)
+  · refine pos_of_mul_pos_left ?_ (Nat.cast_nonneg p)
     rw [← hk]
     positivity
   lift k to ℕ using hk₀.le
@@ -237,7 +237,7 @@ theorem sum_four_squares (n : ℕ) : ∃ a b c d : ℕ, a ^ 2 + b ^ 2 + c ^ 2 +
     rcases hm with ⟨a, b, c, d, rfl⟩
     rcases hn with ⟨w, x, y, z, rfl⟩
     exact ⟨_, _, _, _, euler_four_squares _ _ _ _ _ _ _ _⟩
-  
+
 #align nat.sum_four_squares Nat.sum_four_squares
 
 end Nat