Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

e8638a0f

(last sync)

feat(algebra/divisibility/basic): Dot notation aliases (#18698)

A few convenience shortcuts for dvd along with some simple nat lemmas. Also

Drop neg_dvd_of_dvd/dvd_of_neg_dvd/dvd_neg_of_dvd/dvd_of_dvd_neg in favor of the aforementioned shortcuts.
Remove explicit arguments to dvd_neg/neg_dvd.
Drop int.of_nat_dvd_of_dvd_nat_abs/int.dvd_nat_abs_of_of_nat_dvd because they are the two directions of int.coe_nat_dvd_left.
Move group_with_zero.to_cancel_monoid_with_zero from algebra.group_with_zero.units.basic back to algebra.group_with_zero.basic. It was erroneously moved during the Great Splits.

Diff

@@ -129,8 +129,8 @@ begin
   { -- x even, y even
     exfalso,
     apply nat.not_coprime_of_dvd_of_dvd (dec_trivial : 1 < 2) _ _ hc,
-    { apply int.dvd_nat_abs_of_of_nat_dvd, apply int.dvd_of_mod_eq_zero hx },
-    { apply int.dvd_nat_abs_of_of_nat_dvd, apply int.dvd_of_mod_eq_zero hy } },
+    { apply int.coe_nat_dvd_left.1, apply int.dvd_of_mod_eq_zero hx },
+    { apply int.coe_nat_dvd_left.1, apply int.dvd_of_mod_eq_zero hy } },
   { left, exact ⟨hx, hy⟩ },  -- x even, y odd
   { right, exact ⟨hx, hy⟩ }, -- x odd, y even
   { -- x odd, y odd
@@ -334,8 +334,7 @@ begin
     apply mt (int.dvd_gcd (int.coe_nat_dvd_left.mpr hpm)) hnp,
     apply (or_self _).mp, apply int.prime.dvd_mul' hp,
     rw (by ring : n * n = - (m ^ 2 - n ^ 2) + m * m),
-    apply dvd_add (dvd_neg_of_dvd hp1),
-    exact dvd_mul_of_dvd_left (int.coe_nat_dvd_left.mpr hpm) m },
+    exact hp1.neg_right.add ((int.coe_nat_dvd_left.2 hpm).mul_right _) },
   rw int.gcd_comm at hnp,
   apply mt (int.dvd_gcd (int.coe_nat_dvd_left.mpr hpn)) hnp,
   apply (or_self _).mp, apply int.prime.dvd_mul' hp,

70fd9563

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

e8638a0f

bump to nightly-2024-04-19-08

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

a9e81450

Diff

@@ -43,7 +43,7 @@ theorem sq_ne_two_fin_zmod_four (z : ZMod 4) : z * z ≠ 2 :=
 theorem Int.sq_ne_two_mod_four (z : ℤ) : z * z % 4 ≠ 2 :=
   by
   suffices ¬z * z % (4 : ℕ) = 2 % (4 : ℕ) by norm_num at this
-  rw [← ZMod.int_cast_eq_int_cast_iff']
+  rw [← ZMod.intCast_eq_intCast_iff']
   simpa using sq_ne_two_fin_zmod_four _
 #align int.sq_ne_two_mod_four Int.sq_ne_two_mod_four
 -/

e8638a0f

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -9,7 +9,7 @@ import Tactic.Ring
 import Tactic.RingExp
 import Tactic.FieldSimp
 import Data.Int.NatPrime
-import Data.Zmod.Basic
+import Data.ZMod.Basic
 
 #align_import number_theory.pythagorean_triples from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"
 
@@ -158,15 +158,17 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
   by
   cases' Int.emod_two_eq_zero_or_one x with hx hx <;>
     cases' Int.emod_two_eq_zero_or_one y with hy hy
-  · exfalso
+  · -- x even, y even
+    exfalso
     apply Nat.not_coprime_of_dvd_of_dvd (by decide : 1 < 2) _ _ hc
-    · apply Int.coe_nat_dvd_left.1; apply Int.dvd_of_emod_eq_zero hx
-    · apply Int.coe_nat_dvd_left.1; apply Int.dvd_of_emod_eq_zero hy
+    · apply Int.natCast_dvd.1; apply Int.dvd_of_emod_eq_zero hx
+    · apply Int.natCast_dvd.1; apply Int.dvd_of_emod_eq_zero hy
   · left; exact ⟨hx, hy⟩
   -- x even, y odd
   · right; exact ⟨hx, hy⟩
   -- x odd, y even
-  · exfalso
+  · -- x odd, y odd
+    exfalso
     obtain ⟨x0, y0, rfl, rfl⟩ : ∃ x0 y0, x = x0 * 2 + 1 ∧ y = y0 * 2 + 1 :=
       by
       cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hx) with x0 hx2
@@ -277,7 +279,7 @@ theorem coprime_of_coprime (hc : Int.gcd x y = 1) : Int.gcd y z = 1 :=
   rw [← hc]
   apply Nat.dvd_gcd (Int.Prime.dvd_natAbs_of_coe_dvd_sq hp _ _) hpy
   rw [sq, eq_sub_of_add_eq h]
-  rw [← Int.coe_nat_dvd_left] at hpy hpz
+  rw [← Int.natCast_dvd] at hpy hpz
   exact dvd_sub (hpz.mul_right _) (hpy.mul_right _)
 #align pythagorean_triple.coprime_of_coprime PythagoreanTriple.coprime_of_coprime
 -/
@@ -310,7 +312,7 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
   left_inv x := by
     have h2 : (1 + 1 : K) = 2 := rfl
     have h3 : (2 : K) ≠ 0 := by convert hk 1; rw [one_pow 2, h2]
-    field_simp [hk x, h2, add_assoc, add_comm, add_sub_cancel'_right, mul_comm]
+    field_simp [hk x, h2, add_assoc, add_comm, add_sub_cancel, mul_comm]
   right_inv := fun ⟨⟨x, y⟩, hxy, hy⟩ =>
     by
     change x ^ 2 + y ^ 2 = 1 at hxy
@@ -349,7 +351,7 @@ private theorem coprime_sq_sub_sq_add_of_even_odd {m n : ℤ} (h : Int.gcd m n =
   by
   by_contra H
   obtain ⟨p, hp, hp1, hp2⟩ := nat.prime.not_coprime_iff_dvd.mp H
-  rw [← Int.coe_nat_dvd_left] at hp1 hp2
+  rw [← Int.natCast_dvd] at hp1 hp2
   have h2m : (p : ℤ) ∣ 2 * m ^ 2 := by convert dvd_add hp2 hp1; ring
   have h2n : (p : ℤ) ∣ 2 * n ^ 2 := by convert dvd_sub hp2 hp1; ring
   have hmc : p = 2 ∨ p ∣ Int.natAbs m := prime_two_or_dvd_of_dvd_two_mul_pow_self_two hp h2m
@@ -374,7 +376,7 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
   by
   by_contra H
   obtain ⟨p, hp, hp1, hp2⟩ := nat.prime.not_coprime_iff_dvd.mp H
-  rw [← Int.coe_nat_dvd_left] at hp1 hp2
+  rw [← Int.natCast_dvd] at hp1 hp2
   have hnp : ¬(p : ℤ) ∣ Int.gcd m n := by rw [h]; norm_cast;
     exact mt nat.dvd_one.mp (Nat.Prime.ne_one hp)
   cases' Int.Prime.dvd_mul hp hp2 with hp2m hpn
@@ -387,7 +389,7 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
     apply mt (Int.dvd_gcd (int.coe_nat_dvd_left.mpr hpm)) hnp
     apply (or_self_iff _).mp; apply Int.Prime.dvd_mul' hp
     rw [(by ring : n * n = -(m ^ 2 - n ^ 2) + m * m)]
-    exact hp1.neg_right.add ((Int.coe_nat_dvd_left.2 hpm).mul_right _)
+    exact hp1.neg_right.add ((Int.natCast_dvd.2 hpm).mul_right _)
   rw [Int.gcd_comm] at hnp
   apply mt (Int.dvd_gcd (int.coe_nat_dvd_left.mpr hpn)) hnp
   apply (or_self_iff _).mp; apply Int.Prime.dvd_mul' hp
@@ -431,7 +433,7 @@ private theorem coprime_sq_sub_sq_sum_of_odd_odd {m n : ℤ} (h : Int.gcd m n =
   obtain ⟨p, hp, hp1, hp2⟩ := nat.prime.not_coprime_iff_dvd.mp h4
   apply hp.not_dvd_one
   rw [← h]
-  rw [← Int.coe_nat_dvd_left] at hp1 hp2
+  rw [← Int.natCast_dvd] at hp1 hp2
   apply Nat.dvd_gcd
   · apply Int.Prime.dvd_natAbs_of_coe_dvd_sq hp
     convert dvd_add hp1 hp2; ring
@@ -505,7 +507,8 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
   have hmncp : Int.gcd m n = 1 := by rw [Int.gcd_comm]; exact hnmcp
   cases' Int.emod_two_eq_zero_or_one m with hm2 hm2 <;>
     cases' Int.emod_two_eq_zero_or_one n with hn2 hn2
-  · exfalso
+  · -- m even, n even
+    exfalso
     have h1 : 2 ∣ (Int.gcd n m : ℤ) :=
       Int.dvd_gcd (Int.dvd_of_emod_eq_zero hn2) (Int.dvd_of_emod_eq_zero hm2)
     rw [hnmcp] at h1; revert h1; norm_num
@@ -517,7 +520,8 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
     apply h.is_primitive_classified_aux hc hzpos hm2n2 hv2 hw2 _ hmncp
     · apply Or.intro_right; exact And.intro hm2 hn2
     apply coprime_sq_sub_sq_add_of_odd_even hmncp hm2 hn2
-  · exfalso
+  · -- m odd, n odd
+    exfalso
     have h1 :
       2 ∣ m ^ 2 + n ^ 2 ∧
         2 ∣ m ^ 2 - n ^ 2 ∧

e8638a0f

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -34,7 +34,7 @@ the bulk of the proof below.
 #print sq_ne_two_fin_zmod_four /-
 theorem sq_ne_two_fin_zmod_four (z : ZMod 4) : z * z ≠ 2 :=
   by
-  change Fin 4 at z 
+  change Fin 4 at z
   fin_cases z <;> norm_num [Fin.ext_iff, Fin.val_bit0, Fin.val_bit1]
 #align sq_ne_two_fin_zmod_four sq_ne_two_fin_zmod_four
 -/
@@ -42,7 +42,7 @@ theorem sq_ne_two_fin_zmod_four (z : ZMod 4) : z * z ≠ 2 :=
 #print Int.sq_ne_two_mod_four /-
 theorem Int.sq_ne_two_mod_four (z : ℤ) : z * z % 4 ≠ 2 :=
   by
-  suffices ¬z * z % (4 : ℕ) = 2 % (4 : ℕ) by norm_num at this 
+  suffices ¬z * z % (4 : ℕ) = 2 % (4 : ℕ) by norm_num at this
   rw [← ZMod.int_cast_eq_int_cast_iff']
   simpa using sq_ne_two_fin_zmod_four _
 #align int.sq_ne_two_mod_four Int.sq_ne_two_mod_four
@@ -158,8 +158,7 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
   by
   cases' Int.emod_two_eq_zero_or_one x with hx hx <;>
     cases' Int.emod_two_eq_zero_or_one y with hy hy
-  · -- x even, y even
-    exfalso
+  · exfalso
     apply Nat.not_coprime_of_dvd_of_dvd (by decide : 1 < 2) _ _ hc
     · apply Int.coe_nat_dvd_left.1; apply Int.dvd_of_emod_eq_zero hx
     · apply Int.coe_nat_dvd_left.1; apply Int.dvd_of_emod_eq_zero hy
@@ -167,13 +166,12 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
   -- x even, y odd
   · right; exact ⟨hx, hy⟩
   -- x odd, y even
-  · -- x odd, y odd
-    exfalso
+  · exfalso
     obtain ⟨x0, y0, rfl, rfl⟩ : ∃ x0 y0, x = x0 * 2 + 1 ∧ y = y0 * 2 + 1 :=
       by
       cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hx) with x0 hx2
       cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hy) with y0 hy2
-      rw [sub_eq_iff_eq_add] at hx2 hy2 ; exact ⟨x0, y0, hx2, hy2⟩
+      rw [sub_eq_iff_eq_add] at hx2 hy2; exact ⟨x0, y0, hx2, hy2⟩
     apply Int.sq_ne_two_mod_four z
     rw [show z * z = 4 * (x0 * x0 + x0 + y0 * y0 + y0) + 2 by rw [← h.eq]; ring]
     norm_num [Int.add_emod]
@@ -214,9 +212,9 @@ theorem normalize : PythagoreanTriple (x / Int.gcd x y) (y / Int.gcd x y) (z / I
   obtain ⟨k, x0, y0, k0, h2, rfl, rfl⟩ :
     ∃ (k : ℕ) (x0 y0 : _), 0 < k ∧ Int.gcd x0 y0 = 1 ∧ x = x0 * k ∧ y = y0 * k :=
     Int.exists_gcd_one' (Nat.pos_of_ne_zero h0)
-  have hk : (k : ℤ) ≠ 0 := by norm_cast; rwa [pos_iff_ne_zero] at k0 
+  have hk : (k : ℤ) ≠ 0 := by norm_cast; rwa [pos_iff_ne_zero] at k0
   rw [Int.gcd_mul_right, h2, Int.natAbs_ofNat, one_mul] at h ⊢
-  rw [mul_comm x0, mul_comm y0, mul_iff k hk] at h 
+  rw [mul_comm x0, mul_comm y0, mul_iff k hk] at h
   rwa [Int.mul_ediv_cancel _ hk, Int.mul_ediv_cancel _ hk, Int.mul_ediv_cancel_left _ hk]
 #align pythagorean_triple.normalize PythagoreanTriple.normalize
 -/
@@ -249,7 +247,7 @@ theorem isClassified_of_normalize_isPrimitiveClassified (hc : h.normalize.IsPrim
 #print PythagoreanTriple.ne_zero_of_coprime /-
 theorem ne_zero_of_coprime (hc : Int.gcd x y = 1) : z ≠ 0 :=
   by
-  suffices 0 < z * z by rintro rfl; norm_num at this 
+  suffices 0 < z * z by rintro rfl; norm_num at this
   rw [← h.eq, ← sq, ← sq]
   have hc' : Int.gcd x y ≠ 0 := by rw [hc]; exact one_ne_zero
   cases' Int.ne_zero_of_gcd hc' with hxz hyz
@@ -262,8 +260,8 @@ theorem ne_zero_of_coprime (hc : Int.gcd x y = 1) : z ≠ 0 :=
 theorem isPrimitiveClassified_of_coprime_of_zero_left (hc : Int.gcd x y = 1) (hx : x = 0) :
     h.IsPrimitiveClassified := by
   subst x
-  change Nat.gcd 0 (Int.natAbs y) = 1 at hc 
-  rw [Nat.gcd_zero_left (Int.natAbs y)] at hc 
+  change Nat.gcd 0 (Int.natAbs y) = 1 at hc
+  rw [Nat.gcd_zero_left (Int.natAbs y)] at hc
   cases' Int.natAbs_eq y with hy hy
   · use 1, 0; rw [hy, hc, Int.gcd_zero_right]; norm_num
   · use 0, 1; rw [hy, hc, Int.gcd_zero_left]; norm_num
@@ -279,7 +277,7 @@ theorem coprime_of_coprime (hc : Int.gcd x y = 1) : Int.gcd y z = 1 :=
   rw [← hc]
   apply Nat.dvd_gcd (Int.Prime.dvd_natAbs_of_coe_dvd_sq hp _ _) hpy
   rw [sq, eq_sub_of_add_eq h]
-  rw [← Int.coe_nat_dvd_left] at hpy hpz 
+  rw [← Int.coe_nat_dvd_left] at hpy hpz
   exact dvd_sub (hpz.mul_right _) (hpy.mul_right _)
 #align pythagorean_triple.coprime_of_coprime PythagoreanTriple.coprime_of_coprime
 -/
@@ -315,7 +313,7 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
     field_simp [hk x, h2, add_assoc, add_comm, add_sub_cancel'_right, mul_comm]
   right_inv := fun ⟨⟨x, y⟩, hxy, hy⟩ =>
     by
-    change x ^ 2 + y ^ 2 = 1 at hxy 
+    change x ^ 2 + y ^ 2 = 1 at hxy
     have h2 : y + 1 ≠ 0 := mt eq_neg_of_add_eq_zero_left hy
     have h3 : (y + 1) ^ 2 + x ^ 2 = 2 * (y + 1) := by
       rw [(add_neg_eq_iff_eq_add.mpr hxy.symm).symm]; ring
@@ -351,15 +349,15 @@ private theorem coprime_sq_sub_sq_add_of_even_odd {m n : ℤ} (h : Int.gcd m n =
   by
   by_contra H
   obtain ⟨p, hp, hp1, hp2⟩ := nat.prime.not_coprime_iff_dvd.mp H
-  rw [← Int.coe_nat_dvd_left] at hp1 hp2 
+  rw [← Int.coe_nat_dvd_left] at hp1 hp2
   have h2m : (p : ℤ) ∣ 2 * m ^ 2 := by convert dvd_add hp2 hp1; ring
   have h2n : (p : ℤ) ∣ 2 * n ^ 2 := by convert dvd_sub hp2 hp1; ring
   have hmc : p = 2 ∨ p ∣ Int.natAbs m := prime_two_or_dvd_of_dvd_two_mul_pow_self_two hp h2m
   have hnc : p = 2 ∨ p ∣ Int.natAbs n := prime_two_or_dvd_of_dvd_two_mul_pow_self_two hp h2n
   by_cases h2 : p = 2
   · have h3 : (m ^ 2 + n ^ 2) % 2 = 1 := by norm_num [sq, Int.add_emod, Int.mul_emod, hm, hn]
-    have h4 : (m ^ 2 + n ^ 2) % 2 = 0 := by apply Int.emod_eq_zero_of_dvd; rwa [h2] at hp2 
-    rw [h4] at h3 ; exact zero_ne_one h3
+    have h4 : (m ^ 2 + n ^ 2) % 2 = 0 := by apply Int.emod_eq_zero_of_dvd; rwa [h2] at hp2
+    rw [h4] at h3; exact zero_ne_one h3
   · apply hp.not_dvd_one
     rw [← h]
     exact Nat.dvd_gcd (Or.resolve_left hmc h2) (Or.resolve_left hnc h2)
@@ -376,11 +374,11 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
   by
   by_contra H
   obtain ⟨p, hp, hp1, hp2⟩ := nat.prime.not_coprime_iff_dvd.mp H
-  rw [← Int.coe_nat_dvd_left] at hp1 hp2 
+  rw [← Int.coe_nat_dvd_left] at hp1 hp2
   have hnp : ¬(p : ℤ) ∣ Int.gcd m n := by rw [h]; norm_cast;
     exact mt nat.dvd_one.mp (Nat.Prime.ne_one hp)
   cases' Int.Prime.dvd_mul hp hp2 with hp2m hpn
-  · rw [Int.natAbs_mul] at hp2m 
+  · rw [Int.natAbs_mul] at hp2m
     cases' (Nat.Prime.dvd_mul hp).mp hp2m with hp2 hpm
     · have hp2' : p = 2 := (Nat.le_of_dvd zero_lt_two hp2).antisymm hp.two_le
       revert hp1; rw [hp2']
@@ -390,7 +388,7 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
     apply (or_self_iff _).mp; apply Int.Prime.dvd_mul' hp
     rw [(by ring : n * n = -(m ^ 2 - n ^ 2) + m * m)]
     exact hp1.neg_right.add ((Int.coe_nat_dvd_left.2 hpm).mul_right _)
-  rw [Int.gcd_comm] at hnp 
+  rw [Int.gcd_comm] at hnp
   apply mt (Int.dvd_gcd (int.coe_nat_dvd_left.mpr hpn)) hnp
   apply (or_self_iff _).mp; apply Int.Prime.dvd_mul' hp
   rw [(by ring : m * m = m ^ 2 - n ^ 2 + n * n)]
@@ -420,7 +418,7 @@ private theorem coprime_sq_sub_sq_sum_of_odd_odd {m n : ℤ} (h : Int.gcd m n =
   by
   cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hm) with m0 hm2
   cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hn) with n0 hn2
-  rw [sub_eq_iff_eq_add] at hm2 hn2 ; subst m; subst n
+  rw [sub_eq_iff_eq_add] at hm2 hn2; subst m; subst n
   have h1 : (m0 * 2 + 1) ^ 2 + (n0 * 2 + 1) ^ 2 = 2 * (2 * (m0 ^ 2 + n0 ^ 2 + m0 + n0) + 1) := by
     ring
   have h2 : (m0 * 2 + 1) ^ 2 - (n0 * 2 + 1) ^ 2 = 2 * (2 * (m0 ^ 2 - n0 ^ 2 + m0 - n0)) := by ring
@@ -433,7 +431,7 @@ private theorem coprime_sq_sub_sq_sum_of_odd_odd {m n : ℤ} (h : Int.gcd m n =
   obtain ⟨p, hp, hp1, hp2⟩ := nat.prime.not_coprime_iff_dvd.mp h4
   apply hp.not_dvd_one
   rw [← h]
-  rw [← Int.coe_nat_dvd_left] at hp1 hp2 
+  rw [← Int.coe_nat_dvd_left] at hp1 hp2
   apply Nat.dvd_gcd
   · apply Int.Prime.dvd_natAbs_of_coe_dvd_sq hp
     convert dvd_add hp1 hp2; ring
@@ -474,7 +472,7 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
   have hvz : v ≠ 0 := by field_simp [hz]; exact h0
   have hw1 : w ≠ -1 := by
     contrapose! hvz with hw1
-    rw [hw1, neg_sq, one_pow, add_left_eq_self] at hq 
+    rw [hw1, neg_sq, one_pow, add_left_eq_self] at hq
     exact pow_eq_zero hq
   have hQ : ∀ x : ℚ, 1 + x ^ 2 ≠ 0 := by intro q; apply ne_of_gt;
     exact lt_add_of_pos_of_le zero_lt_one (sq_nonneg q)
@@ -507,11 +505,10 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
   have hmncp : Int.gcd m n = 1 := by rw [Int.gcd_comm]; exact hnmcp
   cases' Int.emod_two_eq_zero_or_one m with hm2 hm2 <;>
     cases' Int.emod_two_eq_zero_or_one n with hn2 hn2
-  · -- m even, n even
-    exfalso
+  · exfalso
     have h1 : 2 ∣ (Int.gcd n m : ℤ) :=
       Int.dvd_gcd (Int.dvd_of_emod_eq_zero hn2) (Int.dvd_of_emod_eq_zero hm2)
-    rw [hnmcp] at h1 ; revert h1; norm_num
+    rw [hnmcp] at h1; revert h1; norm_num
   · -- m even, n odd
     apply h.is_primitive_classified_aux hc hzpos hm2n2 hv2 hw2 _ hmncp
     · apply Or.intro_left; exact And.intro hm2 hn2
@@ -520,8 +517,7 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
     apply h.is_primitive_classified_aux hc hzpos hm2n2 hv2 hw2 _ hmncp
     · apply Or.intro_right; exact And.intro hm2 hn2
     apply coprime_sq_sub_sq_add_of_odd_even hmncp hm2 hn2
-  · -- m odd, n odd
-    exfalso
+  · exfalso
     have h1 :
       2 ∣ m ^ 2 + n ^ 2 ∧
         2 ∣ m ^ 2 - n ^ 2 ∧
@@ -534,7 +530,7 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
         rw [Int.ediv_mul_cancel h1.1, Int.ediv_mul_cancel h1.2.1, hw2]; norm_cast
       · apply (mul_lt_mul_right (by norm_num : 0 < (2 : ℤ))).mp
         rw [Int.ediv_mul_cancel h1.1, MulZeroClass.zero_mul]; exact hm2n2
-    rw [h2.1, h1.2.2.1] at hyo 
+    rw [h2.1, h1.2.2.1] at hyo
     revert hyo
     norm_num
 #align pythagorean_triple.is_primitive_classified_of_coprime_of_odd_of_pos PythagoreanTriple.isPrimitiveClassified_of_coprime_of_odd_of_pos
@@ -546,7 +542,7 @@ theorem isPrimitiveClassified_of_coprime_of_pos (hc : Int.gcd x y = 1) (hzpos :
   by
   cases' h.even_odd_of_coprime hc with h1 h2
   · exact h.is_primitive_classified_of_coprime_of_odd_of_pos hc h1.right hzpos
-  rw [Int.gcd_comm] at hc 
+  rw [Int.gcd_comm] at hc
   obtain ⟨m, n, H⟩ := h.symm.is_primitive_classified_of_coprime_of_odd_of_pos hc h2.left hzpos
   use m, n; tauto
 #align pythagorean_triple.is_primitive_classified_of_coprime_of_pos PythagoreanTriple.isPrimitiveClassified_of_coprime_of_pos
@@ -628,7 +624,7 @@ theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
         exact imp_false.mpr (not_lt.mpr (neg_nonpos.mpr (add_nonneg (sq_nonneg m) (sq_nonneg n))))
     exfalso
     rcases h_even with ⟨rfl, -⟩
-    rw [mul_assoc, Int.mul_emod_right] at h_parity 
+    rw [mul_assoc, Int.mul_emod_right] at h_parity
     exact zero_ne_one h_parity
   · use-m, -n
     cases' ht1 with h_odd h_even
@@ -646,7 +642,7 @@ theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
         exact imp_false.mpr (not_lt.mpr (neg_nonpos.mpr (add_nonneg (sq_nonneg m) (sq_nonneg n))))
     exfalso
     rcases h_even with ⟨rfl, -⟩
-    rw [mul_assoc, Int.mul_emod_right] at h_parity 
+    rw [mul_assoc, Int.mul_emod_right] at h_parity
     exact zero_ne_one h_parity
 #align pythagorean_triple.coprime_classification' PythagoreanTriple.coprime_classification'
 -/

e8638a0f

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,13 +3,13 @@ Copyright (c) 2020 Paul van Wamelen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul van Wamelen
 -/
-import Mathbin.Algebra.Field.Basic
-import Mathbin.RingTheory.Int.Basic
-import Mathbin.Tactic.Ring
-import Mathbin.Tactic.RingExp
-import Mathbin.Tactic.FieldSimp
-import Mathbin.Data.Int.NatPrime
-import Mathbin.Data.Zmod.Basic
+import Algebra.Field.Basic
+import RingTheory.Int.Basic
+import Tactic.Ring
+import Tactic.RingExp
+import Tactic.FieldSimp
+import Data.Int.NatPrime
+import Data.Zmod.Basic
 
