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

@@ -215,7 +215,7 @@ theorem cos_eq_iff_quadratic {z w : ℂ} :
 #align complex.cos_eq_iff_quadratic Complex.cos_eq_iff_quadratic
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (w «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (w «expr ≠ » 0) -/
 #print Complex.cos_surjective /-
 theorem cos_surjective : Function.Surjective cos :=
   by
@@ -229,7 +229,7 @@ theorem cos_surjective : Function.Surjective cos :=
     rintro rfl
     simpa only [zero_add, one_ne_zero, MulZeroClass.mul_zero] using hw
   refine' ⟨log w / I, cos_eq_iff_quadratic.2 _⟩
-  rw [div_mul_cancel _ I_ne_zero, exp_log w₀]
+  rw [div_mul_cancel₀ _ I_ne_zero, exp_log w₀]
   convert hw
   ring
 #align complex.cos_surjective Complex.cos_surjective

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

@@ -81,7 +81,7 @@ theorem sin_ne_zero_iff {θ : ℂ} : sin θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π
 theorem tan_eq_zero_iff {θ : ℂ} : tan θ = 0 ↔ ∃ k : ℤ, θ = k * π / 2 :=
   by
   have h := (sin_two_mul θ).symm
-  rw [mul_assoc] at h 
+  rw [mul_assoc] at h
   rw [tan, div_eq_zero_iff, ← mul_eq_zero, ← MulZeroClass.zero_mul (1 / 2 : ℂ), mul_one_div,
     CancelDenoms.cancel_factors_eq_div h two_ne_zero, mul_comm]
   simpa only [zero_div, MulZeroClass.zero_mul, Ne.def, not_false_iff, field_simps] using
@@ -143,7 +143,7 @@ theorem tan_add {x y : ℂ}
       div_self (cos_ne_zero_iff.mpr h2)]
   · obtain ⟨t, hx, hy, hxy⟩ := tan_int_mul_pi_div_two, t (2 * k + 1), t (2 * l + 1),
       t (2 * k + 1 + (2 * l + 1))
-    simp only [Int.cast_add, Int.cast_bit0, Int.cast_mul, Int.cast_one, hx, hy] at hx hy hxy 
+    simp only [Int.cast_add, Int.cast_bit0, Int.cast_mul, Int.cast_one, hx, hy] at hx hy hxy
     rw [hx, hy, add_zero, zero_div, mul_div_assoc, mul_div_assoc, ←
       add_mul (2 * (k : ℂ) + 1) (2 * l + 1) (π / 2), ← mul_div_assoc, hxy]
 #align complex.tan_add Complex.tan_add
@@ -162,7 +162,7 @@ theorem tan_two_mul {z : ℂ} : tan (2 * z) = 2 * tan z / (1 - tan z ^ 2) :=
   by
   by_cases h : ∀ k : ℤ, z ≠ (2 * k + 1) * π / 2
   · rw [two_mul, two_mul, sq, tan_add (Or.inl ⟨h, h⟩)]
-  · rw [not_forall_not] at h 
+  · rw [not_forall_not] at h
     rw [two_mul, two_mul, sq, tan_add (Or.inr ⟨h, h⟩)]
 #align complex.tan_two_mul Complex.tan_two_mul
 -/

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

@@ -34,10 +34,13 @@ open scoped Real
 #print Complex.cos_eq_zero_iff /-
 theorem cos_eq_zero_iff {θ : ℂ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1) * π / 2 :=
   by
-  have h : (exp (θ * I) + exp (-θ * I)) / 2 = 0 ↔ exp (2 * θ * I) = -1 :=
+  have h :
+    (NormedSpace.exp (θ * I) + NormedSpace.exp (-θ * I)) / 2 = 0 ↔
+      NormedSpace.exp (2 * θ * I) = -1 :=
     by
-    rw [@div_eq_iff _ _ (exp (θ * I) + exp (-θ * I)) 2 0 two_ne_zero, MulZeroClass.zero_mul,
-      add_eq_zero_iff_eq_neg, neg_eq_neg_one_mul, ← div_eq_iff (exp_ne_zero _), ← exp_sub]
+    rw [@div_eq_iff _ _ (NormedSpace.exp (θ * I) + NormedSpace.exp (-θ * I)) 2 0 two_ne_zero,
+      MulZeroClass.zero_mul, add_eq_zero_iff_eq_neg, neg_eq_neg_one_mul, ←
+      div_eq_iff (exp_ne_zero _), ← exp_sub]
     field_simp only; congr 3; ring
   rw [cos, h, ← exp_pi_mul_I, exp_eq_exp_iff_exists_int, mul_right_comm]
   refine' exists_congr fun x => _
@@ -206,7 +209,7 @@ theorem cos_eq_iff_quadratic {z w : ℂ} :
     cos z = w ↔ exp (z * I) ^ 2 - 2 * w * exp (z * I) + 1 = 0 :=
   by
   rw [← sub_eq_zero]
-  field_simp [cos, exp_neg, exp_ne_zero]
+  field_simp [cos, NormedSpace.exp_neg, exp_ne_zero]
   refine' Eq.congr _ rfl
   ring
 #align complex.cos_eq_iff_quadratic Complex.cos_eq_iff_quadratic

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

@@ -3,8 +3,8 @@ Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
 -/
-import Mathbin.Algebra.QuadraticDiscriminant
-import Mathbin.Analysis.Convex.SpecificFunctions.Deriv
+import Algebra.QuadraticDiscriminant
+import Analysis.Convex.SpecificFunctions.Deriv
 
 #align_import analysis.special_functions.trigonometric.complex from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
 
@@ -212,7 +212,7 @@ theorem cos_eq_iff_quadratic {z w : ℂ} :
 #align complex.cos_eq_iff_quadratic Complex.cos_eq_iff_quadratic
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (w «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (w «expr ≠ » 0) -/
 #print Complex.cos_surjective /-
 theorem cos_surjective : Function.Surjective cos :=
   by

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

@@ -110,7 +110,7 @@ theorem cos_eq_cos_iff {x y : ℂ} : cos x = cos y ↔ ∃ k : ℤ, y = 2 * k *
       apply or_congr <;>
         field_simp [sin_eq_zero_iff, (by norm_num : -(2 : ℂ) ≠ 0), eq_sub_iff_add_eq',
           sub_eq_iff_eq_add, mul_comm (2 : ℂ), mul_right_comm _ (2 : ℂ)]
-      constructor <;> · rintro ⟨k, rfl⟩; use -k; simp
+      constructor <;> · rintro ⟨k, rfl⟩; use-k; simp
     _ ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = 2 * k * π - x := exists_or.symm
 #align complex.cos_eq_cos_iff Complex.cos_eq_cos_iff
 -/

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

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-
-! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.complex
-! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.QuadraticDiscriminant
 import Mathbin.Analysis.Convex.SpecificFunctions.Deriv
 
+#align_import analysis.special_functions.trigonometric.complex from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
 /-!
 # Complex trigonometric functions
 
@@ -215,7 +212,7 @@ theorem cos_eq_iff_quadratic {z w : ℂ} :
 #align complex.cos_eq_iff_quadratic Complex.cos_eq_iff_quadratic
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (w «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (w «expr ≠ » 0) -/
 #print Complex.cos_surjective /-
 theorem cos_surjective : Function.Surjective cos :=
   by

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

@@ -34,6 +34,7 @@ open Set Filter
 
 open scoped Real
 
+#print Complex.cos_eq_zero_iff /-
 theorem cos_eq_zero_iff {θ : ℂ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1) * π / 2 :=
   by
   have h : (exp (θ * I) + exp (-θ * I)) / 2 = 0 ↔ exp (2 * θ * I) = -1 :=
@@ -46,11 +47,15 @@ theorem cos_eq_zero_iff {θ : ℂ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1
   refine' (iff_of_eq <| congr_arg _ _).trans (mul_right_inj' <| mul_ne_zero two_ne_zero I_ne_zero)
   field_simp; ring
 #align complex.cos_eq_zero_iff Complex.cos_eq_zero_iff
+-/
 