 #align_import number_theory.pythagorean_triples from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"
 
@@ -461,7 +461,7 @@ theorem isPrimitiveClassified_aux (hc : x.gcd y = 1) (hzpos : 0 < z) {m n : ℤ}
 #align pythagorean_triple.is_primitive_classified_aux PythagoreanTriple.isPrimitiveClassified_aux
 -/
 
-/- ./././Mathport/Syntax/Translate/Tactic/Lean3.lean:132:4: warning: unsupported: rw with cfg: { occs := occurrences.pos[occurrences.pos] «expr[ ,]»([2, 3]) } -/
+/- ./././Mathport/Syntax/Translate/Tactic/Lean3.lean:133:4: warning: unsupported: rw with cfg: { occs := occurrences.pos[occurrences.pos] «expr[ ,]»([2, 3]) } -/
 #print PythagoreanTriple.isPrimitiveClassified_of_coprime_of_odd_of_pos /-
 theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (hyo : y % 2 = 1)
     (hzpos : 0 < z) : h.IsPrimitiveClassified :=

e8638a0f

bump to nightly-2023-08-02-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

7aca3f15

Diff

@@ -630,7 +630,7 @@ theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
     rcases h_even with ⟨rfl, -⟩
     rw [mul_assoc, Int.mul_emod_right] at h_parity 
     exact zero_ne_one h_parity
-  · use -m, -n
+  · use-m, -n
     cases' ht1 with h_odd h_even
     · rw [neg_sq m]
       rw [neg_sq n]

e8638a0f

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Paul van Wamelen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul van Wamelen
-
-! This file was ported from Lean 3 source module number_theory.pythagorean_triples
-! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Field.Basic
 import Mathbin.RingTheory.Int.Basic
@@ -16,6 +11,8 @@ import Mathbin.Tactic.FieldSimp
 import Mathbin.Data.Int.NatPrime
 import Mathbin.Data.Zmod.Basic
 
+#align_import number_theory.pythagorean_triples from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"
+
 /-!
 # Pythagorean Triples

e8638a0f

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -34,11 +34,13 @@ the bulk of the proof below.
 -/
 
 
+#print sq_ne_two_fin_zmod_four /-
 theorem sq_ne_two_fin_zmod_four (z : ZMod 4) : z * z ≠ 2 :=
   by
   change Fin 4 at z 
   fin_cases z <;> norm_num [Fin.ext_iff, Fin.val_bit0, Fin.val_bit1]
 #align sq_ne_two_fin_zmod_four sq_ne_two_fin_zmod_four
+-/
 
 #print Int.sq_ne_two_mod_four /-
 theorem Int.sq_ne_two_mod_four (z : ℤ) : z * z % 4 ≠ 2 :=
@@ -79,8 +81,6 @@ namespace PythagoreanTriple
 
 variable {x y z : ℤ} (h : PythagoreanTriple x y z)
 
-include h
-
 #print PythagoreanTriple.eq /-
 theorem eq : x * x + y * y = z * z :=
   h
@@ -104,8 +104,6 @@ theorem mul (k : ℤ) : PythagoreanTriple (k * x) (k * y) (k * z) :=
 #align pythagorean_triple.mul PythagoreanTriple.mul
 -/
 
-omit h
-
 #print PythagoreanTriple.mul_iff /-
 /-- `(k*x, k*y, k*z)` is a Pythagorean triple if and only if
 `(x, y, z)` is also a triple. -/
@@ -120,8 +118,6 @@ theorem mul_iff (k : ℤ) (hk : k ≠ 0) :
 #align pythagorean_triple.mul_iff PythagoreanTriple.mul_iff
 -/
 
-include h
-
 #print PythagoreanTriple.IsClassified /-
 /-- A Pythagorean triple `x, y, z` is “classified” if there exist integers `k, m, n` such that
 either
@@ -187,6 +183,7 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
 #align pythagorean_triple.even_odd_of_coprime PythagoreanTriple.even_odd_of_coprime
 -/
 
+#print PythagoreanTriple.gcd_dvd /-
 theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z :=
   by
   by_cases h0 : Int.gcd x y = 0
@@ -204,6 +201,7 @@ theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z :=
   rw [(by ring : x0 * k * (x0 * k) + y0 * k * (y0 * k) = k ^ 2 * (x0 * x0 + y0 * y0))]
   exact dvd_mul_right _ _
 #align pythagorean_triple.gcd_dvd PythagoreanTriple.gcd_dvd
+-/
 
 #print PythagoreanTriple.normalize /-
 theorem normalize : PythagoreanTriple (x / Int.gcd x y) (y / Int.gcd x y) (z / Int.gcd x y) :=
@@ -302,6 +300,7 @@ For the classification of pythogorean triples, we will use a parametrization of
 
 variable {K : Type _} [Field K]
 
+#print circleEquivGen /-
 /-- A parameterization of the unit circle that is useful for classifying Pythagorean triples.
  (To be applied in the case where `K = ℚ`.) -/
 def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
@@ -329,19 +328,24 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
     · field_simp [h3]; ring
     · field_simp [h3]; rw [← add_neg_eq_iff_eq_add.mpr hxy.symm]; ring
 #align circle_equiv_gen circleEquivGen
+-/
 
+#print circleEquivGen_apply /-
 @[simp]
 theorem circleEquivGen_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
     (circleEquivGen hk x : K × K) = ⟨2 * x / (1 + x ^ 2), (1 - x ^ 2) / (1 + x ^ 2)⟩ :=
   rfl
 #align circle_equiv_apply circleEquivGen_apply
+-/
 
+#print circleEquivGen_symm_apply /-
 @[simp]
 theorem circleEquivGen_symm_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0)
     (v : { p : K × K // p.1 ^ 2 + p.2 ^ 2 = 1 ∧ p.2 ≠ -1 }) :
     (circleEquivGen hk).symm v = (v : K × K).1 / ((v : K × K).2 + 1) :=
   rfl
 #align circle_equiv_symm_apply circleEquivGen_symm_apply
+-/
 
 end circleEquivGen
 
@@ -443,8 +447,7 @@ namespace PythagoreanTriple
 
 variable {x y z : ℤ} (h : PythagoreanTriple x y z)
 
-include h
-
+#print PythagoreanTriple.isPrimitiveClassified_aux /-
 theorem isPrimitiveClassified_aux (hc : x.gcd y = 1) (hzpos : 0 < z) {m n : ℤ}
     (hm2n2 : 0 < m ^ 2 + n ^ 2) (hv2 : (x : ℚ) / z = 2 * m * n / (m ^ 2 + n ^ 2))
     (hw2 : (y : ℚ) / z = (m ^ 2 - n ^ 2) / (m ^ 2 + n ^ 2))
@@ -459,6 +462,7 @@ theorem isPrimitiveClassified_aux (hc : x.gcd y = 1) (hzpos : 0 < z) {m n : ℤ}
   rw [← Rat.coe_int_inj _ _, ← div_left_inj' ((mt (Rat.coe_int_inj z 0).mp) hz), hv2, h2.right]
   norm_cast
 #align pythagorean_triple.is_primitive_classified_aux PythagoreanTriple.isPrimitiveClassified_aux
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Lean3.lean:132:4: warning: unsupported: rw with cfg: { occs := occurrences.pos[occurrences.pos] «expr[ ,]»([2, 3]) } -/
 #print PythagoreanTriple.isPrimitiveClassified_of_coprime_of_odd_of_pos /-
@@ -576,8 +580,7 @@ theorem classified : h.IsClassified :=
 #align pythagorean_triple.classified PythagoreanTriple.classified
 -/
 
-omit h
-
+#print PythagoreanTriple.coprime_classification /-
 theorem coprime_classification :
     PythagoreanTriple x y z ∧ Int.gcd x y = 1 ↔
       ∃ m n,
@@ -602,7 +605,9 @@ theorem coprime_classification :
       | · constructor; · ring; exact coprime_sq_sub_mul co pp
       | · constructor; · ring; rw [Int.gcd_comm]; exact coprime_sq_sub_mul co pp
 #align pythagorean_triple.coprime_classification PythagoreanTriple.coprime_classification
+-/
 
+#print PythagoreanTriple.coprime_classification' /-
 /-- by assuming `x` is odd and `z` is positive we get a slightly more precise classification of
 the pythagorean triple `x ^ 2 + y ^ 2 = z ^ 2`-/
 theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
@@ -647,7 +652,9 @@ theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
     rw [mul_assoc, Int.mul_emod_right] at h_parity 
     exact zero_ne_one h_parity
 #align pythagorean_triple.coprime_classification' PythagoreanTriple.coprime_classification'
+-/
 
+#print PythagoreanTriple.classification /-
 /-- **Formula for Pythagorean Triples** -/
 theorem classification :
     PythagoreanTriple x y z ↔
@@ -669,6 +676,7 @@ theorem classification :
       simpa using eq_or_eq_neg_of_sq_eq_sq _ _ this
   · rintro ⟨k, m, n, ⟨rfl, rfl⟩ | ⟨rfl, rfl⟩, rfl | rfl⟩ <;> delta PythagoreanTriple <;> ring
 #align pythagorean_triple.classification PythagoreanTriple.classification
+-/
 
 end PythagoreanTriple

e8638a0f

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -101,7 +101,6 @@ theorem mul (k : ℤ) : PythagoreanTriple (k * x) (k * y) (k * z) :=
     k * x * (k * x) + k * y * (k * y) = k ^ 2 * (x * x + y * y) := by ring
     _ = k ^ 2 * (z * z) := by rw [h.eq]
     _ = k * z * (k * z) := by ring
-    
 #align pythagorean_triple.mul PythagoreanTriple.mul
 -/

e8638a0f

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -242,7 +242,8 @@ theorem isClassified_of_isPrimitiveClassified (hp : h.IsPrimitiveClassified) : h
 theorem isClassified_of_normalize_isPrimitiveClassified (hc : h.normalize.IsPrimitiveClassified) :
     h.IsClassified :=
   by
-  convert h.normalize.mul_is_classified (Int.gcd x y)
+  convert
+      h.normalize.mul_is_classified (Int.gcd x y)
         (is_classified_of_is_primitive_classified h.normalize hc) <;>
     rw [Int.mul_ediv_cancel']
   · exact Int.gcd_dvd_left x y
@@ -477,7 +478,7 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
     exact pow_eq_zero hq
   have hQ : ∀ x : ℚ, 1 + x ^ 2 ≠ 0 := by intro q; apply ne_of_gt;
     exact lt_add_of_pos_of_le zero_lt_one (sq_nonneg q)
-  have hp : (⟨v, w⟩ : ℚ × ℚ) ∈ { p : ℚ × ℚ | p.1 ^ 2 + p.2 ^ 2 = 1 ∧ p.2 ≠ -1 } := ⟨hq, hw1⟩
+  have hp : (⟨v, w⟩ : ℚ × ℚ) ∈ {p : ℚ × ℚ | p.1 ^ 2 + p.2 ^ 2 = 1 ∧ p.2 ≠ -1} := ⟨hq, hw1⟩
   let q := (circleEquivGen hQ).symm ⟨⟨v, w⟩, hp⟩
   have ht4 : v = 2 * q / (1 + q ^ 2) ∧ w = (1 - q ^ 2) / (1 + q ^ 2) :=
     by

e8638a0f

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -36,14 +36,14 @@ the bulk of the proof below.
 
 theorem sq_ne_two_fin_zmod_four (z : ZMod 4) : z * z ≠ 2 :=
   by
-  change Fin 4 at z
+  change Fin 4 at z 
   fin_cases z <;> norm_num [Fin.ext_iff, Fin.val_bit0, Fin.val_bit1]
 #align sq_ne_two_fin_zmod_four sq_ne_two_fin_zmod_four
 
 #print Int.sq_ne_two_mod_four /-
 theorem Int.sq_ne_two_mod_four (z : ℤ) : z * z % 4 ≠ 2 :=
   by
-  suffices ¬z * z % (4 : ℕ) = 2 % (4 : ℕ) by norm_num at this
+  suffices ¬z * z % (4 : ℕ) = 2 % (4 : ℕ) by norm_num at this 
   rw [← ZMod.int_cast_eq_int_cast_iff']
   simpa using sq_ne_two_fin_zmod_four _
 #align int.sq_ne_two_mod_four Int.sq_ne_two_mod_four
@@ -181,7 +181,7 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
       by
       cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hx) with x0 hx2
       cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hy) with y0 hy2
-      rw [sub_eq_iff_eq_add] at hx2 hy2; exact ⟨x0, y0, hx2, hy2⟩
+      rw [sub_eq_iff_eq_add] at hx2 hy2 ; exact ⟨x0, y0, hx2, hy2⟩
     apply Int.sq_ne_two_mod_four z
     rw [show z * z = 4 * (x0 * x0 + x0 + y0 * y0 + y0) + 2 by rw [← h.eq]; ring]
     norm_num [Int.add_emod]
@@ -198,7 +198,7 @@ theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z :=
         or_self_iff] using h
     simp only [hz, dvd_zero]
   obtain ⟨k, x0, y0, k0, h2, rfl, rfl⟩ :
-    ∃ (k : ℕ)(x0 y0 : _), 0 < k ∧ Int.gcd x0 y0 = 1 ∧ x = x0 * k ∧ y = y0 * k :=
+    ∃ (k : ℕ) (x0 y0 : _), 0 < k ∧ Int.gcd x0 y0 = 1 ∧ x = x0 * k ∧ y = y0 * k :=
     Int.exists_gcd_one' (Nat.pos_of_ne_zero h0)
   rw [Int.gcd_mul_right, h2, Int.natAbs_ofNat, one_mul]
   rw [← Int.pow_dvd_pow_iff zero_lt_two, sq z, ← h.eq]
@@ -218,11 +218,11 @@ theorem normalize : PythagoreanTriple (x / Int.gcd x y) (y / Int.gcd x y) (z / I
     simp only [hx, hy, hz, Int.zero_div]; exact zero
   rcases h.gcd_dvd with ⟨z0, rfl⟩
   obtain ⟨k, x0, y0, k0, h2, rfl, rfl⟩ :
-    ∃ (k : ℕ)(x0 y0 : _), 0 < k ∧ Int.gcd x0 y0 = 1 ∧ x = x0 * k ∧ y = y0 * k :=
+    ∃ (k : ℕ) (x0 y0 : _), 0 < k ∧ Int.gcd x0 y0 = 1 ∧ x = x0 * k ∧ y = y0 * k :=
     Int.exists_gcd_one' (Nat.pos_of_ne_zero h0)
-  have hk : (k : ℤ) ≠ 0 := by norm_cast; rwa [pos_iff_ne_zero] at k0
-  rw [Int.gcd_mul_right, h2, Int.natAbs_ofNat, one_mul] at h⊢
-  rw [mul_comm x0, mul_comm y0, mul_iff k hk] at h
+  have hk : (k : ℤ) ≠ 0 := by norm_cast; rwa [pos_iff_ne_zero] at k0 
+  rw [Int.gcd_mul_right, h2, Int.natAbs_ofNat, one_mul] at h ⊢
+  rw [mul_comm x0, mul_comm y0, mul_iff k hk] at h 
   rwa [Int.mul_ediv_cancel _ hk, Int.mul_ediv_cancel _ hk, Int.mul_ediv_cancel_left _ hk]
 #align pythagorean_triple.normalize PythagoreanTriple.normalize
 -/
@@ -254,7 +254,7 @@ theorem isClassified_of_normalize_isPrimitiveClassified (hc : h.normalize.IsPrim
 #print PythagoreanTriple.ne_zero_of_coprime /-
 theorem ne_zero_of_coprime (hc : Int.gcd x y = 1) : z ≠ 0 :=
   by
-  suffices 0 < z * z by rintro rfl; norm_num at this
+  suffices 0 < z * z by rintro rfl; norm_num at this 
   rw [← h.eq, ← sq, ← sq]
   have hc' : Int.gcd x y ≠ 0 := by rw [hc]; exact one_ne_zero
   cases' Int.ne_zero_of_gcd hc' with hxz hyz
@@ -267,8 +267,8 @@ theorem ne_zero_of_coprime (hc : Int.gcd x y = 1) : z ≠ 0 :=
 theorem isPrimitiveClassified_of_coprime_of_zero_left (hc : Int.gcd x y = 1) (hx : x = 0) :
     h.IsPrimitiveClassified := by
   subst x
-  change Nat.gcd 0 (Int.natAbs y) = 1 at hc
-  rw [Nat.gcd_zero_left (Int.natAbs y)] at hc
+  change Nat.gcd 0 (Int.natAbs y) = 1 at hc 
+  rw [Nat.gcd_zero_left (Int.natAbs y)] at hc 
   cases' Int.natAbs_eq y with hy hy
   · use 1, 0; rw [hy, hc, Int.gcd_zero_right]; norm_num
   · use 0, 1; rw [hy, hc, Int.gcd_zero_left]; norm_num
@@ -284,7 +284,7 @@ theorem coprime_of_coprime (hc : Int.gcd x y = 1) : Int.gcd y z = 1 :=
   rw [← hc]
   apply Nat.dvd_gcd (Int.Prime.dvd_natAbs_of_coe_dvd_sq hp _ _) hpy
   rw [sq, eq_sub_of_add_eq h]
-  rw [← Int.coe_nat_dvd_left] at hpy hpz
+  rw [← Int.coe_nat_dvd_left] at hpy hpz 
   exact dvd_sub (hpz.mul_right _) (hpy.mul_right _)
 #align pythagorean_triple.coprime_of_coprime PythagoreanTriple.coprime_of_coprime
 -/
@@ -308,7 +308,7 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
     K ≃ { p : K × K // p.1 ^ 2 + p.2 ^ 2 = 1 ∧ p.2 ≠ -1 }
     where
   toFun x :=
-    ⟨⟨2 * x / (1 + x ^ 2), (1 - x ^ 2) / (1 + x ^ 2)⟩, by field_simp [hk x, div_pow] ; ring,
+    ⟨⟨2 * x / (1 + x ^ 2), (1 - x ^ 2) / (1 + x ^ 2)⟩, by field_simp [hk x, div_pow]; ring,
       by
       simp only [Ne.def, div_eq_iff (hk x), neg_mul, one_mul, neg_add, sub_eq_add_neg, add_left_inj]
       simpa only [eq_neg_iff_add_eq_zero, one_pow] using hk 1⟩
@@ -319,15 +319,15 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
     field_simp [hk x, h2, add_assoc, add_comm, add_sub_cancel'_right, mul_comm]
   right_inv := fun ⟨⟨x, y⟩, hxy, hy⟩ =>
     by
-    change x ^ 2 + y ^ 2 = 1 at hxy
+    change x ^ 2 + y ^ 2 = 1 at hxy 
     have h2 : y + 1 ≠ 0 := mt eq_neg_of_add_eq_zero_left hy
     have h3 : (y + 1) ^ 2 + x ^ 2 = 2 * (y + 1) := by
       rw [(add_neg_eq_iff_eq_add.mpr hxy.symm).symm]; ring
     have h4 : (2 : K) ≠ 0 := by convert hk 1; rw [one_pow 2]; rfl
     simp only [Prod.mk.inj_iff, Subtype.mk_eq_mk]
     constructor
-    · field_simp [h3] ; ring
-    · field_simp [h3] ; rw [← add_neg_eq_iff_eq_add.mpr hxy.symm]; ring
+    · field_simp [h3]; ring
+    · field_simp [h3]; rw [← add_neg_eq_iff_eq_add.mpr hxy.symm]; ring
 #align circle_equiv_gen circleEquivGen
 