+#print Complex.cos_ne_zero_iff /-
 theorem cos_ne_zero_iff {θ : ℂ} : cos θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ (2 * k + 1) * π / 2 := by
   rw [← not_exists, not_iff_not, cos_eq_zero_iff]
 #align complex.cos_ne_zero_iff Complex.cos_ne_zero_iff
+-/
 
+#print Complex.sin_eq_zero_iff /-
 theorem sin_eq_zero_iff {θ : ℂ} : sin θ = 0 ↔ ∃ k : ℤ, θ = k * π :=
   by
   rw [← Complex.cos_sub_pi_div_two, cos_eq_zero_iff]
@@ -64,11 +69,15 @@ theorem sin_eq_zero_iff {θ : ℂ} : sin θ = 0 ↔ ∃ k : ℤ, θ = k * π :=
     field_simp
     ring
 #align complex.sin_eq_zero_iff Complex.sin_eq_zero_iff
+-/
 
+#print Complex.sin_ne_zero_iff /-
 theorem sin_ne_zero_iff {θ : ℂ} : sin θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π := by
   rw [← not_exists, not_iff_not, sin_eq_zero_iff]
 #align complex.sin_ne_zero_iff Complex.sin_ne_zero_iff
+-/
 
+#print Complex.tan_eq_zero_iff /-
 theorem tan_eq_zero_iff {θ : ℂ} : tan θ = 0 ↔ ∃ k : ℤ, θ = k * π / 2 :=
   by
   have h := (sin_two_mul θ).symm
@@ -78,10 +87,13 @@ theorem tan_eq_zero_iff {θ : ℂ} : tan θ = 0 ↔ ∃ k : ℤ, θ = k * π / 2
   simpa only [zero_div, MulZeroClass.zero_mul, Ne.def, not_false_iff, field_simps] using
     sin_eq_zero_iff
 #align complex.tan_eq_zero_iff Complex.tan_eq_zero_iff
+-/
 
+#print Complex.tan_ne_zero_iff /-
 theorem tan_ne_zero_iff {θ : ℂ} : tan θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π / 2 := by
   rw [← not_exists, not_iff_not, tan_eq_zero_iff]
 #align complex.tan_ne_zero_iff Complex.tan_ne_zero_iff
+-/
 
 #print Complex.tan_int_mul_pi_div_two /-
 theorem tan_int_mul_pi_div_two (n : ℤ) : tan (n * π / 2) = 0 :=
@@ -89,6 +101,7 @@ theorem tan_int_mul_pi_div_two (n : ℤ) : tan (n * π / 2) = 0 :=
 #align complex.tan_int_mul_pi_div_two Complex.tan_int_mul_pi_div_two
 -/
 
+#print Complex.cos_eq_cos_iff /-
 theorem cos_eq_cos_iff {x y : ℂ} : cos x = cos y ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = 2 * k * π - x :=
   calc
     cos x = cos y ↔ cos x - cos y = 0 := sub_eq_zero.symm
@@ -103,14 +116,18 @@ theorem cos_eq_cos_iff {x y : ℂ} : cos x = cos y ↔ ∃ k : ℤ, y = 2 * k *
       constructor <;> · rintro ⟨k, rfl⟩; use -k; simp
     _ ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = 2 * k * π - x := exists_or.symm
 #align complex.cos_eq_cos_iff Complex.cos_eq_cos_iff
+-/
 
+#print Complex.sin_eq_sin_iff /-
 theorem sin_eq_sin_iff {x y : ℂ} :
     sin x = sin y ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = (2 * k + 1) * π - x :=
   by
   simp only [← Complex.cos_sub_pi_div_two, cos_eq_cos_iff, sub_eq_iff_eq_add]
   refine' exists_congr fun k => or_congr _ _ <;> refine' Eq.congr rfl _ <;> field_simp <;> ring
 #align complex.sin_eq_sin_iff Complex.sin_eq_sin_iff
+-/
 
+#print Complex.tan_add /-
 theorem tan_add {x y : ℂ}
     (h :
       ((∀ k : ℤ, x ≠ (2 * k + 1) * π / 2) ∧ ∀ l : ℤ, y ≠ (2 * l + 1) * π / 2) ∨
@@ -130,12 +147,15 @@ theorem tan_add {x y : ℂ}
     rw [hx, hy, add_zero, zero_div, mul_div_assoc, mul_div_assoc, ←
       add_mul (2 * (k : ℂ) + 1) (2 * l + 1) (π / 2), ← mul_div_assoc, hxy]
 #align complex.tan_add Complex.tan_add
+-/
 
+#print Complex.tan_add' /-
 theorem tan_add' {x y : ℂ}
     (h : (∀ k : ℤ, x ≠ (2 * k + 1) * π / 2) ∧ ∀ l : ℤ, y ≠ (2 * l + 1) * π / 2) :
     tan (x + y) = (tan x + tan y) / (1 - tan x * tan y) :=
   tan_add (Or.inl h)
 #align complex.tan_add' Complex.tan_add'
+-/
 
 #print Complex.tan_two_mul /-
 theorem tan_two_mul {z : ℂ} : tan (2 * z) = 2 * tan z / (1 - tan z ^ 2) :=
@@ -147,6 +167,7 @@ theorem tan_two_mul {z : ℂ} : tan (2 * z) = 2 * tan z / (1 - tan z ^ 2) :=
 #align complex.tan_two_mul Complex.tan_two_mul
 -/
 
+#print Complex.tan_add_mul_I /-
 theorem tan_add_mul_I {x y : ℂ}
     (h :
       ((∀ k : ℤ, x ≠ (2 * k + 1) * π / 2) ∧ ∀ l : ℤ, y * I ≠ (2 * l + 1) * π / 2) ∨
@@ -154,7 +175,9 @@ theorem tan_add_mul_I {x y : ℂ}
     tan (x + y * I) = (tan x + tanh y * I) / (1 - tan x * tanh y * I) := by
   rw [tan_add h, tan_mul_I, mul_assoc]
 #align complex.tan_add_mul_I Complex.tan_add_mul_I
+-/
 
+#print Complex.tan_eq /-
 theorem tan_eq {z : ℂ}
     (h :
       ((∀ k : ℤ, (z.re : ℂ) ≠ (2 * k + 1) * π / 2) ∧
@@ -164,18 +187,24 @@ theorem tan_eq {z : ℂ}
     tan z = (tan z.re + tanh z.im * I) / (1 - tan z.re * tanh z.im * I) := by
   convert tan_add_mul_I h <;> exact (re_add_im z).symm
 #align complex.tan_eq Complex.tan_eq
+-/
 
 open scoped Topology
 
+#print Complex.continuousOn_tan /-
 theorem continuousOn_tan : ContinuousOn tan {x | cos x ≠ 0} :=
   continuousOn_sin.div continuousOn_cos fun x => id
 #align complex.continuous_on_tan Complex.continuousOn_tan
+-/
 
+#print Complex.continuous_tan /-
 @[continuity]
 theorem continuous_tan : Continuous fun x : {x | cos x ≠ 0} => tan x :=
   continuousOn_iff_continuous_restrict.1 continuousOn_tan
 #align complex.continuous_tan Complex.continuous_tan
+-/
 