 @[simp]
@@ -350,15 +350,15 @@ private theorem coprime_sq_sub_sq_add_of_even_odd {m n : ℤ} (h : Int.gcd m n =
   by
   by_contra H
   obtain ⟨p, hp, hp1, hp2⟩ := nat.prime.not_coprime_iff_dvd.mp H
-  rw [← Int.coe_nat_dvd_left] at hp1 hp2
+  rw [← Int.coe_nat_dvd_left] at hp1 hp2 
   have h2m : (p : ℤ) ∣ 2 * m ^ 2 := by convert dvd_add hp2 hp1; ring
   have h2n : (p : ℤ) ∣ 2 * n ^ 2 := by convert dvd_sub hp2 hp1; ring
   have hmc : p = 2 ∨ p ∣ Int.natAbs m := prime_two_or_dvd_of_dvd_two_mul_pow_self_two hp h2m
   have hnc : p = 2 ∨ p ∣ Int.natAbs n := prime_two_or_dvd_of_dvd_two_mul_pow_self_two hp h2n
   by_cases h2 : p = 2
   · have h3 : (m ^ 2 + n ^ 2) % 2 = 1 := by norm_num [sq, Int.add_emod, Int.mul_emod, hm, hn]
-    have h4 : (m ^ 2 + n ^ 2) % 2 = 0 := by apply Int.emod_eq_zero_of_dvd; rwa [h2] at hp2
-    rw [h4] at h3; exact zero_ne_one h3
+    have h4 : (m ^ 2 + n ^ 2) % 2 = 0 := by apply Int.emod_eq_zero_of_dvd; rwa [h2] at hp2 
+    rw [h4] at h3 ; exact zero_ne_one h3
   · apply hp.not_dvd_one
     rw [← h]
     exact Nat.dvd_gcd (Or.resolve_left hmc h2) (Or.resolve_left hnc h2)
@@ -375,11 +375,11 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
   by
   by_contra H
   obtain ⟨p, hp, hp1, hp2⟩ := nat.prime.not_coprime_iff_dvd.mp H
-  rw [← Int.coe_nat_dvd_left] at hp1 hp2
+  rw [← Int.coe_nat_dvd_left] at hp1 hp2 
   have hnp : ¬(p : ℤ) ∣ Int.gcd m n := by rw [h]; norm_cast;
     exact mt nat.dvd_one.mp (Nat.Prime.ne_one hp)
   cases' Int.Prime.dvd_mul hp hp2 with hp2m hpn
-  · rw [Int.natAbs_mul] at hp2m
+  · rw [Int.natAbs_mul] at hp2m 
     cases' (Nat.Prime.dvd_mul hp).mp hp2m with hp2 hpm
     · have hp2' : p = 2 := (Nat.le_of_dvd zero_lt_two hp2).antisymm hp.two_le
       revert hp1; rw [hp2']
@@ -389,7 +389,7 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
     apply (or_self_iff _).mp; apply Int.Prime.dvd_mul' hp
     rw [(by ring : n * n = -(m ^ 2 - n ^ 2) + m * m)]
     exact hp1.neg_right.add ((Int.coe_nat_dvd_left.2 hpm).mul_right _)
-  rw [Int.gcd_comm] at hnp
+  rw [Int.gcd_comm] at hnp 
   apply mt (Int.dvd_gcd (int.coe_nat_dvd_left.mpr hpn)) hnp
   apply (or_self_iff _).mp; apply Int.Prime.dvd_mul' hp
   rw [(by ring : m * m = m ^ 2 - n ^ 2 + n * n)]
@@ -419,7 +419,7 @@ private theorem coprime_sq_sub_sq_sum_of_odd_odd {m n : ℤ} (h : Int.gcd m n =
   by
   cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hm) with m0 hm2
   cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hn) with n0 hn2
-  rw [sub_eq_iff_eq_add] at hm2 hn2; subst m; subst n
+  rw [sub_eq_iff_eq_add] at hm2 hn2 ; subst m; subst n
   have h1 : (m0 * 2 + 1) ^ 2 + (n0 * 2 + 1) ^ 2 = 2 * (2 * (m0 ^ 2 + n0 ^ 2 + m0 + n0) + 1) := by
     ring
   have h2 : (m0 * 2 + 1) ^ 2 - (n0 * 2 + 1) ^ 2 = 2 * (2 * (m0 ^ 2 - n0 ^ 2 + m0 - n0)) := by ring
@@ -432,7 +432,7 @@ private theorem coprime_sq_sub_sq_sum_of_odd_odd {m n : ℤ} (h : Int.gcd m n =
   obtain ⟨p, hp, hp1, hp2⟩ := nat.prime.not_coprime_iff_dvd.mp h4
   apply hp.not_dvd_one
   rw [← h]
-  rw [← Int.coe_nat_dvd_left] at hp1 hp2
+  rw [← Int.coe_nat_dvd_left] at hp1 hp2 
   apply Nat.dvd_gcd
   · apply Int.Prime.dvd_natAbs_of_coe_dvd_sq hp
     convert dvd_add hp1 hp2; ring
@@ -469,11 +469,11 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
   let v := (x : ℚ) / z
   let w := (y : ℚ) / z
   have hz : z ≠ 0; apply ne_of_gt hzpos
-  have hq : v ^ 2 + w ^ 2 = 1 := by field_simp [hz, sq] ; norm_cast; exact h
-  have hvz : v ≠ 0 := by field_simp [hz] ; exact h0
+  have hq : v ^ 2 + w ^ 2 = 1 := by field_simp [hz, sq]; norm_cast; exact h
+  have hvz : v ≠ 0 := by field_simp [hz]; exact h0
   have hw1 : w ≠ -1 := by
     contrapose! hvz with hw1
-    rw [hw1, neg_sq, one_pow, add_left_eq_self] at hq
+    rw [hw1, neg_sq, one_pow, add_left_eq_self] at hq 
     exact pow_eq_zero hq
   have hQ : ∀ x : ℚ, 1 + x ^ 2 ≠ 0 := by intro q; apply ne_of_gt;
     exact lt_add_of_pos_of_le zero_lt_one (sq_nonneg q)
@@ -510,7 +510,7 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
     exfalso
     have h1 : 2 ∣ (Int.gcd n m : ℤ) :=
       Int.dvd_gcd (Int.dvd_of_emod_eq_zero hn2) (Int.dvd_of_emod_eq_zero hm2)
-    rw [hnmcp] at h1; revert h1; norm_num
+    rw [hnmcp] at h1 ; revert h1; norm_num
   · -- m even, n odd
     apply h.is_primitive_classified_aux hc hzpos hm2n2 hv2 hw2 _ hmncp
     · apply Or.intro_left; exact And.intro hm2 hn2
@@ -533,7 +533,7 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
         rw [Int.ediv_mul_cancel h1.1, Int.ediv_mul_cancel h1.2.1, hw2]; norm_cast
       · apply (mul_lt_mul_right (by norm_num : 0 < (2 : ℤ))).mp
         rw [Int.ediv_mul_cancel h1.1, MulZeroClass.zero_mul]; exact hm2n2
-    rw [h2.1, h1.2.2.1] at hyo
+    rw [h2.1, h1.2.2.1] at hyo 
     revert hyo
     norm_num
 #align pythagorean_triple.is_primitive_classified_of_coprime_of_odd_of_pos PythagoreanTriple.isPrimitiveClassified_of_coprime_of_odd_of_pos
@@ -545,7 +545,7 @@ theorem isPrimitiveClassified_of_coprime_of_pos (hc : Int.gcd x y = 1) (hzpos :
   by
   cases' h.even_odd_of_coprime hc with h1 h2
   · exact h.is_primitive_classified_of_coprime_of_odd_of_pos hc h1.right hzpos
-  rw [Int.gcd_comm] at hc
+  rw [Int.gcd_comm] at hc 
   obtain ⟨m, n, H⟩ := h.symm.is_primitive_classified_of_coprime_of_odd_of_pos hc h2.left hzpos
   use m, n; tauto
 #align pythagorean_triple.is_primitive_classified_of_coprime_of_pos PythagoreanTriple.isPrimitiveClassified_of_coprime_of_pos
@@ -599,10 +599,8 @@ theorem coprime_classification :
   · delta PythagoreanTriple
     rintro ⟨m, n, ⟨rfl, rfl⟩ | ⟨rfl, rfl⟩, rfl | rfl, co, pp⟩ <;>
       first
-        |· constructor; · ring;
-          exact
-            coprime_sq_sub_mul co
-              pp|· constructor; · ring; rw [Int.gcd_comm]; exact coprime_sq_sub_mul co pp
+      | · constructor; · ring; exact coprime_sq_sub_mul co pp
+      | · constructor; · ring; rw [Int.gcd_comm]; exact coprime_sq_sub_mul co pp
 #align pythagorean_triple.coprime_classification PythagoreanTriple.coprime_classification
 
 /-- by assuming `x` is odd and `z` is positive we get a slightly more precise classification of
@@ -628,7 +626,7 @@ theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
         exact imp_false.mpr (not_lt.mpr (neg_nonpos.mpr (add_nonneg (sq_nonneg m) (sq_nonneg n))))
     exfalso
     rcases h_even with ⟨rfl, -⟩
-    rw [mul_assoc, Int.mul_emod_right] at h_parity
+    rw [mul_assoc, Int.mul_emod_right] at h_parity 
     exact zero_ne_one h_parity
   · use -m, -n
     cases' ht1 with h_odd h_even
@@ -646,7 +644,7 @@ theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
         exact imp_false.mpr (not_lt.mpr (neg_nonpos.mpr (add_nonneg (sq_nonneg m) (sq_nonneg n))))
     exfalso
     rcases h_even with ⟨rfl, -⟩
-    rw [mul_assoc, Int.mul_emod_right] at h_parity
+    rw [mul_assoc, Int.mul_emod_right] at h_parity 
     exact zero_ne_one h_parity
 #align pythagorean_triple.coprime_classification' PythagoreanTriple.coprime_classification'

e8638a0f

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -51,7 +51,7 @@ theorem Int.sq_ne_two_mod_four (z : ℤ) : z * z % 4 ≠ 2 :=
 
 noncomputable section
 
-open Classical
+open scoped Classical
 
 #print PythagoreanTriple /-
 /-- Three integers `x`, `y`, and `z` form a Pythagorean triple if `x * x + y * y = z * z`. -/

e8638a0f

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -34,12 +34,6 @@ the bulk of the proof below.
 -/
 
 
-/- warning: sq_ne_two_fin_zmod_four -> sq_ne_two_fin_zmod_four is a dubious translation:
-lean 3 declaration is
-  forall (z : ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))), Ne.{1} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{0, 0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (instHMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Distrib.toHasMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toDistrib.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))) z z) (OfNat.ofNat.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 2 (OfNat.mk.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 2 (bit0.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Distrib.toHasAdd.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Ring.toDistrib.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (CommRing.toRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (ZMod.commRing (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (One.one.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddMonoidWithOne.toOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Ring.toAddCommGroupWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (CommRing.toRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (ZMod.commRing (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))
-but is expected to have type
-  forall (z : ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))), Ne.{1} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (HMul.hMul.{0, 0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (instHMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (NonUnitalNonAssocRing.toMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (NonAssocRing.toNonUnitalNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))))) z z) (OfNat.ofNat.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) 2 (instOfNat.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) 2 (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
-Case conversion may be inaccurate. Consider using '#align sq_ne_two_fin_zmod_four sq_ne_two_fin_zmod_fourₓ'. -/
 theorem sq_ne_two_fin_zmod_four (z : ZMod 4) : z * z ≠ 2 :=
   by
   change Fin 4 at z
@@ -194,12 +188,6 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
 #align pythagorean_triple.even_odd_of_coprime PythagoreanTriple.even_odd_of_coprime
 -/
 
-/- warning: pythagorean_triple.gcd_dvd -> PythagoreanTriple.gcd_dvd is a dubious translation:
-lean 3 declaration is
-  forall {x : Int} {y : Int} {z : Int}, (PythagoreanTriple x y z) -> (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))) (Int.gcd x y)) z)
-but is expected to have type
-  forall {x : Int} {y : Int} {z : Int}, (PythagoreanTriple x y z) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt (Int.gcd x y)) z)
-Case conversion may be inaccurate. Consider using '#align pythagorean_triple.gcd_dvd PythagoreanTriple.gcd_dvdₓ'. -/
 theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z :=
   by
   by_cases h0 : Int.gcd x y = 0
@@ -314,12 +302,6 @@ For the classification of pythogorean triples, we will use a parametrization of
 
 variable {K : Type _} [Field K]
 
-/- warning: circle_equiv_gen -> circleEquivGen is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align circle_equiv_gen circleEquivGenₓ'. -/
 /-- A parameterization of the unit circle that is useful for classifying Pythagorean triples.
  (To be applied in the case where `K = ℚ`.) -/
 def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
@@ -348,18 +330,12 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
     · field_simp [h3] ; rw [← add_neg_eq_iff_eq_add.mpr hxy.symm]; ring
 #align circle_equiv_gen circleEquivGen
 
-/- warning: circle_equiv_apply -> circleEquivGen_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align circle_equiv_apply circleEquivGen_applyₓ'. -/
 @[simp]
 theorem circleEquivGen_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
     (circleEquivGen hk x : K × K) = ⟨2 * x / (1 + x ^ 2), (1 - x ^ 2) / (1 + x ^ 2)⟩ :=
   rfl
 #align circle_equiv_apply circleEquivGen_apply
 
-/- warning: circle_equiv_symm_apply -> circleEquivGen_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align circle_equiv_symm_apply circleEquivGen_symm_applyₓ'. -/
 @[simp]
 theorem circleEquivGen_symm_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0)
     (v : { p : K × K // p.1 ^ 2 + p.2 ^ 2 = 1 ∧ p.2 ≠ -1 }) :
@@ -469,9 +445,6 @@ variable {x y z : ℤ} (h : PythagoreanTriple x y z)
 
 include h
 
-/- warning: pythagorean_triple.is_primitive_classified_aux -> PythagoreanTriple.isPrimitiveClassified_aux is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align pythagorean_triple.is_primitive_classified_aux PythagoreanTriple.isPrimitiveClassified_auxₓ'. -/
 theorem isPrimitiveClassified_aux (hc : x.gcd y = 1) (hzpos : 0 < z) {m n : ℤ}
     (hm2n2 : 0 < m ^ 2 + n ^ 2) (hv2 : (x : ℚ) / z = 2 * m * n / (m ^ 2 + n ^ 2))
     (hw2 : (y : ℚ) / z = (m ^ 2 - n ^ 2) / (m ^ 2 + n ^ 2))
@@ -605,12 +578,6 @@ theorem classified : h.IsClassified :=
 
 omit h
 
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-Case conversion may be inaccurate. Consider using '#align pythagorean_triple.coprime_classification PythagoreanTriple.coprime_classificationₓ'. -/
 theorem coprime_classification :
     PythagoreanTriple x y z ∧ Int.gcd x y = 1 ↔
       ∃ m n,
@@ -638,12 +605,6 @@ theorem coprime_classification :
               pp|· constructor; · ring; rw [Int.gcd_comm]; exact coprime_sq_sub_mul co pp
 #align pythagorean_triple.coprime_classification PythagoreanTriple.coprime_classification
 
-/- warning: pythagorean_triple.coprime_classification' -> PythagoreanTriple.coprime_classification' is a dubious translation:
-lean 3 declaration is
-  forall {x : Int} {y : Int} {z : Int}, (PythagoreanTriple x y z) -> (Eq.{1} Nat (Int.gcd x y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) -> (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) x (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (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)))) -> (LT.lt.{0} Int Int.hasLt (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) z) -> (Exists.{1} Int (fun (m : Int) => Exists.{1} Int (fun (n : Int) => And (Eq.{1} Int x (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (And (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) m) n)) (And (Eq.{1} Int z (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (And (Eq.{1} Nat (Int.gcd m n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (And (Or (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) m (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (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))))) (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) m (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (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)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))))) (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) m))))))))
-but is expected to have type
-  forall {x : Int} {y : Int} {z : Int}, (PythagoreanTriple x y z) -> (Eq.{1} Nat (Int.gcd x y) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) x (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) -> (LT.lt.{0} Int Int.instLTInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z) -> (Exists.{1} Int (fun (m : Int) => Exists.{1} Int (fun (n : Int) => And (Eq.{1} Int x (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (And (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) m) n)) (And (Eq.{1} Int z (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (And (Eq.{1} Nat (Int.gcd m n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (And (Or (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) m (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))) (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) m (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))))) (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) m))))))))
-Case conversion may be inaccurate. Consider using '#align pythagorean_triple.coprime_classification' PythagoreanTriple.coprime_classification'ₓ'. -/
 /-- by assuming `x` is odd and `z` is positive we get a slightly more precise classification of
 the pythagorean triple `x ^ 2 + y ^ 2 = z ^ 2`-/
 theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
@@ -689,12 +650,6 @@ theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
     exact zero_ne_one h_parity
 #align pythagorean_triple.coprime_classification' PythagoreanTriple.coprime_classification'
 
-/- warning: pythagorean_triple.classification -> PythagoreanTriple.classification is a dubious translation:
-lean 3 declaration is
-  forall {x : Int} {y : Int} {z : Int}, Iff (PythagoreanTriple x y z) (Exists.{1} Int (fun (k : Int) => Exists.{1} Int (fun (m : Int) => Exists.{1} Int (fun (n : Int) => And (Or (And (Eq.{1} Int x (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) m) n)))) (And (Eq.{1} Int x (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) m) n))) (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))) (Or (Eq.{1} Int z (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) (Eq.{1} Int z (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (Neg.neg.{0} Int Int.hasNeg k) (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))
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-  forall {x : Int} {y : Int} {z : Int}, (PythagoreanTriple x y z) -> (Iff (PythagoreanTriple x y z) (Exists.{1} Int (fun (k : Int) => Exists.{1} Int (fun (m : Int) => Exists.{1} Int (fun (n : Int) => And (Or (And (Eq.{1} Int x (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) m) n)))) (And (Eq.{1} Int x (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) m) n))) (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))) (Or (Eq.{1} Int z (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (Eq.{1} Int z (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (Neg.neg.{0} Int Int.instNegInt k) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))))))))
-Case conversion may be inaccurate. Consider using '#align pythagorean_triple.classification PythagoreanTriple.classificationₓ'. -/
 /-- **Formula for Pythagorean Triples** -/
 theorem classification :
     PythagoreanTriple x y z ↔

e8638a0f

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -69,10 +69,8 @@ def PythagoreanTriple (x y z : ℤ) : Prop :=
 #print pythagoreanTriple_comm /-
 /-- Pythagorean triples are interchangable, i.e `x * x + y * y = y * y + x * x = z * z`.
 This comes from additive commutativity. -/
-theorem pythagoreanTriple_comm {x y z : ℤ} : PythagoreanTriple x y z ↔ PythagoreanTriple y x z :=
-  by
-  delta PythagoreanTriple
-  rw [add_comm]
+theorem pythagoreanTriple_comm {x y z : ℤ} : PythagoreanTriple x y z ↔ PythagoreanTriple y x z := by
+  delta PythagoreanTriple; rw [add_comm]
 #align pythagorean_triple_comm pythagoreanTriple_comm
 -/
 
@@ -163,14 +161,8 @@ def IsPrimitiveClassified :=
 theorem mul_isClassified (k : ℤ) (hc : h.IsClassified) : (h.mul k).IsClassified :=
   by
   obtain ⟨l, m, n, ⟨⟨rfl, rfl⟩ | ⟨rfl, rfl⟩, co⟩⟩ := hc
-  · use k * l, m, n
-    apply And.intro _ co
-    left
-    constructor <;> ring
-  · use k * l, m, n
-    apply And.intro _ co
-    right
-    constructor <;> ring
+  · use k * l, m, n; apply And.intro _ co; left; constructor <;> ring
+  · use k * l, m, n; apply And.intro _ co; right; constructor <;> ring
 #align pythagorean_triple.mul_is_classified PythagoreanTriple.mul_isClassified
 -/
 
@@ -183,15 +175,11 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
   · -- x even, y even
     exfalso
     apply Nat.not_coprime_of_dvd_of_dvd (by decide : 1 < 2) _ _ hc
-    · apply Int.coe_nat_dvd_left.1
-      apply Int.dvd_of_emod_eq_zero hx
-    · apply Int.coe_nat_dvd_left.1
-      apply Int.dvd_of_emod_eq_zero hy
-  · left
-    exact ⟨hx, hy⟩
+    · apply Int.coe_nat_dvd_left.1; apply Int.dvd_of_emod_eq_zero hx
+    · apply Int.coe_nat_dvd_left.1; apply Int.dvd_of_emod_eq_zero hy
+  · left; exact ⟨hx, hy⟩
   -- x even, y odd
-  · right
-    exact ⟨hx, hy⟩
+  · right; exact ⟨hx, hy⟩
   -- x odd, y even
   · -- x odd, y odd
     exfalso
@@ -199,13 +187,9 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
       by
       cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hx) with x0 hx2
       cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hy) with y0 hy2
-      rw [sub_eq_iff_eq_add] at hx2 hy2
-      exact ⟨x0, y0, hx2, hy2⟩
+      rw [sub_eq_iff_eq_add] at hx2 hy2; exact ⟨x0, y0, hx2, hy2⟩
     apply Int.sq_ne_two_mod_four z
-    rw [show z * z = 4 * (x0 * x0 + x0 + y0 * y0 + y0) + 2
-        by
-        rw [← h.eq]
-        ring]
+    rw [show z * z = 4 * (x0 * x0 + x0 + y0 * y0 + y0) + 2 by rw [← h.eq]; ring]
     norm_num [Int.add_emod]
 #align pythagorean_triple.even_odd_of_coprime PythagoreanTriple.even_odd_of_coprime
 -/
@@ -219,12 +203,8 @@ Case conversion may be inaccurate. Consider using '#align pythagorean_triple.gcd
 theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z :=
   by
   by_cases h0 : Int.gcd x y = 0
-  · have hx : x = 0 := by
-      apply int.nat_abs_eq_zero.mp
-      apply Nat.eq_zero_of_gcd_eq_zero_left h0
-    have hy : y = 0 := by
-      apply int.nat_abs_eq_zero.mp
-      apply Nat.eq_zero_of_gcd_eq_zero_right h0
+  · have hx : x = 0 := by apply int.nat_abs_eq_zero.mp; apply Nat.eq_zero_of_gcd_eq_zero_left h0
+    have hy : y = 0 := by apply int.nat_abs_eq_zero.mp; apply Nat.eq_zero_of_gcd_eq_zero_right h0
     have hz : z = 0 := by
       simpa only [PythagoreanTriple, hx, hy, add_zero, zero_eq_mul, MulZeroClass.mul_zero,
         or_self_iff] using h
@@ -242,24 +222,17 @@ theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z :=
 theorem normalize : PythagoreanTriple (x / Int.gcd x y) (y / Int.gcd x y) (z / Int.gcd x y) :=
   by
   by_cases h0 : Int.gcd x y = 0
-  · have hx : x = 0 := by
-      apply int.nat_abs_eq_zero.mp
-      apply Nat.eq_zero_of_gcd_eq_zero_left h0
-    have hy : y = 0 := by
-      apply int.nat_abs_eq_zero.mp
-      apply Nat.eq_zero_of_gcd_eq_zero_right h0
+  · have hx : x = 0 := by apply int.nat_abs_eq_zero.mp; apply Nat.eq_zero_of_gcd_eq_zero_left h0
+    have hy : y = 0 := by apply int.nat_abs_eq_zero.mp; apply Nat.eq_zero_of_gcd_eq_zero_right h0
     have hz : z = 0 := by
       simpa only [PythagoreanTriple, hx, hy, add_zero, zero_eq_mul, MulZeroClass.mul_zero,
         or_self_iff] using h
-    simp only [hx, hy, hz, Int.zero_div]
-    exact zero
+    simp only [hx, hy, hz, Int.zero_div]; exact zero
   rcases h.gcd_dvd with ⟨z0, rfl⟩
   obtain ⟨k, x0, y0, k0, h2, rfl, rfl⟩ :
     ∃ (k : ℕ)(x0 y0 : _), 0 < k ∧ Int.gcd x0 y0 = 1 ∧ x = x0 * k ∧ y = y0 * k :=
     Int.exists_gcd_one' (Nat.pos_of_ne_zero h0)
-  have hk : (k : ℤ) ≠ 0 := by
-    norm_cast
-    rwa [pos_iff_ne_zero] at k0
+  have hk : (k : ℤ) ≠ 0 := by norm_cast; rwa [pos_iff_ne_zero] at k0
   rw [Int.gcd_mul_right, h2, Int.natAbs_ofNat, one_mul] at h⊢
   rw [mul_comm x0, mul_comm y0, mul_iff k hk] at h
   rwa [Int.mul_ediv_cancel _ hk, Int.mul_ediv_cancel _ hk, Int.mul_ediv_cancel_left _ hk]
@@ -293,13 +266,9 @@ theorem isClassified_of_normalize_isPrimitiveClassified (hc : h.normalize.IsPrim
 #print PythagoreanTriple.ne_zero_of_coprime /-
 theorem ne_zero_of_coprime (hc : Int.gcd x y = 1) : z ≠ 0 :=
   by
-  suffices 0 < z * z by
-    rintro rfl
-    norm_num at this
+  suffices 0 < z * z by rintro rfl; norm_num at this
   rw [← h.eq, ← sq, ← sq]
-  have hc' : Int.gcd x y ≠ 0 := by
-    rw [hc]
-    exact one_ne_zero
+  have hc' : Int.gcd x y ≠ 0 := by rw [hc]; exact one_ne_zero
   cases' Int.ne_zero_of_gcd hc' with hxz hyz
   · apply lt_add_of_pos_of_le (sq_pos_of_ne_zero x hxz) (sq_nonneg y)
   · apply lt_add_of_le_of_pos (sq_nonneg x) (sq_pos_of_ne_zero y hyz)
@@ -313,12 +282,8 @@ theorem isPrimitiveClassified_of_coprime_of_zero_left (hc : Int.gcd x y = 1) (hx
   change Nat.gcd 0 (Int.natAbs y) = 1 at hc
   rw [Nat.gcd_zero_left (Int.natAbs y)] at hc
   cases' Int.natAbs_eq y with hy hy
-  · use 1, 0
-    rw [hy, hc, Int.gcd_zero_right]
-    norm_num
-  · use 0, 1
-    rw [hy, hc, Int.gcd_zero_left]
-    norm_num
+  · use 1, 0; rw [hy, hc, Int.gcd_zero_right]; norm_num
+  · use 0, 1; rw [hy, hc, Int.gcd_zero_left]; norm_num
 #align pythagorean_triple.is_primitive_classified_of_coprime_of_zero_left PythagoreanTriple.isPrimitiveClassified_of_coprime_of_zero_left
 -/
 
@@ -361,39 +326,26 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
     K ≃ { p : K × K // p.1 ^ 2 + p.2 ^ 2 = 1 ∧ p.2 ≠ -1 }
     where
   toFun x :=
-    ⟨⟨2 * x / (1 + x ^ 2), (1 - x ^ 2) / (1 + x ^ 2)⟩,
-      by
-      field_simp [hk x, div_pow]
-      ring,
+    ⟨⟨2 * x / (1 + x ^ 2), (1 - x ^ 2) / (1 + x ^ 2)⟩, by field_simp [hk x, div_pow] ; ring,
       by
       simp only [Ne.def, div_eq_iff (hk x), neg_mul, one_mul, neg_add, sub_eq_add_neg, add_left_inj]
       simpa only [eq_neg_iff_add_eq_zero, one_pow] using hk 1⟩
   invFun p := (p : K × K).1 / ((p : K × K).2 + 1)
   left_inv x := by
     have h2 : (1 + 1 : K) = 2 := rfl
-    have h3 : (2 : K) ≠ 0 := by
-      convert hk 1
-      rw [one_pow 2, h2]
+    have h3 : (2 : K) ≠ 0 := by convert hk 1; rw [one_pow 2, h2]
     field_simp [hk x, h2, add_assoc, add_comm, add_sub_cancel'_right, mul_comm]
   right_inv := fun ⟨⟨x, y⟩, hxy, hy⟩ =>
     by
     change x ^ 2 + y ^ 2 = 1 at hxy
     have h2 : y + 1 ≠ 0 := mt eq_neg_of_add_eq_zero_left hy
-    have h3 : (y + 1) ^ 2 + x ^ 2 = 2 * (y + 1) :=
-      by
-      rw [(add_neg_eq_iff_eq_add.mpr hxy.symm).symm]
-      ring
-    have h4 : (2 : K) ≠ 0 := by
-      convert hk 1
-      rw [one_pow 2]
-      rfl
+    have h3 : (y + 1) ^ 2 + x ^ 2 = 2 * (y + 1) := by
+      rw [(add_neg_eq_iff_eq_add.mpr hxy.symm).symm]; ring
+    have h4 : (2 : K) ≠ 0 := by convert hk 1; rw [one_pow 2]; rfl
     simp only [Prod.mk.inj_iff, Subtype.mk_eq_mk]
     constructor
-    · field_simp [h3]
-      ring
-    · field_simp [h3]
-      rw [← add_neg_eq_iff_eq_add.mpr hxy.symm]
-      ring
+    · field_simp [h3] ; ring
+    · field_simp [h3] ; rw [← add_neg_eq_iff_eq_add.mpr hxy.symm]; ring
 #align circle_equiv_gen circleEquivGen
 
 /- warning: circle_equiv_apply -> circleEquivGen_apply is a dubious translation:
@@ -423,22 +375,14 @@ private theorem coprime_sq_sub_sq_add_of_even_odd {m n : ℤ} (h : Int.gcd m n =
   by_contra H
   obtain ⟨p, hp, hp1, hp2⟩ := nat.prime.not_coprime_iff_dvd.mp H
   rw [← Int.coe_nat_dvd_left] at hp1 hp2
-  have h2m : (p : ℤ) ∣ 2 * m ^ 2 := by
-    convert dvd_add hp2 hp1
-    ring
-  have h2n : (p : ℤ) ∣ 2 * n ^ 2 := by
-    convert dvd_sub hp2 hp1
-    ring
+  have h2m : (p : ℤ) ∣ 2 * m ^ 2 := by convert dvd_add hp2 hp1; ring
+  have h2n : (p : ℤ) ∣ 2 * n ^ 2 := by convert dvd_sub hp2 hp1; ring
   have hmc : p = 2 ∨ p ∣ Int.natAbs m := prime_two_or_dvd_of_dvd_two_mul_pow_self_two hp h2m
   have hnc : p = 2 ∨ p ∣ Int.natAbs n := prime_two_or_dvd_of_dvd_two_mul_pow_self_two hp h2n
   by_cases h2 : p = 2
   · have h3 : (m ^ 2 + n ^ 2) % 2 = 1 := by norm_num [sq, Int.add_emod, Int.mul_emod, hm, hn]
-    have h4 : (m ^ 2 + n ^ 2) % 2 = 0 :=
-      by
-      apply Int.emod_eq_zero_of_dvd
-      rwa [h2] at hp2
-    rw [h4] at h3
-    exact zero_ne_one h3
+    have h4 : (m ^ 2 + n ^ 2) % 2 = 0 := by apply Int.emod_eq_zero_of_dvd; rwa [h2] at hp2
+    rw [h4] at h3; exact zero_ne_one h3
   · apply hp.not_dvd_one
     rw [← h]
     exact Nat.dvd_gcd (Or.resolve_left hmc h2) (Or.resolve_left hnc h2)
@@ -456,27 +400,22 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
   by_contra H
   obtain ⟨p, hp, hp1, hp2⟩ := nat.prime.not_coprime_iff_dvd.mp H
   rw [← Int.coe_nat_dvd_left] at hp1 hp2
-  have hnp : ¬(p : ℤ) ∣ Int.gcd m n := by
-    rw [h]
-    norm_cast
+  have hnp : ¬(p : ℤ) ∣ Int.gcd m n := by rw [h]; norm_cast;
     exact mt nat.dvd_one.mp (Nat.Prime.ne_one hp)
   cases' Int.Prime.dvd_mul hp hp2 with hp2m hpn
   · rw [Int.natAbs_mul] at hp2m
     cases' (Nat.Prime.dvd_mul hp).mp hp2m with hp2 hpm
     · have hp2' : p = 2 := (Nat.le_of_dvd zero_lt_two hp2).antisymm hp.two_le
-      revert hp1
-      rw [hp2']
+      revert hp1; rw [hp2']
       apply mt Int.emod_eq_zero_of_dvd
       norm_num [sq, Int.sub_emod, Int.mul_emod, hm, hn]
     apply mt (Int.dvd_gcd (int.coe_nat_dvd_left.mpr hpm)) hnp
-    apply (or_self_iff _).mp
-    apply Int.Prime.dvd_mul' hp
+    apply (or_self_iff _).mp; apply Int.Prime.dvd_mul' hp
     rw [(by ring : n * n = -(m ^ 2 - n ^ 2) + m * m)]
     exact hp1.neg_right.add ((Int.coe_nat_dvd_left.2 hpm).mul_right _)
   rw [Int.gcd_comm] at hnp
   apply mt (Int.dvd_gcd (int.coe_nat_dvd_left.mpr hpn)) hnp
-  apply (or_self_iff _).mp
-  apply Int.Prime.dvd_mul' hp
+  apply (or_self_iff _).mp; apply Int.Prime.dvd_mul' hp
   rw [(by ring : m * m = m ^ 2 - n ^ 2 + n * n)]
   apply dvd_add hp1
   exact (int.coe_nat_dvd_left.mpr hpn).mul_right n
@@ -504,16 +443,12 @@ private theorem coprime_sq_sub_sq_sum_of_odd_odd {m n : ℤ} (h : Int.gcd m n =
   by
   cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hm) with m0 hm2
   cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hn) with n0 hn2
-  rw [sub_eq_iff_eq_add] at hm2 hn2
-  subst m
-  subst n
+  rw [sub_eq_iff_eq_add] at hm2 hn2; subst m; subst n
   have h1 : (m0 * 2 + 1) ^ 2 + (n0 * 2 + 1) ^ 2 = 2 * (2 * (m0 ^ 2 + n0 ^ 2 + m0 + n0) + 1) := by
     ring
   have h2 : (m0 * 2 + 1) ^ 2 - (n0 * 2 + 1) ^ 2 = 2 * (2 * (m0 ^ 2 - n0 ^ 2 + m0 - n0)) := by ring
-  have h3 : ((m0 * 2 + 1) ^ 2 - (n0 * 2 + 1) ^ 2) / 2 % 2 = 0 :=
-    by
-    rw [h2, Int.mul_ediv_cancel_left, Int.mul_emod_right]
-    exact by decide
+  have h3 : ((m0 * 2 + 1) ^ 2 - (n0 * 2 + 1) ^ 2) / 2 % 2 = 0 := by
+    rw [h2, Int.mul_ediv_cancel_left, Int.mul_emod_right]; exact by decide
   refine' ⟨⟨_, h1⟩, ⟨_, h2⟩, h3, _⟩
   have h20 : (2 : ℤ) ≠ 0 := by decide
   rw [h1, h2, Int.mul_ediv_cancel_left _ h20, Int.mul_ediv_cancel_left _ h20]
@@ -524,11 +459,9 @@ private theorem coprime_sq_sub_sq_sum_of_odd_odd {m n : ℤ} (h : Int.gcd m n =
   rw [← Int.coe_nat_dvd_left] at hp1 hp2
   apply Nat.dvd_gcd
   · apply Int.Prime.dvd_natAbs_of_coe_dvd_sq hp
-    convert dvd_add hp1 hp2
-    ring
+    convert dvd_add hp1 hp2; ring
   · apply Int.Prime.dvd_natAbs_of_coe_dvd_sq hp
-    convert dvd_sub hp2 hp1
-    ring
+    convert dvd_sub hp2 hp1; ring
 
 namespace PythagoreanTriple
 
@@ -545,16 +478,10 @@ theorem isPrimitiveClassified_aux (hc : x.gcd y = 1) (hzpos : 0 < z) {m n : ℤ}
     (H : Int.gcd (m ^ 2 - n ^ 2) (m ^ 2 + n ^ 2) = 1) (co : Int.gcd m n = 1)
     (pp : m % 2 = 0 ∧ n % 2 = 1 ∨ m % 2 = 1 ∧ n % 2 = 0) : h.IsPrimitiveClassified :=
   by
-  have hz : z ≠ 0
-  apply ne_of_gt hzpos
-  have h2 : y = m ^ 2 - n ^ 2 ∧ z = m ^ 2 + n ^ 2 :=
-    by
-    apply Rat.div_int_inj hzpos hm2n2 (h.coprime_of_coprime hc) H
-    rw [hw2]
-    norm_cast
-  use m, n
-  apply And.intro _ (And.intro co pp)
-  right
+  have hz : z ≠ 0; apply ne_of_gt hzpos
+  have h2 : y = m ^ 2 - n ^ 2 ∧ z = m ^ 2 + n ^ 2 := by
+    apply Rat.div_int_inj hzpos hm2n2 (h.coprime_of_coprime hc) H; rw [hw2]; norm_cast
+  use m, n; apply And.intro _ (And.intro co pp); right
   refine' ⟨_, h2.left⟩
   rw [← Rat.coe_int_inj _ _, ← div_left_inj' ((mt (Rat.coe_int_inj z 0).mp) hz), hv2, h2.right]
   norm_cast
@@ -565,26 +492,17 @@ theorem isPrimitiveClassified_aux (hc : x.gcd y = 1) (hzpos : 0 < z) {m n : ℤ}
 theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (hyo : y % 2 = 1)
     (hzpos : 0 < z) : h.IsPrimitiveClassified :=
   by
-  by_cases h0 : x = 0
-  · exact h.is_primitive_classified_of_coprime_of_zero_left hc h0
+  by_cases h0 : x = 0; · exact h.is_primitive_classified_of_coprime_of_zero_left hc h0
   let v := (x : ℚ) / z
   let w := (y : ℚ) / z
-  have hz : z ≠ 0
-  apply ne_of_gt hzpos
-  have hq : v ^ 2 + w ^ 2 = 1 := by
-    field_simp [hz, sq]
-    norm_cast
-    exact h
-  have hvz : v ≠ 0 := by
-    field_simp [hz]
-    exact h0
+  have hz : z ≠ 0; apply ne_of_gt hzpos
+  have hq : v ^ 2 + w ^ 2 = 1 := by field_simp [hz, sq] ; norm_cast; exact h
+  have hvz : v ≠ 0 := by field_simp [hz] ; exact h0
   have hw1 : w ≠ -1 := by
     contrapose! hvz with hw1
     rw [hw1, neg_sq, one_pow, add_left_eq_self] at hq
     exact pow_eq_zero hq
-  have hQ : ∀ x : ℚ, 1 + x ^ 2 ≠ 0 := by
-    intro q
-    apply ne_of_gt
+  have hQ : ∀ x : ℚ, 1 + x ^ 2 ≠ 0 := by intro q; apply ne_of_gt;
     exact lt_add_of_pos_of_le zero_lt_one (sq_nonneg q)
   have hp : (⟨v, w⟩ : ℚ × ℚ) ∈ { p : ℚ × ℚ | p.1 ^ 2 + p.2 ^ 2 = 1 ∧ p.2 ≠ -1 } := ⟨hq, hw1⟩
   let q := (circleEquivGen hQ).symm ⟨⟨v, w⟩, hp⟩
@@ -595,53 +513,38 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
     exact congr_arg Subtype.val this
   let m := (q.denom : ℤ)
   let n := q.num
-  have hm0 : m ≠ 0 := by
-    norm_cast
-    apply Rat.den_nz q
+  have hm0 : m ≠ 0 := by norm_cast; apply Rat.den_nz q
   have hq2 : q = n / m := (Rat.num_div_den q).symm
   have hm2n2 : 0 < m ^ 2 + n ^ 2 :=
     by
     apply lt_add_of_pos_of_le _ (sq_nonneg n)
     exact lt_of_le_of_ne (sq_nonneg m) (Ne.symm (pow_ne_zero 2 hm0))
-  have hw2 : w = (m ^ 2 - n ^ 2) / (m ^ 2 + n ^ 2) :=
-    by
-    rw [ht4.2, hq2]
+  have hw2 : w = (m ^ 2 - n ^ 2) / (m ^ 2 + n ^ 2) := by rw [ht4.2, hq2];
     field_simp [hm2n2, Rat.den_nz q, -Rat.num_div_den]
-  have hm2n20 : (m : ℚ) ^ 2 + (n : ℚ) ^ 2 ≠ 0 :=
-    by
-    norm_cast
+  have hm2n20 : (m : ℚ) ^ 2 + (n : ℚ) ^ 2 ≠ 0 := by norm_cast;
     simpa only [Int.coe_nat_pow] using ne_of_gt hm2n2
   have hv2 : v = 2 * m * n / (m ^ 2 + n ^ 2) :=
     by
-    apply Eq.symm
-    apply (div_eq_iff hm2n20).mpr
-    rw [ht4.1]
-    field_simp [hQ q]
+    apply Eq.symm; apply (div_eq_iff hm2n20).mpr; rw [ht4.1]; field_simp [hQ q]
     rw [hq2]
     field_simp [Rat.den_nz q, -Rat.num_div_den]
     ring
   have hnmcp : Int.gcd n m = 1 := q.cop
-  have hmncp : Int.gcd m n = 1 := by
-    rw [Int.gcd_comm]
-    exact hnmcp
+  have hmncp : Int.gcd m n = 1 := by rw [Int.gcd_comm]; exact hnmcp
   cases' Int.emod_two_eq_zero_or_one m with hm2 hm2 <;>
     cases' Int.emod_two_eq_zero_or_one n with hn2 hn2
   · -- m even, n even
     exfalso
     have h1 : 2 ∣ (Int.gcd n m : ℤ) :=
       Int.dvd_gcd (Int.dvd_of_emod_eq_zero hn2) (Int.dvd_of_emod_eq_zero hm2)
-    rw [hnmcp] at h1
-    revert h1
-    norm_num
+    rw [hnmcp] at h1; revert h1; norm_num
   · -- m even, n odd
     apply h.is_primitive_classified_aux hc hzpos hm2n2 hv2 hw2 _ hmncp
-    · apply Or.intro_left
-      exact And.intro hm2 hn2
+    · apply Or.intro_left; exact And.intro hm2 hn2
     · apply coprime_sq_sub_sq_add_of_even_odd hmncp hm2 hn2
   · -- m odd, n even
     apply h.is_primitive_classified_aux hc hzpos hm2n2 hv2 hw2 _ hmncp
-    · apply Or.intro_right
-      exact And.intro hm2 hn2
+    · apply Or.intro_right; exact And.intro hm2 hn2
     apply coprime_sq_sub_sq_add_of_odd_even hmncp hm2 hn2
   · -- m odd, n odd
     exfalso
@@ -653,13 +556,10 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
     have h2 : y = (m ^ 2 - n ^ 2) / 2 ∧ z = (m ^ 2 + n ^ 2) / 2 :=
       by
       apply Rat.div_int_inj hzpos _ (h.coprime_of_coprime hc) h1.2.2.2
-      · show w = _
-        rw [← Rat.divInt_eq_div, ← Rat.divInt_mul_right (by norm_num : (2 : ℤ) ≠ 0)]
-        rw [Int.ediv_mul_cancel h1.1, Int.ediv_mul_cancel h1.2.1, hw2]
-        norm_cast
+      · show w = _; rw [← Rat.divInt_eq_div, ← Rat.divInt_mul_right (by norm_num : (2 : ℤ) ≠ 0)]
+        rw [Int.ediv_mul_cancel h1.1, Int.ediv_mul_cancel h1.2.1, hw2]; norm_cast
       · apply (mul_lt_mul_right (by norm_num : 0 < (2 : ℤ))).mp
-        rw [Int.ediv_mul_cancel h1.1, MulZeroClass.zero_mul]
-        exact hm2n2
+        rw [Int.ediv_mul_cancel h1.1, MulZeroClass.zero_mul]; exact hm2n2
     rw [h2.1, h1.2.2.1] at hyo
     revert hyo
     norm_num
@@ -694,14 +594,9 @@ theorem isPrimitiveClassified_of_coprime (hc : Int.gcd x y = 1) : h.IsPrimitiveC
 theorem classified : h.IsClassified :=
   by
   by_cases h0 : Int.gcd x y = 0
-  · have hx : x = 0 := by
-      apply int.nat_abs_eq_zero.mp
-      apply Nat.eq_zero_of_gcd_eq_zero_left h0
-    have hy : y = 0 := by
-      apply int.nat_abs_eq_zero.mp
-      apply Nat.eq_zero_of_gcd_eq_zero_right h0
-    use 0, 1, 0
-    norm_num [hx, hy]
+  · have hx : x = 0 := by apply int.nat_abs_eq_zero.mp; apply Nat.eq_zero_of_gcd_eq_zero_left h0
+    have hy : y = 0 := by apply int.nat_abs_eq_zero.mp; apply Nat.eq_zero_of_gcd_eq_zero_right h0
+    use 0, 1, 0; norm_num [hx, hy]
   apply h.is_classified_of_normalize_is_primitive_classified
   apply h.normalize.is_primitive_classified_of_coprime
   apply Int.gcd_div_gcd_div_gcd (Nat.pos_of_ne_zero h0)
@@ -729,28 +624,18 @@ theorem coprime_classification :
     use m, n
     rcases H with ⟨⟨rfl, rfl⟩ | ⟨rfl, rfl⟩, co, pp⟩
     · refine' ⟨Or.inl ⟨rfl, rfl⟩, _, co, pp⟩
-      have : z ^ 2 = (m ^ 2 + n ^ 2) ^ 2 :=
-        by
-        rw [sq, ← h.left.eq]
-        ring
+      have : z ^ 2 = (m ^ 2 + n ^ 2) ^ 2 := by rw [sq, ← h.left.eq]; ring
       simpa using eq_or_eq_neg_of_sq_eq_sq _ _ this
     · refine' ⟨Or.inr ⟨rfl, rfl⟩, _, co, pp⟩
-      have : z ^ 2 = (m ^ 2 + n ^ 2) ^ 2 :=
-        by
-        rw [sq, ← h.left.eq]
-        ring
+      have : z ^ 2 = (m ^ 2 + n ^ 2) ^ 2 := by rw [sq, ← h.left.eq]; ring
       simpa using eq_or_eq_neg_of_sq_eq_sq _ _ this
   · delta PythagoreanTriple
     rintro ⟨m, n, ⟨rfl, rfl⟩ | ⟨rfl, rfl⟩, rfl | rfl, co, pp⟩ <;>
       first
-        |·
-          constructor
-          · ring
-          exact coprime_sq_sub_mul co pp|·
-          constructor
-          · ring
-          rw [Int.gcd_comm]
-          exact coprime_sq_sub_mul co pp
+        |· constructor; · ring;
+          exact
+            coprime_sq_sub_mul co
+              pp|· constructor; · ring; rw [Int.gcd_comm]; exact coprime_sq_sub_mul co pp
 #align pythagorean_triple.coprime_classification PythagoreanTriple.coprime_classification
 
 /- warning: pythagorean_triple.coprime_classification' -> PythagoreanTriple.coprime_classification' is a dubious translation:
@@ -778,9 +663,7 @@ theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
       apply And.intro h_odd.2
       cases' ht2 with h_pos h_neg
       · apply And.intro h_pos (And.intro ht3 (And.intro ht4 hm))
-      · exfalso
-        revert h_pos
-        rw [h_neg]
+      · exfalso; revert h_pos; rw [h_neg]
         exact imp_false.mpr (not_lt.mpr (neg_nonpos.mpr (add_nonneg (sq_nonneg m) (sq_nonneg n))))
     exfalso
     rcases h_even with ⟨rfl, -⟩
@@ -791,21 +674,14 @@ theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
     · rw [neg_sq m]
       rw [neg_sq n]
       apply And.intro h_odd.1
-      constructor
-      · rw [h_odd.2]
-        ring
+      constructor; · rw [h_odd.2]; ring
       cases' ht2 with h_pos h_neg
       · apply And.intro h_pos
         constructor
-        · delta Int.gcd
-          rw [Int.natAbs_neg, Int.natAbs_neg]
-          exact ht3
+        · delta Int.gcd; rw [Int.natAbs_neg, Int.natAbs_neg]; exact ht3
         · rw [Int.neg_emod_two, Int.neg_emod_two]
-          apply And.intro ht4
-          linarith
-      · exfalso
-        revert h_pos
-        rw [h_neg]
+          apply And.intro ht4; linarith
+      · exfalso; revert h_pos; rw [h_neg]
         exact imp_false.mpr (not_lt.mpr (neg_nonpos.mpr (add_nonneg (sq_nonneg m) (sq_nonneg n))))
     exfalso
     rcases h_even with ⟨rfl, -⟩
@@ -833,16 +709,10 @@ theorem classification :
     use k, m, n
     rcases H with (⟨rfl, rfl⟩ | ⟨rfl, rfl⟩)
     · refine' ⟨Or.inl ⟨rfl, rfl⟩, _⟩
-      have : z ^ 2 = (k * (m ^ 2 + n ^ 2)) ^ 2 :=
-        by
-        rw [sq, ← h.eq]
-        ring
+      have : z ^ 2 = (k * (m ^ 2 + n ^ 2)) ^ 2 := by rw [sq, ← h.eq]; ring
       simpa using eq_or_eq_neg_of_sq_eq_sq _ _ this
     · refine' ⟨Or.inr ⟨rfl, rfl⟩, _⟩
-      have : z ^ 2 = (k * (m ^ 2 + n ^ 2)) ^ 2 :=
-        by
-        rw [sq, ← h.eq]
-        ring
+      have : z ^ 2 = (k * (m ^ 2 + n ^ 2)) ^ 2 := by rw [sq, ← h.eq]; ring
       simpa using eq_or_eq_neg_of_sq_eq_sq _ _ this
   · rintro ⟨k, m, n, ⟨rfl, rfl⟩ | ⟨rfl, rfl⟩, rfl | rfl⟩ <;> delta PythagoreanTriple <;> ring
 #align pythagorean_triple.classification PythagoreanTriple.classification

e8638a0f

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -397,10 +397,7 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
 #align circle_equiv_gen circleEquivGen
 
 /- warning: circle_equiv_apply -> circleEquivGen_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align circle_equiv_apply circleEquivGen_applyₓ'. -/
 @[simp]
 theorem circleEquivGen_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
@@ -409,10 +406,7 @@ theorem circleEquivGen_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
 #align circle_equiv_apply circleEquivGen_apply
 
 /- warning: circle_equiv_symm_apply -> circleEquivGen_symm_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align circle_equiv_symm_apply circleEquivGen_symm_applyₓ'. -/
 @[simp]
 theorem circleEquivGen_symm_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0)
@@ -448,7 +442,6 @@ private theorem coprime_sq_sub_sq_add_of_even_odd {m n : ℤ} (h : Int.gcd m n =
   · apply hp.not_dvd_one
     rw [← h]
     exact Nat.dvd_gcd (Or.resolve_left hmc h2) (Or.resolve_left hnc h2)
-#align coprime_sq_sub_sq_add_of_even_odd coprime_sq_sub_sq_add_of_even_odd
 
 private theorem coprime_sq_sub_sq_add_of_odd_even {m n : ℤ} (h : Int.gcd m n = 1) (hm : m % 2 = 1)
     (hn : n % 2 = 0) : Int.gcd (m ^ 2 - n ^ 2) (m ^ 2 + n ^ 2) = 1 :=
@@ -456,7 +449,6 @@ private theorem coprime_sq_sub_sq_add_of_odd_even {m n : ℤ} (h : Int.gcd m n =
   rw [Int.gcd, ← Int.natAbs_neg (m ^ 2 - n ^ 2)]
   rw [(by ring : -(m ^ 2 - n ^ 2) = n ^ 2 - m ^ 2), add_comm]
   apply coprime_sq_sub_sq_add_of_even_odd _ hn hm; rwa [Int.gcd_comm]
-#align coprime_sq_sub_sq_add_of_odd_even coprime_sq_sub_sq_add_of_odd_even
 
 private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1) (hm : m % 2 = 0)
     (hn : n % 2 = 1) : Int.gcd (m ^ 2 - n ^ 2) (2 * m * n) = 1 :=
@@ -488,7 +480,6 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
   rw [(by ring : m * m = m ^ 2 - n ^ 2 + n * n)]
   apply dvd_add hp1
   exact (int.coe_nat_dvd_left.mpr hpn).mul_right n
-#align coprime_sq_sub_mul_of_even_odd coprime_sq_sub_mul_of_even_odd
 
 private theorem coprime_sq_sub_mul_of_odd_even {m n : ℤ} (h : Int.gcd m n = 1) (hm : m % 2 = 1)
     (hn : n % 2 = 0) : Int.gcd (m ^ 2 - n ^ 2) (2 * m * n) = 1 :=
@@ -496,7 +487,6 @@ private theorem coprime_sq_sub_mul_of_odd_even {m n : ℤ} (h : Int.gcd m n = 1)
   rw [Int.gcd, ← Int.natAbs_neg (m ^ 2 - n ^ 2)]
   rw [(by ring : 2 * m * n = 2 * n * m), (by ring : -(m ^ 2 - n ^ 2) = n ^ 2 - m ^ 2)]
   apply coprime_sq_sub_mul_of_even_odd _ hn hm; rwa [Int.gcd_comm]
-#align coprime_sq_sub_mul_of_odd_even coprime_sq_sub_mul_of_odd_even
 
 private theorem coprime_sq_sub_mul {m n : ℤ} (h : Int.gcd m n = 1)
     (hmn : m % 2 = 0 ∧ n % 2 = 1 ∨ m % 2 = 1 ∧ n % 2 = 0) :
@@ -505,7 +495,6 @@ private theorem coprime_sq_sub_mul {m n : ℤ} (h : Int.gcd m n = 1)
   cases' hmn with h1 h2
   · exact coprime_sq_sub_mul_of_even_odd h h1.left h1.right
   · exact coprime_sq_sub_mul_of_odd_even h h2.left h2.right
-#align coprime_sq_sub_mul coprime_sq_sub_mul
 
 private theorem coprime_sq_sub_sq_sum_of_odd_odd {m n : ℤ} (h : Int.gcd m n = 1) (hm : m % 2 = 1)
     (hn : n % 2 = 1) :
@@ -540,7 +529,6 @@ private theorem coprime_sq_sub_sq_sum_of_odd_odd {m n : ℤ} (h : Int.gcd m n =
   · apply Int.Prime.dvd_natAbs_of_coe_dvd_sq hp
     convert dvd_sub hp2 hp1
     ring
-#align coprime_sq_sub_sq_sum_of_odd_odd coprime_sq_sub_sq_sum_of_odd_odd
 
 namespace PythagoreanTriple
 
@@ -549,10 +537,7 @@ variable {x y z : ℤ} (h : PythagoreanTriple x y z)
 include h
 
 /- warning: pythagorean_triple.is_primitive_classified_aux -> PythagoreanTriple.isPrimitiveClassified_aux is a dubious translation:
-lean 3 declaration is
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(Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) m (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (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))))) (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) m (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (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)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))))) -> (PythagoreanTriple.IsPrimitiveClassified x y z h))
-but is expected to have type
-  forall {x : Int} {y : Int} {z : Int} (h : PythagoreanTriple x y z), (Eq.{1} Nat (Int.gcd x y) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (LT.lt.{0} Int Int.instLTInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z) -> (forall {m : Int} {n : Int}, (LT.lt.{0} Int Int.instLTInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) -> (Eq.{1} Rat (HDiv.hDiv.{0, 0, 0} Rat Rat Rat (instHDiv.{0} Rat Rat.instDivRat) (Int.cast.{0} Rat Rat.instIntCastRat x) (Int.cast.{0} Rat Rat.instIntCastRat z)) (HDiv.hDiv.{0, 0, 0} Rat Rat Rat (instHDiv.{0} Rat Rat.instDivRat) (HMul.hMul.{0, 0, 0} Rat Rat Rat (instHMul.{0} Rat Rat.instMulRat) (HMul.hMul.{0, 0, 0} Rat Rat Rat (instHMul.{0} Rat Rat.instMulRat) (OfNat.ofNat.{0} Rat 2 (Rat.instOfNatRat 2)) (Int.cast.{0} Rat Rat.instIntCastRat m)) (Int.cast.{0} Rat Rat.instIntCastRat n)) (HAdd.hAdd.{0, 0, 0} Rat Rat Rat (instHAdd.{0} Rat Rat.instAddRat) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) (Int.cast.{0} Rat Rat.instIntCastRat m) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) (Int.cast.{0} Rat Rat.instIntCastRat n) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) -> (Eq.{1} Rat (HDiv.hDiv.{0, 0, 0} Rat Rat Rat (instHDiv.{0} Rat Rat.instDivRat) (Int.cast.{0} Rat Rat.instIntCastRat y) (Int.cast.{0} Rat Rat.instIntCastRat z)) (HDiv.hDiv.{0, 0, 0} Rat Rat Rat (instHDiv.{0} Rat Rat.instDivRat) (HSub.hSub.{0, 0, 0} Rat Rat Rat (instHSub.{0} Rat Rat.instSubRat) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) (Int.cast.{0} Rat Rat.instIntCastRat m) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) (Int.cast.{0} Rat Rat.instIntCastRat n) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HAdd.hAdd.{0, 0, 0} Rat Rat Rat (instHAdd.{0} Rat Rat.instAddRat) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) (Int.cast.{0} Rat Rat.instIntCastRat m) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) (Int.cast.{0} Rat Rat.instIntCastRat n) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) -> (Eq.{1} Nat (Int.gcd (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (Eq.{1} Nat (Int.gcd m n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (Or (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) m (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))) (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) m (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))))) -> (PythagoreanTriple.IsPrimitiveClassified x y z h))
+<too large>
 Case conversion may be inaccurate. Consider using '#align pythagorean_triple.is_primitive_classified_aux PythagoreanTriple.isPrimitiveClassified_auxₓ'. -/
 theorem isPrimitiveClassified_aux (hc : x.gcd y = 1) (hzpos : 0 < z) {m n : ℤ}
     (hm2n2 : 0 < m ^ 2 + n ^ 2) (hv2 : (x : ℚ) / z = 2 * m * n / (m ^ 2 + n ^ 2))

e8638a0f

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -400,7 +400,7 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] (hk : forall (x : K), Ne.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) (x : K), Eq.{succ u1} (Prod.{u1, u1} K K) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))))) (Prod.{u1, u1} K K) (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))))) (Prod.{u1, u1} K K) (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K 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 but is expected to have type
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(CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (x : K), Eq.{succ u1} (Prod.{u1, u1} K K) (Subtype.val.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K 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K (Field.toSemifield.{u1} K _inst_1)))))))))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))))) (circleEquivGen.{u1} K _inst_1 hk) x)) (Prod.mk.{u1, u1} K K (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K _inst_1)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K 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(NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] (hk : forall (x : K), Ne.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (x : K), Eq.{succ u1} (Prod.{u1, u1} K K) (Subtype.val.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : K) => Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))))) (circleEquivGen.{u1} K _inst_1 hk) x)) (Prod.mk.{u1, u1} K K (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K _inst_1)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K _inst_1)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
 Case conversion may be inaccurate. Consider using '#align circle_equiv_apply circleEquivGen_applyₓ'. -/
 @[simp]
 theorem circleEquivGen_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
@@ -412,7 +412,7 @@ theorem circleEquivGen_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] (hk : forall (x : K), Ne.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) (v : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))))), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (Equiv.{succ 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))))) K) (fun (_x : Equiv.{succ u1, succ u1} (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))))) K) => (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) 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 but is expected to have type
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(Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) => K) v) _inst_1))))))))
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(CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (v : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K 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(Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) => K) v) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) => K) v) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) => K) v) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) => K) v) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) => K) v) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) => K) v) _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align circle_equiv_symm_apply circleEquivGen_symm_applyₓ'. -/
 @[simp]
 theorem circleEquivGen_symm_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0)

e8638a0f

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -38,7 +38,7 @@ the bulk of the proof below.
 lean 3 declaration is
   forall (z : ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))), Ne.{1} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{0, 0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (instHMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Distrib.toHasMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toDistrib.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))) z z) (OfNat.ofNat.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 2 (OfNat.mk.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 2 (bit0.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Distrib.toHasAdd.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Ring.toDistrib.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (CommRing.toRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (ZMod.commRing (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (One.one.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddMonoidWithOne.toOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Ring.toAddCommGroupWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (CommRing.toRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (ZMod.commRing (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))
 but is expected to have type
-  forall (z : ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))), Ne.{1} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (HMul.hMul.{0, 0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (instHMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (NonUnitalNonAssocRing.toMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (NonAssocRing.toNonUnitalNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))))) z z) (OfNat.ofNat.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) 2 (instOfNat.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) 2 (NonAssocRing.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+  forall (z : ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))), Ne.{1} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (HMul.hMul.{0, 0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (instHMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (NonUnitalNonAssocRing.toMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (NonAssocRing.toNonUnitalNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))))) z z) (OfNat.ofNat.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) 2 (instOfNat.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) 2 (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
 Case conversion may be inaccurate. Consider using '#align sq_ne_two_fin_zmod_four sq_ne_two_fin_zmod_fourₓ'. -/
 theorem sq_ne_two_fin_zmod_four (z : ZMod 4) : z * z ≠ 2 :=
   by
@@ -353,7 +353,7 @@ variable {K : Type _} [Field K]
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K], (forall (x : K), Ne.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) -> (Equiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K], (forall (x : K), Ne.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) -> (Equiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K], (forall (x : K), Ne.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) -> (Equiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))))
 Case conversion may be inaccurate. Consider using '#align circle_equiv_gen circleEquivGenₓ'. -/
 /-- A parameterization of the unit circle that is useful for classifying Pythagorean triples.
  (To be applied in the case where `K = ℚ`.) -/
@@ -400,7 +400,7 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] (hk : forall (x : K), Ne.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) (x : K), Eq.{succ u1} (Prod.{u1, u1} K K) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K 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(DivisionRing.toDivInvMonoid.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (SubNegMonoid.toHasSub.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
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(Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (x : K), Eq.{succ u1} (Prod.{u1, u1} K K) (Subtype.val.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : K) => Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) (circleEquivGen.{u1} K _inst_1 hk) x)) (Prod.mk.{u1, u1} K K (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K _inst_1)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (NonAssocRing.toNatCast.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K _inst_1)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] (hk : forall (x : K), Ne.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (x : K), Eq.{succ u1} (Prod.{u1, u1} K K) (Subtype.val.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : K) => Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))))) (circleEquivGen.{u1} K _inst_1 hk) x)) (Prod.mk.{u1, u1} K K (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K _inst_1)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K _inst_1)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
 Case conversion may be inaccurate. Consider using '#align circle_equiv_apply circleEquivGen_applyₓ'. -/
 @[simp]
 theorem circleEquivGen_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
@@ -412,7 +412,7 @@ theorem circleEquivGen_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] (hk : forall (x : K), Ne.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) (v : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))))), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (Equiv.{succ 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 but is expected to have type
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K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (Prod.snd.{u1, u1} K K (Subtype.val.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) v)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) (NonAssocRing.toOne.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) _inst_1))))))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] (hk : forall (x : K), Ne.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K 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(Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) => K) v) _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align circle_equiv_symm_apply circleEquivGen_symm_applyₓ'. -/
 @[simp]
 theorem circleEquivGen_symm_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0)

e8638a0f

bump to nightly-2023-04-06-02

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

89485060

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul van Wamelen
 
 ! This file was ported from Lean 3 source module number_theory.pythagorean_triples
-! leanprover-community/mathlib commit 97eab48559068f3d6313da387714ef25768fb730
+! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -183,9 +183,9 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
   · -- x even, y even
     exfalso
     apply Nat.not_coprime_of_dvd_of_dvd (by decide : 1 < 2) _ _ hc
-    · apply Int.dvd_natAbs_of_ofNat_dvd
+    · apply Int.coe_nat_dvd_left.1
       apply Int.dvd_of_emod_eq_zero hx
-    · apply Int.dvd_natAbs_of_ofNat_dvd
+    · apply Int.coe_nat_dvd_left.1
       apply Int.dvd_of_emod_eq_zero hy
   · left
     exact ⟨hx, hy⟩
@@ -480,8 +480,7 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
     apply (or_self_iff _).mp
     apply Int.Prime.dvd_mul' hp
     rw [(by ring : n * n = -(m ^ 2 - n ^ 2) + m * m)]
-    apply dvd_add (dvd_neg_of_dvd hp1)
-    exact dvd_mul_of_dvd_left (int.coe_nat_dvd_left.mpr hpm) m
+    exact hp1.neg_right.add ((Int.coe_nat_dvd_left.2 hpm).mul_right _)
   rw [Int.gcd_comm] at hnp
   apply mt (Int.dvd_gcd (int.coe_nat_dvd_left.mpr hpn)) hnp
   apply (or_self_iff _).mp

97eab485

bump to nightly-2023-03-27-10

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

1caedb6b

Diff

@@ -34,24 +34,24 @@ the bulk of the proof below.
 -/
 
 
-/- warning: sq_ne_two_fin_zmod_four -> sq_ne_two_fin_zMod_four is a dubious translation:
+/- warning: sq_ne_two_fin_zmod_four -> sq_ne_two_fin_zmod_four is a dubious translation:
 lean 3 declaration is
   forall (z : ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))), Ne.{1} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{0, 0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (instHMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Distrib.toHasMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toDistrib.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))) z z) (OfNat.ofNat.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 2 (OfNat.mk.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 2 (bit0.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Distrib.toHasAdd.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Ring.toDistrib.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (CommRing.toRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (ZMod.commRing (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (One.one.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddMonoidWithOne.toOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Ring.toAddCommGroupWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (CommRing.toRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (ZMod.commRing (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))
 but is expected to have type
   forall (z : ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))), Ne.{1} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (HMul.hMul.{0, 0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (instHMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (NonUnitalNonAssocRing.toMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (NonAssocRing.toNonUnitalNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))))) z z) (OfNat.ofNat.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) 2 (instOfNat.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) 2 (NonAssocRing.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
-Case conversion may be inaccurate. Consider using '#align sq_ne_two_fin_zmod_four sq_ne_two_fin_zMod_fourₓ'. -/
-theorem sq_ne_two_fin_zMod_four (z : ZMod 4) : z * z ≠ 2 :=
+Case conversion may be inaccurate. Consider using '#align sq_ne_two_fin_zmod_four sq_ne_two_fin_zmod_fourₓ'. -/
+theorem sq_ne_two_fin_zmod_four (z : ZMod 4) : z * z ≠ 2 :=
   by
   change Fin 4 at z
   fin_cases z <;> norm_num [Fin.ext_iff, Fin.val_bit0, Fin.val_bit1]
-#align sq_ne_two_fin_zmod_four sq_ne_two_fin_zMod_four
+#align sq_ne_two_fin_zmod_four sq_ne_two_fin_zmod_four
 
 #print Int.sq_ne_two_mod_four /-
 theorem Int.sq_ne_two_mod_four (z : ℤ) : z * z % 4 ≠ 2 :=
   by
   suffices ¬z * z % (4 : ℕ) = 2 % (4 : ℕ) by norm_num at this
   rw [← ZMod.int_cast_eq_int_cast_iff']
-  simpa using sq_ne_two_fin_zMod_four _
+  simpa using sq_ne_two_fin_zmod_four _
 #align int.sq_ne_two_mod_four Int.sq_ne_two_mod_four
 -/
 
@@ -396,30 +396,30 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
       ring
 #align circle_equiv_gen circleEquivGen
 
-/- warning: circle_equiv_apply -> circle_equiv_apply is a dubious translation:
+/- warning: circle_equiv_apply -> circleEquivGen_apply 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 circle_equiv_apply circle_equiv_applyₓ'. -/
+Case conversion may be inaccurate. Consider using '#align circle_equiv_apply circleEquivGen_applyₓ'. -/
 @[simp]
-theorem circle_equiv_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
+theorem circleEquivGen_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
     (circleEquivGen hk x : K × K) = ⟨2 * x / (1 + x ^ 2), (1 - x ^ 2) / (1 + x ^ 2)⟩ :=
   rfl
-#align circle_equiv_apply circle_equiv_apply
+#align circle_equiv_apply circleEquivGen_apply
 
-/- warning: circle_equiv_symm_apply -> circle_equiv_symm_apply is a dubious translation:
+/- warning: circle_equiv_symm_apply -> circleEquivGen_symm_apply 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 circle_equiv_symm_apply circle_equiv_symm_applyₓ'. -/
+Case conversion may be inaccurate. Consider using '#align circle_equiv_symm_apply circleEquivGen_symm_applyₓ'. -/
 @[simp]
-theorem circle_equiv_symm_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0)
+theorem circleEquivGen_symm_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0)
     (v : { p : K × K // p.1 ^ 2 + p.2 ^ 2 = 1 ∧ p.2 ≠ -1 }) :
     (circleEquivGen hk).symm v = (v : K × K).1 / ((v : K × K).2 + 1) :=
   rfl
-#align circle_equiv_symm_apply circle_equiv_symm_apply
+#align circle_equiv_symm_apply circleEquivGen_symm_apply
 
 end circleEquivGen

97eab485

bump to nightly-2023-03-27-02

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

0e4ebd8c

Diff

@@ -36,7 +36,7 @@ the bulk of the proof below.
 
 /- warning: sq_ne_two_fin_zmod_four -> sq_ne_two_fin_zMod_four is a dubious translation:
 lean 3 declaration is
-  forall (z : ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))), Ne.{1} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{0, 0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (instHMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Distrib.toHasMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toDistrib.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))) z z) (OfNat.ofNat.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 2 (OfNat.mk.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 2 (bit0.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Distrib.toHasAdd.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Ring.toDistrib.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (CommRing.toRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (ZMod.commRing (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (One.one.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddMonoidWithOne.toOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (NonAssocRing.toAddGroupWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Ring.toNonAssocRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (CommRing.toRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (ZMod.commRing (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))
+  forall (z : ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))), Ne.{1} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{0, 0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (instHMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Distrib.toHasMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toDistrib.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))) z z) (OfNat.ofNat.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 2 (OfNat.mk.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 2 (bit0.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Distrib.toHasAdd.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Ring.toDistrib.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (CommRing.toRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (ZMod.commRing (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (One.one.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddMonoidWithOne.toOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Ring.toAddCommGroupWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (CommRing.toRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (ZMod.commRing (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))
 but is expected to have type
   forall (z : ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))), Ne.{1} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (HMul.hMul.{0, 0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (instHMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (NonUnitalNonAssocRing.toMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (NonAssocRing.toNonUnitalNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))))) z z) (OfNat.ofNat.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) 2 (instOfNat.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) 2 (NonAssocRing.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
 Case conversion may be inaccurate. Consider using '#align sq_ne_two_fin_zmod_four sq_ne_two_fin_zMod_fourₓ'. -/
@@ -351,7 +351,7 @@ variable {K : Type _} [Field K]
 
 /- warning: circle_equiv_gen -> circleEquivGen is a dubious translation:
 lean 3 declaration is
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K], (forall (x : K), Ne.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) -> (Equiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K], (forall (x : K), Ne.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) -> (Equiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))))))
 but is expected to have type
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K], (forall (x : K), Ne.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) -> (Equiv.{succ u1, succ u1} K (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))))
 Case conversion may be inaccurate. Consider using '#align circle_equiv_gen circleEquivGenₓ'. -/
@@ -398,7 +398,7 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
 
 /- warning: circle_equiv_apply -> circle_equiv_apply is a dubious translation:
 lean 3 declaration is
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(OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))))))) (circleEquivGen.{u1} K _inst_1 hk) x)) (Prod.mk.{u1, u1} K K (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 2 (OfNat.mk.{u1} K 2 (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) x) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K 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(AddGroupWithOne.toAddMonoidWithOne.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) (x : K), Eq.{succ u1} (Prod.{u1, u1} K K) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K 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: Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))))) (Prod.{u1, u1} K K) (coeBase.{succ u1, succ u1} (Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K 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 but is expected to have type
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2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) (circleEquivGen.{u1} K _inst_1 hk) x)) (Prod.mk.{u1, u1} K K (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K _inst_1)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (NonAssocRing.toNatCast.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K 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(Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
 Case conversion may be inaccurate. Consider using '#align circle_equiv_apply circle_equiv_applyₓ'. -/
@@ -410,7 +410,7 @@ theorem circle_equiv_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
 
 /- warning: circle_equiv_symm_apply -> circle_equiv_symm_apply is a dubious translation:
 lean 3 declaration is
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K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) (v : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 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(OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))))))))) v)) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))))
 but is expected to have type
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p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) (NonAssocRing.toOne.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align circle_equiv_symm_apply circle_equiv_symm_applyₓ'. -/

97eab485

bump to nightly-2023-03-25-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/d11893b411025250c8e61ff2f12ccbd7ee35ab15

9ce440f0

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul van Wamelen
 
 ! This file was ported from Lean 3 source module number_theory.pythagorean_triples
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 97eab48559068f3d6313da387714ef25768fb730
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -19,6 +19,9 @@ import Mathbin.Data.Zmod.Basic
 /-!
 # Pythagorean Triples
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The main result is the classification of Pythagorean triples. The final result is for general
 Pythagorean triples. It follows from the more interesting relatively prime case. We use the
 "rational parametrization of the circle" method for the proof. The parametrization maps the point

70fd9563

bump to nightly-2023-03-23-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

c81981db

Diff

@@ -31,28 +31,39 @@ the bulk of the proof below.
 -/
 
 
+/- warning: sq_ne_two_fin_zmod_four -> sq_ne_two_fin_zMod_four is a dubious translation:
+lean 3 declaration is
+  forall (z : ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))), Ne.{1} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{0, 0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (instHMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Distrib.toHasMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toDistrib.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))) z z) (OfNat.ofNat.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 2 (OfNat.mk.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 2 (bit0.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Distrib.toHasAdd.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Ring.toDistrib.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (CommRing.toRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (ZMod.commRing (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (One.one.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddMonoidWithOne.toOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (NonAssocRing.toAddGroupWithOne.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Ring.toNonAssocRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (CommRing.toRing.{0} (ZMod (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (ZMod.commRing (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))
+but is expected to have type
+  forall (z : ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))), Ne.{1} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (HMul.hMul.{0, 0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (instHMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (NonUnitalNonAssocRing.toMul.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (NonAssocRing.toNonUnitalNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))))) z z) (OfNat.ofNat.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) 2 (instOfNat.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) 2 (NonAssocRing.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toNonAssocRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+Case conversion may be inaccurate. Consider using '#align sq_ne_two_fin_zmod_four sq_ne_two_fin_zMod_fourₓ'. -/
 theorem sq_ne_two_fin_zMod_four (z : ZMod 4) : z * z ≠ 2 :=
   by
   change Fin 4 at z
   fin_cases z <;> norm_num [Fin.ext_iff, Fin.val_bit0, Fin.val_bit1]
 #align sq_ne_two_fin_zmod_four sq_ne_two_fin_zMod_four
 
+#print Int.sq_ne_two_mod_four /-
 theorem Int.sq_ne_two_mod_four (z : ℤ) : z * z % 4 ≠ 2 :=
   by
   suffices ¬z * z % (4 : ℕ) = 2 % (4 : ℕ) by norm_num at this
   rw [← ZMod.int_cast_eq_int_cast_iff']
   simpa using sq_ne_two_fin_zMod_four _
 #align int.sq_ne_two_mod_four Int.sq_ne_two_mod_four
+-/
 
 noncomputable section
 
 open Classical
 
+#print PythagoreanTriple /-
 /-- Three integers `x`, `y`, and `z` form a Pythagorean triple if `x * x + y * y = z * z`. -/
 def PythagoreanTriple (x y z : ℤ) : Prop :=
   x * x + y * y = z * z
 #align pythagorean_triple PythagoreanTriple
+-/
 
+#print pythagoreanTriple_comm /-
 /-- Pythagorean triples are interchangable, i.e `x * x + y * y = y * y + x * x = z * z`.
 This comes from additive commutativity. -/
 theorem pythagoreanTriple_comm {x y z : ℤ} : PythagoreanTriple x y z ↔ PythagoreanTriple y x z :=
@@ -60,11 +71,14 @@ theorem pythagoreanTriple_comm {x y z : ℤ} : PythagoreanTriple x y z ↔ Pytha
   delta PythagoreanTriple
   rw [add_comm]
 #align pythagorean_triple_comm pythagoreanTriple_comm
+-/
 
+#print PythagoreanTriple.zero /-
 /-- The zeroth Pythagorean triple is all zeros. -/
 theorem PythagoreanTriple.zero : PythagoreanTriple 0 0 0 := by
   simp only [PythagoreanTriple, MulZeroClass.zero_mul, zero_add]
 #align pythagorean_triple.zero PythagoreanTriple.zero
+-/
 
 namespace PythagoreanTriple
 
@@ -72,14 +86,19 @@ variable {x y z : ℤ} (h : PythagoreanTriple x y z)
 
 include h
 
+#print PythagoreanTriple.eq /-
 theorem eq : x * x + y * y = z * z :=
   h
 #align pythagorean_triple.eq PythagoreanTriple.eq
+-/
 
+#print PythagoreanTriple.symm /-
 @[symm]
 theorem symm : PythagoreanTriple y x z := by rwa [pythagoreanTriple_comm]
 #align pythagorean_triple.symm PythagoreanTriple.symm
+-/
 
+#print PythagoreanTriple.mul /-
 /-- A triple is still a triple if you multiply `x`, `y` and `z`
 by a constant `k`. -/
 theorem mul (k : ℤ) : PythagoreanTriple (k * x) (k * y) (k * z) :=
@@ -89,9 +108,11 @@ theorem mul (k : ℤ) : PythagoreanTriple (k * x) (k * y) (k * z) :=
     _ = k * z * (k * z) := by ring
     
 #align pythagorean_triple.mul PythagoreanTriple.mul
+-/
 
 omit h
 
+#print PythagoreanTriple.mul_iff /-
 /-- `(k*x, k*y, k*z)` is a Pythagorean triple if and only if
 `(x, y, z)` is also a triple. -/
 theorem mul_iff (k : ℤ) (hk : k ≠ 0) :
@@ -103,9 +124,11 @@ theorem mul_iff (k : ℤ) (hk : k ≠ 0) :
   rw [← mul_left_inj' (mul_ne_zero hk hk)]
   convert h using 1 <;> ring
 #align pythagorean_triple.mul_iff PythagoreanTriple.mul_iff
+-/
 
 include h
 
+#print PythagoreanTriple.IsClassified /-
 /-- A Pythagorean triple `x, y, z` is “classified” if there exist integers `k, m, n` such that
 either
  * `x = k * (m ^ 2 - n ^ 2)` and `y = k * (2 * m * n)`, or
@@ -117,7 +140,9 @@ def IsClassified :=
         x = k * (2 * m * n) ∧ y = k * (m ^ 2 - n ^ 2)) ∧
       Int.gcd m n = 1
 #align pythagorean_triple.is_classified PythagoreanTriple.IsClassified
+-/
 
+#print PythagoreanTriple.IsPrimitiveClassified /-
 /-- A primitive pythogorean triple `x, y, z` is a pythagorean triple with `x` and `y` coprime.
  Such a triple is “primitively classified” if there exist coprime integers `m, n` such that either
  * `x = m ^ 2 - n ^ 2` and `y = 2 * m * n`, or
@@ -129,7 +154,9 @@ def IsPrimitiveClassified :=
     (x = m ^ 2 - n ^ 2 ∧ y = 2 * m * n ∨ x = 2 * m * n ∧ y = m ^ 2 - n ^ 2) ∧
       Int.gcd m n = 1 ∧ (m % 2 = 0 ∧ n % 2 = 1 ∨ m % 2 = 1 ∧ n % 2 = 0)
 #align pythagorean_triple.is_primitive_classified PythagoreanTriple.IsPrimitiveClassified
+-/
 
+#print PythagoreanTriple.mul_isClassified /-
 theorem mul_isClassified (k : ℤ) (hc : h.IsClassified) : (h.mul k).IsClassified :=
   by
   obtain ⟨l, m, n, ⟨⟨rfl, rfl⟩ | ⟨rfl, rfl⟩, co⟩⟩ := hc
@@ -142,7 +169,9 @@ theorem mul_isClassified (k : ℤ) (hc : h.IsClassified) : (h.mul k).IsClassifie
     right
     constructor <;> ring
 #align pythagorean_triple.mul_is_classified PythagoreanTriple.mul_isClassified
+-/
 
+#print PythagoreanTriple.even_odd_of_coprime /-
 theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
     x % 2 = 0 ∧ y % 2 = 1 ∨ x % 2 = 1 ∧ y % 2 = 0 :=
   by
@@ -176,7 +205,14 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
         ring]
     norm_num [Int.add_emod]
 #align pythagorean_triple.even_odd_of_coprime PythagoreanTriple.even_odd_of_coprime
+-/
 
+/- warning: pythagorean_triple.gcd_dvd -> PythagoreanTriple.gcd_dvd is a dubious translation:
+lean 3 declaration is
+  forall {x : Int} {y : Int} {z : Int}, (PythagoreanTriple x y z) -> (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))) (Int.gcd x y)) z)
+but is expected to have type
+  forall {x : Int} {y : Int} {z : Int}, (PythagoreanTriple x y z) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt (Int.gcd x y)) z)
+Case conversion may be inaccurate. Consider using '#align pythagorean_triple.gcd_dvd PythagoreanTriple.gcd_dvdₓ'. -/
 theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z :=
   by
   by_cases h0 : Int.gcd x y = 0
@@ -199,6 +235,7 @@ theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z :=
   exact dvd_mul_right _ _
 #align pythagorean_triple.gcd_dvd PythagoreanTriple.gcd_dvd
 
+#print PythagoreanTriple.normalize /-
 theorem normalize : PythagoreanTriple (x / Int.gcd x y) (y / Int.gcd x y) (z / Int.gcd x y) :=
   by
   by_cases h0 : Int.gcd x y = 0
@@ -224,7 +261,9 @@ theorem normalize : PythagoreanTriple (x / Int.gcd x y) (y / Int.gcd x y) (z / I
   rw [mul_comm x0, mul_comm y0, mul_iff k hk] at h
   rwa [Int.mul_ediv_cancel _ hk, Int.mul_ediv_cancel _ hk, Int.mul_ediv_cancel_left _ hk]
 #align pythagorean_triple.normalize PythagoreanTriple.normalize
+-/
 
+#print PythagoreanTriple.isClassified_of_isPrimitiveClassified /-
 theorem isClassified_of_isPrimitiveClassified (hp : h.IsPrimitiveClassified) : h.IsClassified :=
   by
   obtain ⟨m, n, H⟩ := hp
@@ -233,7 +272,9 @@ theorem isClassified_of_isPrimitiveClassified (hp : h.IsPrimitiveClassified) : h
   rw [one_mul, one_mul]
   exact ⟨t, co⟩
 #align pythagorean_triple.is_classified_of_is_primitive_classified PythagoreanTriple.isClassified_of_isPrimitiveClassified
+-/
 
+#print PythagoreanTriple.isClassified_of_normalize_isPrimitiveClassified /-
 theorem isClassified_of_normalize_isPrimitiveClassified (hc : h.normalize.IsPrimitiveClassified) :
     h.IsClassified :=
   by
@@ -244,7 +285,9 @@ theorem isClassified_of_normalize_isPrimitiveClassified (hc : h.normalize.IsPrim
   · exact Int.gcd_dvd_right x y
   · exact h.gcd_dvd
 #align pythagorean_triple.is_classified_of_normalize_is_primitive_classified PythagoreanTriple.isClassified_of_normalize_isPrimitiveClassified
+-/
 
+#print PythagoreanTriple.ne_zero_of_coprime /-
 theorem ne_zero_of_coprime (hc : Int.gcd x y = 1) : z ≠ 0 :=
   by
   suffices 0 < z * z by
@@ -258,7 +301,9 @@ theorem ne_zero_of_coprime (hc : Int.gcd x y = 1) : z ≠ 0 :=
   · apply lt_add_of_pos_of_le (sq_pos_of_ne_zero x hxz) (sq_nonneg y)
   · apply lt_add_of_le_of_pos (sq_nonneg x) (sq_pos_of_ne_zero y hyz)
 #align pythagorean_triple.ne_zero_of_coprime PythagoreanTriple.ne_zero_of_coprime
+-/
 
+#print PythagoreanTriple.isPrimitiveClassified_of_coprime_of_zero_left /-
 theorem isPrimitiveClassified_of_coprime_of_zero_left (hc : Int.gcd x y = 1) (hx : x = 0) :
     h.IsPrimitiveClassified := by
   subst x
@@ -272,7 +317,9 @@ theorem isPrimitiveClassified_of_coprime_of_zero_left (hc : Int.gcd x y = 1) (hx
     rw [hy, hc, Int.gcd_zero_left]
     norm_num
 #align pythagorean_triple.is_primitive_classified_of_coprime_of_zero_left PythagoreanTriple.isPrimitiveClassified_of_coprime_of_zero_left
+-/
 
+#print PythagoreanTriple.coprime_of_coprime /-
 theorem coprime_of_coprime (hc : Int.gcd x y = 1) : Int.gcd y z = 1 :=
   by
   by_contra H
@@ -284,6 +331,7 @@ theorem coprime_of_coprime (hc : Int.gcd x y = 1) : Int.gcd y z = 1 :=
   rw [← Int.coe_nat_dvd_left] at hpy hpz
   exact dvd_sub (hpz.mul_right _) (hpy.mul_right _)
 #align pythagorean_triple.coprime_of_coprime PythagoreanTriple.coprime_of_coprime
+-/
 
 end PythagoreanTriple
 
@@ -298,6 +346,12 @@ For the classification of pythogorean triples, we will use a parametrization of
 
 variable {K : Type _} [Field K]
 
+/- warning: circle_equiv_gen -> circleEquivGen 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 circle_equiv_gen circleEquivGenₓ'. -/
 /-- A parameterization of the unit circle that is useful for classifying Pythagorean triples.
  (To be applied in the case where `K = ℚ`.) -/
 def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
@@ -339,12 +393,24 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
       ring
 #align circle_equiv_gen circleEquivGen
 
+/- warning: circle_equiv_apply -> circle_equiv_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align circle_equiv_apply circle_equiv_applyₓ'. -/
 @[simp]
 theorem circle_equiv_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
     (circleEquivGen hk x : K × K) = ⟨2 * x / (1 + x ^ 2), (1 - x ^ 2) / (1 + x ^ 2)⟩ :=
   rfl
 #align circle_equiv_apply circle_equiv_apply
 
+/- warning: circle_equiv_symm_apply -> circle_equiv_symm_apply is a dubious translation:
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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K 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p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) (NonAssocRing.toOne.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K 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_inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{succ u1} (Prod.{u1, u1} K K) (fun (p : Prod.{u1, u1} K K) => And (Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.fst.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Prod.snd.{u1, u1} K K p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Ne.{succ u1} K (Prod.snd.{u1, u1} K K p) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) => K) v) _inst_1))))))))
+Case conversion may be inaccurate. Consider using '#align circle_equiv_symm_apply circle_equiv_symm_applyₓ'. -/
 @[simp]
 theorem circle_equiv_symm_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0)
     (v : { p : K × K // p.1 ^ 2 + p.2 ^ 2 = 1 ∧ p.2 ≠ -1 }) :
@@ -480,6 +546,12 @@ variable {x y z : ℤ} (h : PythagoreanTriple x y z)
 
 include h
 
+/- warning: pythagorean_triple.is_primitive_classified_aux -> PythagoreanTriple.isPrimitiveClassified_aux is a dubious translation:
+lean 3 declaration is
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(HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Rat (HasLiftT.mk.{1, 1} Int Rat (CoeTCₓ.coe.{1, 1} Int Rat (Int.castCoe.{0} Rat Rat.hasIntCast))) m) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Rat (HasLiftT.mk.{1, 1} Int Rat (CoeTCₓ.coe.{1, 1} Int Rat (Int.castCoe.{0} Rat Rat.hasIntCast))) n) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) -> (Eq.{1} Rat (HDiv.hDiv.{0, 0, 0} Rat Rat Rat (instHDiv.{0} Rat Rat.hasDiv) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Rat (HasLiftT.mk.{1, 1} Int Rat (CoeTCₓ.coe.{1, 1} Int Rat (Int.castCoe.{0} Rat Rat.hasIntCast))) y) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Rat (HasLiftT.mk.{1, 1} Int Rat (CoeTCₓ.coe.{1, 1} Int Rat (Int.castCoe.{0} Rat Rat.hasIntCast))) z)) (HDiv.hDiv.{0, 0, 0} Rat Rat Rat (instHDiv.{0} Rat Rat.hasDiv) (HSub.hSub.{0, 0, 0} Rat Rat Rat (instHSub.{0} Rat (SubNegMonoid.toHasSub.{0} Rat (AddGroup.toSubNegMonoid.{0} Rat Rat.addGroup))) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Rat (HasLiftT.mk.{1, 1} Int Rat (CoeTCₓ.coe.{1, 1} Int Rat (Int.castCoe.{0} Rat Rat.hasIntCast))) m) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Rat (HasLiftT.mk.{1, 1} Int Rat (CoeTCₓ.coe.{1, 1} Int Rat (Int.castCoe.{0} Rat Rat.hasIntCast))) n) (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} Rat Rat Rat (instHAdd.{0} Rat Rat.hasAdd) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Rat (HasLiftT.mk.{1, 1} Int Rat (CoeTCₓ.coe.{1, 1} Int Rat (Int.castCoe.{0} Rat Rat.hasIntCast))) m) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Rat (HasLiftT.mk.{1, 1} Int Rat (CoeTCₓ.coe.{1, 1} Int Rat (Int.castCoe.{0} Rat Rat.hasIntCast))) n) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) -> (Eq.{1} Nat (Int.gcd (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (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} 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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) -> (Eq.{1} Nat (Int.gcd m n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) -> (Or (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) m (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (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))))) (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) m (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (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)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))))) -> (PythagoreanTriple.IsPrimitiveClassified x y z h))
+but is expected to have type
+  forall {x : Int} {y : Int} {z : Int} (h : PythagoreanTriple x y z), (Eq.{1} Nat (Int.gcd x y) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (LT.lt.{0} Int Int.instLTInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z) -> (forall {m : Int} {n : Int}, (LT.lt.{0} Int Int.instLTInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) -> (Eq.{1} Rat (HDiv.hDiv.{0, 0, 0} Rat Rat Rat (instHDiv.{0} Rat Rat.instDivRat) (Int.cast.{0} Rat Rat.instIntCastRat x) (Int.cast.{0} Rat Rat.instIntCastRat z)) (HDiv.hDiv.{0, 0, 0} Rat Rat Rat (instHDiv.{0} Rat Rat.instDivRat) (HMul.hMul.{0, 0, 0} Rat Rat Rat (instHMul.{0} Rat Rat.instMulRat) (HMul.hMul.{0, 0, 0} Rat Rat Rat (instHMul.{0} Rat Rat.instMulRat) (OfNat.ofNat.{0} Rat 2 (Rat.instOfNatRat 2)) (Int.cast.{0} Rat Rat.instIntCastRat m)) (Int.cast.{0} Rat Rat.instIntCastRat n)) (HAdd.hAdd.{0, 0, 0} Rat Rat Rat (instHAdd.{0} Rat Rat.instAddRat) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) (Int.cast.{0} Rat Rat.instIntCastRat m) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) (Int.cast.{0} Rat Rat.instIntCastRat n) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) -> (Eq.{1} Rat (HDiv.hDiv.{0, 0, 0} Rat Rat Rat (instHDiv.{0} Rat Rat.instDivRat) (Int.cast.{0} Rat Rat.instIntCastRat y) (Int.cast.{0} Rat Rat.instIntCastRat z)) (HDiv.hDiv.{0, 0, 0} Rat Rat Rat (instHDiv.{0} Rat Rat.instDivRat) (HSub.hSub.{0, 0, 0} Rat Rat Rat (instHSub.{0} Rat Rat.instSubRat) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) (Int.cast.{0} Rat Rat.instIntCastRat m) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) (Int.cast.{0} Rat Rat.instIntCastRat n) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HAdd.hAdd.{0, 0, 0} Rat Rat Rat (instHAdd.{0} Rat Rat.instAddRat) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) (Int.cast.{0} Rat Rat.instIntCastRat m) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Rat Nat Rat (instHPow.{0, 0} Rat Nat (Monoid.Pow.{0} Rat Rat.monoid)) (Int.cast.{0} Rat Rat.instIntCastRat n) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) -> (Eq.{1} Nat (Int.gcd (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (Eq.{1} Nat (Int.gcd m n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (Or (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) m (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))) (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) m (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))))) -> (PythagoreanTriple.IsPrimitiveClassified x y z h))
+Case conversion may be inaccurate. Consider using '#align pythagorean_triple.is_primitive_classified_aux PythagoreanTriple.isPrimitiveClassified_auxₓ'. -/
 theorem isPrimitiveClassified_aux (hc : x.gcd y = 1) (hzpos : 0 < z) {m n : ℤ}
     (hm2n2 : 0 < m ^ 2 + n ^ 2) (hv2 : (x : ℚ) / z = 2 * m * n / (m ^ 2 + n ^ 2))
     (hw2 : (y : ℚ) / z = (m ^ 2 - n ^ 2) / (m ^ 2 + n ^ 2))
@@ -502,6 +574,7 @@ theorem isPrimitiveClassified_aux (hc : x.gcd y = 1) (hzpos : 0 < z) {m n : ℤ}
 #align pythagorean_triple.is_primitive_classified_aux PythagoreanTriple.isPrimitiveClassified_aux
 
 /- ./././Mathport/Syntax/Translate/Tactic/Lean3.lean:132:4: warning: unsupported: rw with cfg: { occs := occurrences.pos[occurrences.pos] «expr[ ,]»([2, 3]) } -/
+#print PythagoreanTriple.isPrimitiveClassified_of_coprime_of_odd_of_pos /-
 theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (hyo : y % 2 = 1)
     (hzpos : 0 < z) : h.IsPrimitiveClassified :=
   by
@@ -604,7 +677,9 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
     revert hyo
     norm_num
 #align pythagorean_triple.is_primitive_classified_of_coprime_of_odd_of_pos PythagoreanTriple.isPrimitiveClassified_of_coprime_of_odd_of_pos
+-/
 
+#print PythagoreanTriple.isPrimitiveClassified_of_coprime_of_pos /-
 theorem isPrimitiveClassified_of_coprime_of_pos (hc : Int.gcd x y = 1) (hzpos : 0 < z) :
     h.IsPrimitiveClassified :=
   by
@@ -614,7 +689,9 @@ theorem isPrimitiveClassified_of_coprime_of_pos (hc : Int.gcd x y = 1) (hzpos :
   obtain ⟨m, n, H⟩ := h.symm.is_primitive_classified_of_coprime_of_odd_of_pos hc h2.left hzpos
   use m, n; tauto
 #align pythagorean_triple.is_primitive_classified_of_coprime_of_pos PythagoreanTriple.isPrimitiveClassified_of_coprime_of_pos
+-/
 
+#print PythagoreanTriple.isPrimitiveClassified_of_coprime /-
 theorem isPrimitiveClassified_of_coprime (hc : Int.gcd x y = 1) : h.IsPrimitiveClassified :=
   by
   by_cases hz : 0 < z
@@ -624,7 +701,9 @@ theorem isPrimitiveClassified_of_coprime (hc : Int.gcd x y = 1) : h.IsPrimitiveC
   apply lt_of_le_of_ne _ (h'.ne_zero_of_coprime hc).symm
   exact le_neg.mp (not_lt.mp hz)
 #align pythagorean_triple.is_primitive_classified_of_coprime PythagoreanTriple.isPrimitiveClassified_of_coprime
+-/
 
+#print PythagoreanTriple.classified /-
 theorem classified : h.IsClassified :=
   by
   by_cases h0 : Int.gcd x y = 0
@@ -640,9 +719,16 @@ theorem classified : h.IsClassified :=
   apply h.normalize.is_primitive_classified_of_coprime
   apply Int.gcd_div_gcd_div_gcd (Nat.pos_of_ne_zero h0)
 #align pythagorean_triple.classified PythagoreanTriple.classified
+-/
 
 omit h
 
+/- warning: pythagorean_triple.coprime_classification -> PythagoreanTriple.coprime_classification is a dubious translation:
+lean 3 declaration is
+  forall {x : Int} {y : Int} {z : Int}, Iff (And (PythagoreanTriple x y z) (Eq.{1} Nat (Int.gcd x y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Exists.{1} Int (fun (m : Int) => Exists.{1} Int (fun (n : Int) => And (Or (And (Eq.{1} Int x (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) m) n))) (And (Eq.{1} Int x (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) m) n)) (Eq.{1} Int y (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))) (And (Or (Eq.{1} Int z (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Eq.{1} Int z (Neg.neg.{0} Int Int.hasNeg (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))) (And (Eq.{1} Nat (Int.gcd m n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Or (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) m (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (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))))) (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) m (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (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)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))))))))))
+but is expected to have type
+  forall {x : Int} {y : Int} {z : Int}, Iff (And (PythagoreanTriple x y z) (Eq.{1} Nat (Int.gcd x y) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Exists.{1} Int (fun (m : Int) => Exists.{1} Int (fun (n : Int) => And (Or (And (Eq.{1} Int x (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) m) n))) (And (Eq.{1} Int x (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) m) n)) (Eq.{1} Int y (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) (And (Or (Eq.{1} Int z (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (Eq.{1} Int z (Neg.neg.{0} Int Int.instNegInt (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) (And (Eq.{1} Nat (Int.gcd m n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Or (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) m (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))) (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) m (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))))))))))
+Case conversion may be inaccurate. Consider using '#align pythagorean_triple.coprime_classification PythagoreanTriple.coprime_classificationₓ'. -/
 theorem coprime_classification :
     PythagoreanTriple x y z ∧ Int.gcd x y = 1 ↔
       ∃ m n,
@@ -680,6 +766,12 @@ theorem coprime_classification :
           exact coprime_sq_sub_mul co pp
 #align pythagorean_triple.coprime_classification PythagoreanTriple.coprime_classification
 
+/- warning: pythagorean_triple.coprime_classification' -> PythagoreanTriple.coprime_classification' is a dubious translation:
+lean 3 declaration is
+  forall {x : Int} {y : Int} {z : Int}, (PythagoreanTriple x y z) -> (Eq.{1} Nat (Int.gcd x y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) -> (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) x (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (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)))) -> (LT.lt.{0} Int Int.hasLt (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) z) -> (Exists.{1} Int (fun (m : Int) => Exists.{1} Int (fun (n : Int) => And (Eq.{1} Int x (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (And (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) m) n)) (And (Eq.{1} Int z (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (And (Eq.{1} Nat (Int.gcd m n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (And (Or (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) m (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (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))))) (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) m (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (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)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))))) (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) m))))))))
+but is expected to have type
+  forall {x : Int} {y : Int} {z : Int}, (PythagoreanTriple x y z) -> (Eq.{1} Nat (Int.gcd x y) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) x (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) -> (LT.lt.{0} Int Int.instLTInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z) -> (Exists.{1} Int (fun (m : Int) => Exists.{1} Int (fun (n : Int) => And (Eq.{1} Int x (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (And (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) m) n)) (And (Eq.{1} Int z (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (And (Eq.{1} Nat (Int.gcd m n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (And (Or (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) m (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))) (And (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) m (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))))) (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) m))))))))
+Case conversion may be inaccurate. Consider using '#align pythagorean_triple.coprime_classification' PythagoreanTriple.coprime_classification'ₓ'. -/
 /-- by assuming `x` is odd and `z` is positive we get a slightly more precise classification of
 the pythagorean triple `x ^ 2 + y ^ 2 = z ^ 2`-/
 theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
@@ -734,6 +826,12 @@ theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
     exact zero_ne_one h_parity
 #align pythagorean_triple.coprime_classification' PythagoreanTriple.coprime_classification'
 
+/- warning: pythagorean_triple.classification -> PythagoreanTriple.classification is a dubious translation:
+lean 3 declaration is
+  forall {x : Int} {y : Int} {z : Int}, Iff (PythagoreanTriple x y z) (Exists.{1} Int (fun (k : Int) => Exists.{1} Int (fun (m : Int) => Exists.{1} Int (fun (n : Int) => And (Or (And (Eq.{1} Int x (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) m) n)))) (And (Eq.{1} Int x (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) m) n))) (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))) (Or (Eq.{1} Int z (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) (Eq.{1} Int z (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (Neg.neg.{0} Int Int.hasNeg k) (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)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))
+but is expected to have type
+  forall {x : Int} {y : Int} {z : Int}, (PythagoreanTriple x y z) -> (Iff (PythagoreanTriple x y z) (Exists.{1} Int (fun (k : Int) => Exists.{1} Int (fun (m : Int) => Exists.{1} Int (fun (n : Int) => And (Or (And (Eq.{1} Int x (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) m) n)))) (And (Eq.{1} Int x (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) m) n))) (Eq.{1} Int y (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))) (Or (Eq.{1} Int z (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (Eq.{1} Int z (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (Neg.neg.{0} Int Int.instNegInt k) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))))))))
+Case conversion may be inaccurate. Consider using '#align pythagorean_triple.classification PythagoreanTriple.classificationₓ'. -/
 /-- **Formula for Pythagorean Triples** -/
 theorem classification :
     PythagoreanTriple x y z ↔

70fd9563

bump to nightly-2023-03-18-20

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

1c3193ff

Diff

@@ -40,7 +40,7 @@ theorem sq_ne_two_fin_zMod_four (z : ZMod 4) : z * z ≠ 2 :=
 theorem Int.sq_ne_two_mod_four (z : ℤ) : z * z % 4 ≠ 2 :=
   by
   suffices ¬z * z % (4 : ℕ) = 2 % (4 : ℕ) by norm_num at this
-  rw [← ZMod.int_coe_eq_int_coe_iff']
+  rw [← ZMod.int_cast_eq_int_cast_iff']
   simpa using sq_ne_two_fin_zMod_four _
 #align int.sq_ne_two_mod_four Int.sq_ne_two_mod_four

70fd9563

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -237,8 +237,7 @@ theorem isClassified_of_isPrimitiveClassified (hp : h.IsPrimitiveClassified) : h
 theorem isClassified_of_normalize_isPrimitiveClassified (hc : h.normalize.IsPrimitiveClassified) :
     h.IsClassified :=
   by
-  convert
-      h.normalize.mul_is_classified (Int.gcd x y)
+  convert h.normalize.mul_is_classified (Int.gcd x y)
         (is_classified_of_is_primitive_classified h.normalize hc) <;>
     rw [Int.mul_ediv_cancel']
   · exact Int.gcd_dvd_left x y

70fd9563

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -63,7 +63,7 @@ theorem pythagoreanTriple_comm {x y z : ℤ} : PythagoreanTriple x y z ↔ Pytha
 
 /-- The zeroth Pythagorean triple is all zeros. -/
 theorem PythagoreanTriple.zero : PythagoreanTriple 0 0 0 := by
-  simp only [PythagoreanTriple, zero_mul, zero_add]
+  simp only [PythagoreanTriple, MulZeroClass.zero_mul, zero_add]
 #align pythagorean_triple.zero PythagoreanTriple.zero
 
 namespace PythagoreanTriple
@@ -187,7 +187,8 @@ theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z :=
       apply int.nat_abs_eq_zero.mp
       apply Nat.eq_zero_of_gcd_eq_zero_right h0
     have hz : z = 0 := by
-      simpa only [PythagoreanTriple, hx, hy, add_zero, zero_eq_mul, mul_zero, or_self_iff] using h
+      simpa only [PythagoreanTriple, hx, hy, add_zero, zero_eq_mul, MulZeroClass.mul_zero,
+        or_self_iff] using h
     simp only [hz, dvd_zero]
   obtain ⟨k, x0, y0, k0, h2, rfl, rfl⟩ :
     ∃ (k : ℕ)(x0 y0 : _), 0 < k ∧ Int.gcd x0 y0 = 1 ∧ x = x0 * k ∧ y = y0 * k :=
@@ -208,7 +209,8 @@ theorem normalize : PythagoreanTriple (x / Int.gcd x y) (y / Int.gcd x y) (z / I
       apply int.nat_abs_eq_zero.mp
       apply Nat.eq_zero_of_gcd_eq_zero_right h0
     have hz : z = 0 := by
-      simpa only [PythagoreanTriple, hx, hy, add_zero, zero_eq_mul, mul_zero, or_self_iff] using h
+      simpa only [PythagoreanTriple, hx, hy, add_zero, zero_eq_mul, MulZeroClass.mul_zero,
+        or_self_iff] using h
     simp only [hx, hy, hz, Int.zero_div]
     exact zero
   rcases h.gcd_dvd with ⟨z0, rfl⟩
@@ -597,7 +599,7 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
         rw [Int.ediv_mul_cancel h1.1, Int.ediv_mul_cancel h1.2.1, hw2]
         norm_cast
       · apply (mul_lt_mul_right (by norm_num : 0 < (2 : ℤ))).mp
-        rw [Int.ediv_mul_cancel h1.1, zero_mul]
+        rw [Int.ediv_mul_cancel h1.1, MulZeroClass.zero_mul]
         exact hm2n2
     rw [h2.1, h1.2.2.1] at hyo
     revert hyo

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

e8638a0f

chore: make argument to sq_pos_of_ne_zero/sq_pos_iff implicit (#12288)

This matches our general policy and zpow_two_pos_of_ne_zero.

Also define sq_pos_of_ne_zero as an alias.

ff9ef348

Diff

@@ -233,8 +233,8 @@ theorem ne_zero_of_coprime (hc : Int.gcd x y = 1) : z ≠ 0 := by
     rw [hc]
     exact one_ne_zero
   cases' Int.ne_zero_of_gcd hc' with hxz hyz
-  · apply lt_add_of_pos_of_le (sq_pos_of_ne_zero x hxz) (sq_nonneg y)
-  · apply lt_add_of_le_of_pos (sq_nonneg x) (sq_pos_of_ne_zero y hyz)
+  · apply lt_add_of_pos_of_le (sq_pos_of_ne_zero hxz) (sq_nonneg y)
+  · apply lt_add_of_le_of_pos (sq_nonneg x) (sq_pos_of_ne_zero hyz)
 #align pythagorean_triple.ne_zero_of_coprime PythagoreanTriple.ne_zero_of_coprime
 
 theorem isPrimitiveClassified_of_coprime_of_zero_left (hc : Int.gcd x y = 1) (hx : x = 0) :

e8638a0f

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

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

145460b9

Diff

@@ -35,7 +35,7 @@ theorem sq_ne_two_fin_zmod_four (z : ZMod 4) : z * z ≠ 2 := by
 
 theorem Int.sq_ne_two_mod_four (z : ℤ) : z * z % 4 ≠ 2 := by
   suffices ¬z * z % (4 : ℕ) = 2 % (4 : ℕ) by exact this
-  rw [← ZMod.int_cast_eq_int_cast_iff']
+  rw [← ZMod.intCast_eq_intCast_iff']
   simpa using sq_ne_two_fin_zmod_four _
 #align int.sq_ne_two_mod_four Int.sq_ne_two_mod_four

e8638a0f

Feat: add fermatLastTheoremThree_of_three_dvd_only_c (#11767)

We add fermatLastTheoremThree_of_three_dvd_only_c: To prove FermatLastTheoremFor 3, we may assume that ¬ 3 ∣ a, ¬ 3 ∣ b, a and b are coprime and 3 ∣ c.

From the flt3 project in LFTCM2024.

Co-authored-by: Pietro Monticone <38562595+pitmonticone@users.noreply.github.com>

fcf5d484

Diff

@@ -176,7 +176,7 @@ theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z := by
     ∃ (k : ℕ) (x0 y0 : _), 0 < k ∧ Int.gcd x0 y0 = 1 ∧ x = x0 * k ∧ y = y0 * k :=
     Int.exists_gcd_one' (Nat.pos_of_ne_zero h0)
   rw [Int.gcd_mul_right, h2, Int.natAbs_ofNat, one_mul]
-  rw [← Int.pow_dvd_pow_iff zero_lt_two, sq z, ← h.eq]
+  rw [← Int.pow_dvd_pow_iff two_ne_zero, sq z, ← h.eq]
   rw [(by ring : x0 * k * (x0 * k) + y0 * k * (y0 * k) = (k : ℤ) ^ 2 * (x0 * x0 + y0 * y0))]
   exact dvd_mul_right _ _
 #align pythagorean_triple.gcd_dvd PythagoreanTriple.gcd_dvd

e8638a0f

chore: exact by decide -> decide (#12067)

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

1e53d4f0

Diff

@@ -420,7 +420,7 @@ private theorem coprime_sq_sub_sq_sum_of_odd_odd {m n : ℤ} (h : Int.gcd m n =
   have h2 : (m0 * 2 + 1) ^ 2 - (n0 * 2 + 1) ^ 2 = 2 * (2 * (m0 ^ 2 - n0 ^ 2 + m0 - n0)) := by ring
   have h3 : ((m0 * 2 + 1) ^ 2 - (n0 * 2 + 1) ^ 2) / 2 % 2 = 0 := by
     rw [h2, Int.mul_ediv_cancel_left, Int.mul_emod_right]
-    exact by decide
+    decide
   refine' ⟨⟨_, h1⟩, ⟨_, h2⟩, h3, _⟩
   have h20 : (2 : ℤ) ≠ 0 := by decide
   rw [h1, h2, Int.mul_ediv_cancel_left _ h20, Int.mul_ediv_cancel_left _ h20]

e8638a0f

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

Reduce the diff of #11499

Renames

All in the Int namespace:

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

Also rename Nat.coe_nat_dvd to Nat.cast_dvd_cast

392a24a9

Diff

@@ -135,9 +135,9 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
   -- x even, y even
   · exfalso
     apply Nat.not_coprime_of_dvd_of_dvd (by decide : 1 < 2) _ _ hc
-    · apply Int.coe_nat_dvd_left.1
+    · apply Int.natCast_dvd.1
       apply Int.dvd_of_emod_eq_zero hx
-    · apply Int.coe_nat_dvd_left.1
+    · apply Int.natCast_dvd.1
       apply Int.dvd_of_emod_eq_zero hy
   -- x even, y odd
   · left
@@ -258,7 +258,7 @@ theorem coprime_of_coprime (hc : Int.gcd x y = 1) : Int.gcd y z = 1 := by
   rw [← hc]
   apply Nat.dvd_gcd (Int.Prime.dvd_natAbs_of_coe_dvd_sq hp _ _) hpy
   rw [sq, eq_sub_of_add_eq h]
-  rw [← Int.coe_nat_dvd_left] at hpy hpz
+  rw [← Int.natCast_dvd] at hpy hpz
   exact dvd_sub (hpz.mul_right _) (hpy.mul_right _)
 #align pythagorean_triple.coprime_of_coprime PythagoreanTriple.coprime_of_coprime
 
@@ -330,7 +330,7 @@ private theorem coprime_sq_sub_sq_add_of_even_odd {m n : ℤ} (h : Int.gcd m n =
     (hn : n % 2 = 1) : Int.gcd (m ^ 2 - n ^ 2) (m ^ 2 + n ^ 2) = 1 := by
   by_contra H
   obtain ⟨p, hp, hp1, hp2⟩ := Nat.Prime.not_coprime_iff_dvd.mp H
-  rw [← Int.coe_nat_dvd_left] at hp1 hp2
+  rw [← Int.natCast_dvd] at hp1 hp2
   have h2m : (p : ℤ) ∣ 2 * m ^ 2 := by
     convert dvd_add hp2 hp1 using 1
     ring
@@ -363,7 +363,7 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
     (hn : n % 2 = 1) : Int.gcd (m ^ 2 - n ^ 2) (2 * m * n) = 1 := by
   by_contra H
   obtain ⟨p, hp, hp1, hp2⟩ := Nat.Prime.not_coprime_iff_dvd.mp H
-  rw [← Int.coe_nat_dvd_left] at hp1 hp2
+  rw [← Int.natCast_dvd] at hp1 hp2
   have hnp : ¬(p : ℤ) ∣ Int.gcd m n := by
     rw [h]
     norm_cast
@@ -379,18 +379,18 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
       simp only [sq, Nat.cast_ofNat, Int.sub_emod, Int.mul_emod, hm, hn,
         mul_zero, EuclideanDomain.zero_mod, mul_one, zero_sub]
       decide
-    apply mt (Int.dvd_gcd (Int.coe_nat_dvd_left.mpr hpm)) hnp
+    apply mt (Int.dvd_gcd (Int.natCast_dvd.mpr hpm)) hnp
     apply or_self_iff.mp
     apply Int.Prime.dvd_mul' hp
     rw [(by ring : n * n = -(m ^ 2 - n ^ 2) + m * m)]
-    exact hp1.neg_right.add ((Int.coe_nat_dvd_left.2 hpm).mul_right _)
+    exact hp1.neg_right.add ((Int.natCast_dvd.2 hpm).mul_right _)
   rw [Int.gcd_comm] at hnp
-  apply mt (Int.dvd_gcd (Int.coe_nat_dvd_left.mpr hpn)) hnp
+  apply mt (Int.dvd_gcd (Int.natCast_dvd.mpr hpn)) hnp
   apply or_self_iff.mp
   apply Int.Prime.dvd_mul' hp
   rw [(by ring : m * m = m ^ 2 - n ^ 2 + n * n)]
   apply dvd_add hp1
-  exact (Int.coe_nat_dvd_left.mpr hpn).mul_right n
+  exact (Int.natCast_dvd.mpr hpn).mul_right n
 
 private theorem coprime_sq_sub_mul_of_odd_even {m n : ℤ} (h : Int.gcd m n = 1) (hm : m % 2 = 1)
     (hn : n % 2 = 0) : Int.gcd (m ^ 2 - n ^ 2) (2 * m * n) = 1 := by
@@ -428,7 +428,7 @@ private theorem coprime_sq_sub_sq_sum_of_odd_odd {m n : ℤ} (h : Int.gcd m n =
   obtain ⟨p, hp, hp1, hp2⟩ := Nat.Prime.not_coprime_iff_dvd.mp h4
   apply hp.not_dvd_one
   rw [← h]
-  rw [← Int.coe_nat_dvd_left] at hp1 hp2
+  rw [← Int.natCast_dvd] at hp1 hp2
   apply Nat.dvd_gcd
   · apply Int.Prime.dvd_natAbs_of_coe_dvd_sq hp
     convert dvd_add hp1 hp2

e8638a0f

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11813)

08686b25

Diff

@@ -283,7 +283,7 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
     ⟨⟨2 * x / (1 + x ^ 2), (1 - x ^ 2) / (1 + x ^ 2)⟩, by
       field_simp [hk x, div_pow]
       ring, by
-      simp only [Ne.def, div_eq_iff (hk x), neg_mul, one_mul, neg_add, sub_eq_add_neg, add_left_inj]
+      simp only [Ne, div_eq_iff (hk x), neg_mul, one_mul, neg_add, sub_eq_add_neg, add_left_inj]
       simpa only [eq_neg_iff_add_eq_zero, one_pow] using hk 1⟩
   invFun p := (p : K × K).1 / ((p : K × K).2 + 1)
   left_inv x := by

e8638a0f

chore: Rename mul-div cancellation lemmas (#11530)

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

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

4ea4a86a

Diff

@@ -291,7 +291,7 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
     have h3 : (2 : K) ≠ 0 := by
       convert hk 1
       rw [one_pow 2, h2]
-    field_simp [hk x, h2, add_assoc, add_comm, add_sub_cancel'_right, mul_comm]
+    field_simp [hk x, h2, add_assoc, add_comm, add_sub_cancel, mul_comm]
   right_inv := fun ⟨⟨x, y⟩, hxy, hy⟩ => by
     change x ^ 2 + y ^ 2 = 1 at hxy
     have h2 : y + 1 ≠ 0 := mt eq_neg_of_add_eq_zero_left hy

e8638a0f

chore: scope open Classical (#11199)

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

c747be0a

Diff

@@ -41,7 +41,7 @@ theorem Int.sq_ne_two_mod_four (z : ℤ) : z * z % 4 ≠ 2 := by
 
 noncomputable section
 
-open Classical
+open scoped Classical
 
 /-- Three integers `x`, `y`, and `z` form a Pythagorean triple if `x * x + y * y = z * z`. -/
 def PythagoreanTriple (x y z : ℤ) : Prop :=

e8638a0f

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -473,7 +473,7 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
     exact h0
   have hw1 : w ≠ -1 := by
     contrapose! hvz with hw1
-    -- porting note: `contrapose` unfolds local names, refold them
+    -- Porting note: `contrapose` unfolds local names, refold them
     replace hw1 : w = -1 := hw1; show v = 0
     rw [hw1, neg_sq, one_pow, add_left_eq_self] at hq
     exact pow_eq_zero hq
@@ -604,7 +604,7 @@ theorem coprime_classification :
         (x = m ^ 2 - n ^ 2 ∧ y = 2 * m * n ∨ x = 2 * m * n ∧ y = m ^ 2 - n ^ 2) ∧
           (z = m ^ 2 + n ^ 2 ∨ z = -(m ^ 2 + n ^ 2)) ∧
             Int.gcd m n = 1 ∧ (m % 2 = 0 ∧ n % 2 = 1 ∨ m % 2 = 1 ∧ n % 2 = 0) := by
-  clear h -- porting note: don't want this variable, but can't use `include` / `omit`
+  clear h -- Porting note: don't want this variable, but can't use `include` / `omit`
   constructor
   · intro h
     obtain ⟨m, n, H⟩ := h.left.isPrimitiveClassified_of_coprime h.right

e8638a0f

chore: more backporting of simp changes from #10995 (#11001)

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

d9589c14

Diff

@@ -466,10 +466,10 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
   let v := (x : ℚ) / z
   let w := (y : ℚ) / z
   have hq : v ^ 2 + w ^ 2 = 1 := by
-    field_simp [sq]
+    field_simp [v, w, sq]
     norm_cast
   have hvz : v ≠ 0 := by
-    field_simp
+    field_simp [v]
     exact h0
   have hw1 : w ≠ -1 := by
     contrapose! hvz with hw1

e8638a0f

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

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>

a13e8040

Diff

@@ -446,8 +446,7 @@ theorem isPrimitiveClassified_aux (hc : x.gcd y = 1) (hzpos : 0 < z) {m n : ℤ}
     (hw2 : (y : ℚ) / z = ((m : ℚ) ^ 2 - (n : ℚ) ^ 2) / ((m : ℚ) ^ 2 + (n : ℚ) ^ 2))
     (H : Int.gcd (m ^ 2 - n ^ 2) (m ^ 2 + n ^ 2) = 1) (co : Int.gcd m n = 1)
     (pp : m % 2 = 0 ∧ n % 2 = 1 ∨ m % 2 = 1 ∧ n % 2 = 0) : h.IsPrimitiveClassified := by
-  have hz : z ≠ 0
-  apply ne_of_gt hzpos
+  have hz : z ≠ 0 := ne_of_gt hzpos
   have h2 : y = m ^ 2 - n ^ 2 ∧ z = m ^ 2 + n ^ 2 := by
     apply Rat.div_int_inj hzpos hm2n2 (h.coprime_of_coprime hc) H
     rw [hw2]

e8638a0f

chore: bump Std to leanprover/std4#541 (#9828)

Notable changes: lemmas were added in https://github.com/leanprover/std4/pull/538 about gcd and lcm, that now have implicit arguments. Mostly this is a positive change in Mathlib, we can just delete the arguments. The one to consider in review is in ModEq.

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

b71c5f26

Diff

@@ -219,8 +219,8 @@ theorem isClassified_of_normalize_isPrimitiveClassified (hc : h.normalize.IsPrim
   convert h.normalize.mul_isClassified (Int.gcd x y)
         (isClassified_of_isPrimitiveClassified h.normalize hc) <;>
     rw [Int.mul_ediv_cancel']
-  · exact Int.gcd_dvd_left x y
-  · exact Int.gcd_dvd_right x y
+  · exact Int.gcd_dvd_left
+  · exact Int.gcd_dvd_right
   · exact h.gcd_dvd
 #align pythagorean_triple.is_classified_of_normalize_is_primitive_classified PythagoreanTriple.isClassified_of_normalize_isPrimitiveClassified

e8638a0f

fix: shake the import tree (#9749)

cherry-picked from #9347

Co-Authored-By: @digama0

1d3b4790

Diff

@@ -9,6 +9,7 @@ import Mathlib.Tactic.Ring
 import Mathlib.Tactic.FieldSimp
 import Mathlib.Data.Int.NatPrime
 import Mathlib.Data.ZMod.Basic
+import Mathlib.Algebra.GroupPower.Order
 
 #align_import number_theory.pythagorean_triples from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"

e8638a0f

chore: remove uses of cases' (#9171)

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

3fca282c

Diff

@@ -638,7 +638,7 @@ theorem coprime_classification' {x y z : ℤ} (h : PythagoreanTriple x y z)
             Int.gcd m n = 1 ∧ (m % 2 = 0 ∧ n % 2 = 1 ∨ m % 2 = 1 ∧ n % 2 = 0) ∧ 0 ≤ m := by
   obtain ⟨m, n, ht1, ht2, ht3, ht4⟩ :=
     PythagoreanTriple.coprime_classification.mp (And.intro h h_coprime)
-  cases' le_or_lt 0 m with hm hm
+  rcases le_or_lt 0 m with hm | hm
   · use m, n
     cases' ht1 with h_odd h_even
     · apply And.intro h_odd.1

e8638a0f

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

PR contents

This is the supremum of

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

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

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

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

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

We can get rid of all the

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

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

leanprover/lean4#2722

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

leanprover/lean4#2783

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

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

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

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

40b64f79

Diff

@@ -29,7 +29,7 @@ the bulk of the proof below.
 
 theorem sq_ne_two_fin_zmod_four (z : ZMod 4) : z * z ≠ 2 := by
   change Fin 4 at z
-  fin_cases z <;> norm_num [Fin.ext_iff]
+  fin_cases z <;> decide
 #align sq_ne_two_fin_zmod_four sq_ne_two_fin_zmod_four
 
 theorem Int.sq_ne_two_mod_four (z : ℤ) : z * z % 4 ≠ 2 := by
@@ -155,7 +155,8 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
     rw [show z * z = 4 * (x0 * x0 + x0 + y0 * y0 + y0) + 2 by
         rw [← h.eq]
         ring]
-    norm_num [Int.add_emod]
+    simp only [Int.add_emod, Int.mul_emod_right, zero_add]
+    decide
 #align pythagorean_triple.even_odd_of_coprime PythagoreanTriple.even_odd_of_coprime
 
 theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z := by
@@ -243,10 +244,10 @@ theorem isPrimitiveClassified_of_coprime_of_zero_left (hc : Int.gcd x y = 1) (hx
   cases' Int.natAbs_eq y with hy hy
   · use 1, 0
     rw [hy, hc, Int.gcd_zero_right]
-    norm_num
+    decide
   · use 0, 1
     rw [hy, hc, Int.gcd_zero_left]
-    norm_num
+    decide
 #align pythagorean_triple.is_primitive_classified_of_coprime_of_zero_left PythagoreanTriple.isPrimitiveClassified_of_coprime_of_zero_left
 
 theorem coprime_of_coprime (hc : Int.gcd x y = 1) : Int.gcd y z = 1 := by
@@ -339,7 +340,9 @@ private theorem coprime_sq_sub_sq_add_of_even_odd {m n : ℤ} (h : Int.gcd m n =
   have hnc : p = 2 ∨ p ∣ Int.natAbs n := prime_two_or_dvd_of_dvd_two_mul_pow_self_two hp h2n
   by_cases h2 : p = 2
   -- Porting note: norm_num is not enough to close h3
-  · have h3 : (m ^ 2 + n ^ 2) % 2 = 1 := by field_simp [sq, Int.add_emod, Int.mul_emod, hm, hn]
+  · have h3 : (m ^ 2 + n ^ 2) % 2 = 1 := by
+      simp only [sq, Int.add_emod, Int.mul_emod, hm, hn, dvd_refl, Int.emod_emod_of_dvd]
+      decide
     have h4 : (m ^ 2 + n ^ 2) % 2 = 0 := by
       apply Int.emod_eq_zero_of_dvd
       rwa [h2] at hp2
@@ -372,7 +375,9 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
       rw [hp2']
       apply mt Int.emod_eq_zero_of_dvd
       -- Porting note: norm_num is not enough to close this
-      field_simp [sq, Int.sub_emod, Int.mul_emod, hm, hn]
+      simp only [sq, Nat.cast_ofNat, Int.sub_emod, Int.mul_emod, hm, hn,
+        mul_zero, EuclideanDomain.zero_mod, mul_one, zero_sub]
+      decide
     apply mt (Int.dvd_gcd (Int.coe_nat_dvd_left.mpr hpm)) hnp
     apply or_self_iff.mp
     apply Int.Prime.dvd_mul' hp
@@ -528,7 +533,7 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
       Int.dvd_gcd (Int.dvd_of_emod_eq_zero hn2) (Int.dvd_of_emod_eq_zero hm2)
     rw [hnmcp] at h1
     revert h1
-    norm_num
+    decide
   · -- m even, n odd
     apply h.isPrimitiveClassified_aux hc hzpos hm2n2 hv2 hw2 _ hmncp
     · apply Or.intro_left

e8638a0f

chore: bump Std to Std#340 (#8104)

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

92e16069

Diff

@@ -374,13 +374,13 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
       -- Porting note: norm_num is not enough to close this
       field_simp [sq, Int.sub_emod, Int.mul_emod, hm, hn]
     apply mt (Int.dvd_gcd (Int.coe_nat_dvd_left.mpr hpm)) hnp
-    apply (or_self_iff _).mp
+    apply or_self_iff.mp
     apply Int.Prime.dvd_mul' hp
     rw [(by ring : n * n = -(m ^ 2 - n ^ 2) + m * m)]
     exact hp1.neg_right.add ((Int.coe_nat_dvd_left.2 hpm).mul_right _)
   rw [Int.gcd_comm] at hnp
   apply mt (Int.dvd_gcd (Int.coe_nat_dvd_left.mpr hpn)) hnp
-  apply (or_self_iff _).mp
+  apply or_self_iff.mp
   apply Int.Prime.dvd_mul' hp
   rw [(by ring : m * m = m ^ 2 - n ^ 2 + n * n)]
   apply dvd_add hp1

e8638a0f

chore: bump toolchain to v4.3.0-rc1 (#8051)

This incorporates changes from

#7845
#7847
#7853
#7872 (was never actually made to work, but the diffs in nightly-testing are unexciting: we need to fully qualify a few names)

They can all be closed when this is merged.

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

1ff3bf34

Diff

@@ -485,6 +485,11 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
   let m := (q.den : ℤ)
   let n := q.num
   have hm0 : m ≠ 0 := by
+    -- Added to adapt to leanprover/lean4#2734.
+    -- Without `unfold_let`, `norm_cast` can't see the coercion.
+    -- One might try `zeta := true` in `Tactic.NormCast.derive`,
+    -- but that seems to break many other things.
+    unfold_let m
     norm_cast
     apply Rat.den_nz q
   have hq2 : q = n / m := (Rat.num_div_den q).symm

e8638a0f

feat: fix norm num with arguments (#6600)

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

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

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

49a849ef

Diff

@@ -29,7 +29,7 @@ the bulk of the proof below.
 
 theorem sq_ne_two_fin_zmod_four (z : ZMod 4) : z * z ≠ 2 := by
   change Fin 4 at z
-  fin_cases z <;> norm_num [Fin.ext_iff, Fin.val_bit0, Fin.val_bit1]
+  fin_cases z <;> norm_num [Fin.ext_iff]
 #align sq_ne_two_fin_zmod_four sq_ne_two_fin_zmod_four
 
 theorem Int.sq_ne_two_mod_four (z : ℤ) : z * z % 4 ≠ 2 := by
@@ -155,7 +155,7 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
     rw [show z * z = 4 * (x0 * x0 + x0 + y0 * y0 + y0) + 2 by
         rw [← h.eq]
         ring]
-    field_simp [Int.add_emod] -- Porting note: norm_num is not enough to close this
+    norm_num [Int.add_emod]
 #align pythagorean_triple.even_odd_of_coprime PythagoreanTriple.even_odd_of_coprime
 
 theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z := by

e8638a0f

field_simp: Use positivity as a discharger (#6312)

The main reasons is that having h : 0 < denom in the context should suffice for field_simp to do its job, without the need to manually pass h.ne or similar.

Quite a few have := … ≠ 0 could be dropped, and some field_simp calls no longer need explicit arguments; this is promising.

This does break some proofs where field_simp was not used as a closing tactic, and it now shuffles terms around a bit different. These were fixed. Using field_simp in the middle of a proof seems rather fragile anyways.

As a drive-by contribution, positivity now knows about π > 0.

fixes: #4835

Co-authored-by: Matthew Ballard <matt@mrb.email>

6b391efa

Diff

@@ -460,13 +460,11 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
   · exact h.isPrimitiveClassified_of_coprime_of_zero_left hc h0
   let v := (x : ℚ) / z
   let w := (y : ℚ) / z
-  have hz : z ≠ 0
-  apply ne_of_gt hzpos
   have hq : v ^ 2 + w ^ 2 = 1 := by
-    field_simp [hz, sq]
+    field_simp [sq]
     norm_cast
   have hvz : v ≠ 0 := by
-    field_simp [hz]
+    field_simp
     exact h0
   have hw1 : w ≠ -1 := by
     contrapose! hvz with hw1

e8638a0f

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

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

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

277dea95

Diff

@@ -56,7 +56,7 @@ theorem pythagoreanTriple_comm {x y z : ℤ} : PythagoreanTriple x y z ↔ Pytha
 
 /-- The zeroth Pythagorean triple is all zeros. -/
 theorem PythagoreanTriple.zero : PythagoreanTriple 0 0 0 := by
-  simp only [PythagoreanTriple, MulZeroClass.zero_mul, zero_add]
+  simp only [PythagoreanTriple, zero_mul, zero_add]
 #align pythagorean_triple.zero PythagoreanTriple.zero
 
 namespace PythagoreanTriple
@@ -167,7 +167,7 @@ theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z := by
       apply Int.natAbs_eq_zero.mp
       apply Nat.eq_zero_of_gcd_eq_zero_right h0
     have hz : z = 0 := by
-      simpa only [PythagoreanTriple, hx, hy, add_zero, zero_eq_mul, MulZeroClass.mul_zero,
+      simpa only [PythagoreanTriple, hx, hy, add_zero, zero_eq_mul, mul_zero,
         or_self_iff] using h
     simp only [hz, dvd_zero]
   obtain ⟨k, x0, y0, _, h2, rfl, rfl⟩ :
@@ -188,7 +188,7 @@ theorem normalize : PythagoreanTriple (x / Int.gcd x y) (y / Int.gcd x y) (z / I
       apply Int.natAbs_eq_zero.mp
       apply Nat.eq_zero_of_gcd_eq_zero_right h0
     have hz : z = 0 := by
-      simpa only [PythagoreanTriple, hx, hy, add_zero, zero_eq_mul, MulZeroClass.mul_zero,
+      simpa only [PythagoreanTriple, hx, hy, add_zero, zero_eq_mul, mul_zero,
         or_self_iff] using h
     simp only [hx, hy, hz, Int.zero_div]
     exact zero
@@ -550,7 +550,7 @@ theorem isPrimitiveClassified_of_coprime_of_odd_of_pos (hc : Int.gcd x y = 1) (h
         rw [Int.ediv_mul_cancel h1.1, Int.ediv_mul_cancel h1.2.1, hw2]
         norm_cast
       · apply (mul_lt_mul_right (by norm_num : 0 < (2 : ℤ))).mp
-        rw [Int.ediv_mul_cancel h1.1, MulZeroClass.zero_mul]
+        rw [Int.ediv_mul_cancel h1.1, zero_mul]
         exact hm2n2
     rw [h2.1, h1.2.2.1] at hyo
     revert hyo

e8638a0f

fix(NumberTheory/PythagoreanTriples): clear unnecessary hypothesis of PythagoreanTriple.classification (#6594)

The rcases tactic causes this theorem to pull in an unused assumption, as per this Zulip thread.

Before this PR, PythagoreanTriple.classification includes an unnecessary h:

theorem PythagoreanTriple.classification {x y z : ℤ} (h : PythagoreanTriple x y z) :
  PythagoreanTriple x y z ↔
    ∃ k m n,
      (x = k * (m ^ 2 - n ^ 2) ∧ y = k * (2 * m * n) ∨ x = k * (2 * m * n) ∧ y = k * (m ^ 2 - n ^ 2)) ∧
        (z = k * (m ^ 2 + n ^ 2) ∨ z = -k * (m ^ 2 + n ^ 2))

ab751e1e

Diff

@@ -679,6 +679,7 @@ theorem classification :
         (x = k * (m ^ 2 - n ^ 2) ∧ y = k * (2 * m * n) ∨
             x = k * (2 * m * n) ∧ y = k * (m ^ 2 - n ^ 2)) ∧
           (z = k * (m ^ 2 + n ^ 2) ∨ z = -k * (m ^ 2 + n ^ 2)) := by
+  clear h
   constructor
   · intro h
     obtain ⟨k, m, n, H⟩ := h.classified

e8638a0f

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -271,7 +271,7 @@ For the classification of Pythagorean triples, we will use a parametrization of
 -/
 
 
-variable {K : Type _} [Field K]
+variable {K : Type*} [Field K]
 
 /-- A parameterization of the unit circle that is useful for classifying Pythagorean triples.
  (To be applied in the case where `K = ℚ`.) -/

e8638a0f

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Paul van Wamelen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul van Wamelen
-
-! This file was ported from Lean 3 source module number_theory.pythagorean_triples
-! 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.Field.Basic
 import Mathlib.RingTheory.Int.Basic
@@ -15,6 +10,8 @@ import Mathlib.Tactic.FieldSimp
 import Mathlib.Data.Int.NatPrime
 import Mathlib.Data.ZMod.Basic
 
+#align_import number_theory.pythagorean_triples from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"
+
 /-!
 # Pythagorean Triples

e8638a0f

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

Changes are of the form

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

2a870323

Diff

@@ -202,7 +202,7 @@ theorem normalize : PythagoreanTriple (x / Int.gcd x y) (y / Int.gcd x y) (z / I
   have hk : (k : ℤ) ≠ 0 := by
     norm_cast
     rwa [pos_iff_ne_zero] at k0
-  rw [Int.gcd_mul_right, h2, Int.natAbs_ofNat, one_mul] at h⊢
+  rw [Int.gcd_mul_right, h2, Int.natAbs_ofNat, one_mul] at h ⊢
   rw [mul_comm x0, mul_comm y0, mul_iff k hk] at h
   rwa [Int.mul_ediv_cancel _ hk, Int.mul_ediv_cancel _ hk, Int.mul_ediv_cancel_left _ hk]
 #align pythagorean_triple.normalize PythagoreanTriple.normalize

e8638a0f

chore: formatting issues (#4947)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

5068808d

Diff

@@ -174,7 +174,7 @@ theorem gcd_dvd : (Int.gcd x y : ℤ) ∣ z := by
         or_self_iff] using h
     simp only [hz, dvd_zero]
   obtain ⟨k, x0, y0, _, h2, rfl, rfl⟩ :
-    ∃ (k : ℕ)(x0 y0 : _), 0 < k ∧ Int.gcd x0 y0 = 1 ∧ x = x0 * k ∧ y = y0 * k :=
+    ∃ (k : ℕ) (x0 y0 : _), 0 < k ∧ Int.gcd x0 y0 = 1 ∧ x = x0 * k ∧ y = y0 * k :=
     Int.exists_gcd_one' (Nat.pos_of_ne_zero h0)
   rw [Int.gcd_mul_right, h2, Int.natAbs_ofNat, one_mul]
   rw [← Int.pow_dvd_pow_iff zero_lt_two, sq z, ← h.eq]
@@ -197,7 +197,7 @@ theorem normalize : PythagoreanTriple (x / Int.gcd x y) (y / Int.gcd x y) (z / I
     exact zero
   rcases h.gcd_dvd with ⟨z0, rfl⟩
   obtain ⟨k, x0, y0, k0, h2, rfl, rfl⟩ :
-    ∃ (k : ℕ)(x0 y0 : _), 0 < k ∧ Int.gcd x0 y0 = 1 ∧ x = x0 * k ∧ y = y0 * k :=
+    ∃ (k : ℕ) (x0 y0 : _), 0 < k ∧ Int.gcd x0 y0 = 1 ∧ x = x0 * k ∧ y = y0 * k :=
     Int.exists_gcd_one' (Nat.pos_of_ne_zero h0)
   have hk : (k : ℤ) ≠ 0 := by
     norm_cast

e8638a0f

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -106,7 +106,7 @@ def IsClassified (_ : PythagoreanTriple x y z) :=
       Int.gcd m n = 1
 #align pythagorean_triple.is_classified PythagoreanTriple.IsClassified
 
-/-- A primitive pythogorean triple `x, y, z` is a pythagorean triple with `x` and `y` coprime.
+/-- A primitive Pythagorean triple `x, y, z` is a Pythagorean triple with `x` and `y` coprime.
  Such a triple is “primitively classified” if there exist coprime integers `m, n` such that either
  * `x = m ^ 2 - n ^ 2` and `y = 2 * m * n`, or
  * `x = 2 * m * n` and `y = m ^ 2 - n ^ 2`.

e8638a0f

chore: fix many typos (#4535)

Run codespell Mathlib and keep some suggestions.

92f5c622

Diff

@@ -50,7 +50,7 @@ def PythagoreanTriple (x y z : ℤ) : Prop :=
   x * x + y * y = z * z
 #align pythagorean_triple PythagoreanTriple
 
-/-- Pythagorean triples are interchangable, i.e `x * x + y * y = y * y + x * x = z * z`.
+/-- Pythagorean triples are interchangeable, i.e `x * x + y * y = y * y + x * x = z * z`.
 This comes from additive commutativity. -/
 theorem pythagoreanTriple_comm {x y z : ℤ} : PythagoreanTriple x y z ↔ PythagoreanTriple y x z := by
   delta PythagoreanTriple

e8638a0f

chore: fix #align lines (#3640)

This PR fixes two things:

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

2b42dc7c

Diff

@@ -81,7 +81,6 @@ theorem mul (k : ℤ) : PythagoreanTriple (k * x) (k * y) (k * z) :=
     k * x * (k * x) + k * y * (k * y) = k ^ 2 * (x * x + y * y) := by ring
     _ = k ^ 2 * (z * z) := by rw [h.eq]
     _ = k * z * (k * z) := by ring
-
 #align pythagorean_triple.mul PythagoreanTriple.mul
 
 /-- `(k*x, k*y, k*z)` is a Pythagorean triple if and only if

e8638a0f

feat: Dot notation aliases (#3303)

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

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

4fa401fa

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul van Wamelen
 
 ! This file was ported from Lean 3 source module number_theory.pythagorean_triples
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -138,9 +138,9 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
   -- x even, y even
   · exfalso
     apply Nat.not_coprime_of_dvd_of_dvd (by decide : 1 < 2) _ _ hc
-    · apply Int.dvd_natAbs_of_ofNat_dvd
+    · apply Int.coe_nat_dvd_left.1
       apply Int.dvd_of_emod_eq_zero hx
-    · apply Int.dvd_natAbs_of_ofNat_dvd
+    · apply Int.coe_nat_dvd_left.1
       apply Int.dvd_of_emod_eq_zero hy
   -- x even, y odd
   · left
@@ -381,8 +381,7 @@ private theorem coprime_sq_sub_mul_of_even_odd {m n : ℤ} (h : Int.gcd m n = 1)
     apply (or_self_iff _).mp
     apply Int.Prime.dvd_mul' hp
     rw [(by ring : n * n = -(m ^ 2 - n ^ 2) + m * m)]
-    apply dvd_add (dvd_neg_of_dvd hp1)
-    exact dvd_mul_of_dvd_left (Int.coe_nat_dvd_left.mpr hpm) m
+    exact hp1.neg_right.add ((Int.coe_nat_dvd_left.2 hpm).mul_right _)
   rw [Int.gcd_comm] at hnp
   apply mt (Int.dvd_gcd (Int.coe_nat_dvd_left.mpr hpn)) hnp
   apply (or_self_iff _).mp

70fd9563

chore: tidy various files (#3110)

0bcbc985

Diff

@@ -30,15 +30,15 @@ the bulk of the proof below.
 -/
 
 
-theorem sq_ne_two_fin_zMod_four (z : ZMod 4) : z * z ≠ 2 := by
+theorem sq_ne_two_fin_zmod_four (z : ZMod 4) : z * z ≠ 2 := by
   change Fin 4 at z
   fin_cases z <;> norm_num [Fin.ext_iff, Fin.val_bit0, Fin.val_bit1]
-#align sq_ne_two_fin_zmod_four sq_ne_two_fin_zMod_four
+#align sq_ne_two_fin_zmod_four sq_ne_two_fin_zmod_four
 
 theorem Int.sq_ne_two_mod_four (z : ℤ) : z * z % 4 ≠ 2 := by
   suffices ¬z * z % (4 : ℕ) = 2 % (4 : ℕ) by exact this
   rw [← ZMod.int_cast_eq_int_cast_iff']
-  simpa using sq_ne_two_fin_zMod_four _
+  simpa using sq_ne_two_fin_zmod_four _
 #align int.sq_ne_two_mod_four Int.sq_ne_two_mod_four
 
 noncomputable section
@@ -135,21 +135,21 @@ theorem even_odd_of_coprime (hc : Int.gcd x y = 1) :
     x % 2 = 0 ∧ y % 2 = 1 ∨ x % 2 = 1 ∧ y % 2 = 0 := by
   cases' Int.emod_two_eq_zero_or_one x with hx hx <;>
     cases' Int.emod_two_eq_zero_or_one y with hy hy
-  · -- x even, y even
-    exfalso
+  -- x even, y even
+  · exfalso
     apply Nat.not_coprime_of_dvd_of_dvd (by decide : 1 < 2) _ _ hc
     · apply Int.dvd_natAbs_of_ofNat_dvd
       apply Int.dvd_of_emod_eq_zero hx
     · apply Int.dvd_natAbs_of_ofNat_dvd
       apply Int.dvd_of_emod_eq_zero hy
+  -- x even, y odd
   · left
     exact ⟨hx, hy⟩
-  -- x even, y odd
+  -- x odd, y even
   · right
     exact ⟨hx, hy⟩
-  -- x odd, y even
-  · -- x odd, y odd
-    exfalso
+  -- x odd, y odd
+  · exfalso
     obtain ⟨x0, y0, rfl, rfl⟩ : ∃ x0 y0, x = x0 * 2 + 1 ∧ y = y0 * 2 + 1 := by
       cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hx) with x0 hx2
       cases' exists_eq_mul_left_of_dvd (Int.dvd_sub_of_emod_eq hy) with y0 hy2
@@ -314,17 +314,17 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
 #align circle_equiv_gen circleEquivGen
 
 @[simp]
-theorem circle_equiv_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
+theorem circleEquivGen_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) (x : K) :
     (circleEquivGen hk x : K × K) = ⟨2 * x / (1 + x ^ 2), (1 - x ^ 2) / (1 + x ^ 2)⟩ :=
   rfl
-#align circle_equiv_apply circle_equiv_apply
+#align circle_equiv_apply circleEquivGen_apply
 
 @[simp]
-theorem circle_equiv_symm_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0)
+theorem circleEquivGen_symm_apply (hk : ∀ x : K, 1 + x ^ 2 ≠ 0)
     (v : { p : K × K // p.1 ^ 2 + p.2 ^ 2 = 1 ∧ p.2 ≠ -1 }) :
     (circleEquivGen hk).symm v = (v : K × K).1 / ((v : K × K).2 + 1) :=
   rfl
-#align circle_equiv_symm_apply circle_equiv_symm_apply
+#align circle_equiv_symm_apply circleEquivGen_symm_apply
 
 end circleEquivGen

70fd9563

feat: port NumberTheory.PythagoreanTriples (#3022)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

ab3732ff

`number_theory.pythagorean_triples` ⟷ `Mathlib.NumberTheory.PythagoreanTriples`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 8 + 499

number_theory.pythagorean_triples ⟷ Mathlib.NumberTheory.PythagoreanTriples

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 8 + 499

`number_theory.pythagorean_triples` ⟷ `Mathlib.NumberTheory.PythagoreanTriples`