+#print Complex.cos_eq_iff_quadratic /-
 theorem cos_eq_iff_quadratic {z w : ℂ} :
     cos z = w ↔ exp (z * I) ^ 2 - 2 * w * exp (z * I) + 1 = 0 :=
   by
@@ -184,6 +213,7 @@ theorem cos_eq_iff_quadratic {z w : ℂ} :
   refine' Eq.congr _ rfl
   ring
 #align complex.cos_eq_iff_quadratic Complex.cos_eq_iff_quadratic
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (w «expr ≠ » 0) -/
 #print Complex.cos_surjective /-
@@ -234,35 +264,48 @@ namespace Real
 
 open scoped Real
 
+#print Real.cos_eq_zero_iff /-
 theorem cos_eq_zero_iff {θ : ℝ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1) * π / 2 := by
   exact_mod_cast @Complex.cos_eq_zero_iff θ
 #align real.cos_eq_zero_iff Real.cos_eq_zero_iff
+-/
 
+#print Real.cos_ne_zero_iff /-
 theorem cos_ne_zero_iff {θ : ℝ} : cos θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ (2 * k + 1) * π / 2 := by
   rw [← not_exists, not_iff_not, cos_eq_zero_iff]
 #align real.cos_ne_zero_iff Real.cos_ne_zero_iff
+-/
 
+#print Real.cos_eq_cos_iff /-
 theorem cos_eq_cos_iff {x y : ℝ} : cos x = cos y ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = 2 * k * π - x :=
   by exact_mod_cast @Complex.cos_eq_cos_iff x y
 #align real.cos_eq_cos_iff Real.cos_eq_cos_iff
+-/
 
+#print Real.sin_eq_sin_iff /-
 theorem sin_eq_sin_iff {x y : ℝ} :
     sin x = sin y ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = (2 * k + 1) * π - x := by
   exact_mod_cast @Complex.sin_eq_sin_iff x y
 #align real.sin_eq_sin_iff Real.sin_eq_sin_iff
+-/
 
+#print Real.lt_sin_mul /-
 theorem lt_sin_mul {x : ℝ} (hx : 0 < x) (hx' : x < 1) : x < sin (π / 2 * x) := by
   simpa [mul_comm x] using
     strictConcaveOn_sin_Icc.2 ⟨le_rfl, pi_pos.le⟩ ⟨pi_div_two_pos.le, half_le_self pi_pos.le⟩
       pi_div_two_pos.ne (sub_pos.2 hx') hx
 #align real.lt_sin_mul Real.lt_sin_mul
+-/
 
+#print Real.le_sin_mul /-
 theorem le_sin_mul {x : ℝ} (hx : 0 ≤ x) (hx' : x ≤ 1) : x ≤ sin (π / 2 * x) := by
   simpa [mul_comm x] using
     strict_concave_on_sin_Icc.concave_on.2 ⟨le_rfl, pi_pos.le⟩
       ⟨pi_div_two_pos.le, half_le_self pi_pos.le⟩ (sub_nonneg.2 hx') hx
 #align real.le_sin_mul Real.le_sin_mul
+-/
 
+#print Real.mul_lt_sin /-
 theorem mul_lt_sin {x : ℝ} (hx : 0 < x) (hx' : x < π / 2) : 2 / π * x < sin x :=
   by
   rw [← inv_div]
@@ -270,7 +313,9 @@ theorem mul_lt_sin {x : ℝ} (hx : 0 < x) (hx' : x < π / 2) : 2 / π * x < sin
   · exact mul_pos (inv_pos.2 pi_div_two_pos) hx
   · rwa [← div_eq_inv_mul, div_lt_one pi_div_two_pos]
 #align real.mul_lt_sin Real.mul_lt_sin
+-/
 
+#print Real.mul_le_sin /-
 /-- In the range `[0, π / 2]`, we have a linear lower bound on `sin`. This inequality forms one half
 of Jordan's inequality, the other half is `real.sin_lt` -/
 theorem mul_le_sin {x : ℝ} (hx : 0 ≤ x) (hx' : x ≤ π / 2) : 2 / π * x ≤ sin x :=
@@ -280,6 +325,7 @@ theorem mul_le_sin {x : ℝ} (hx : 0 ≤ x) (hx' : x ≤ π / 2) : 2 / π * x 
   · exact mul_nonneg (inv_nonneg.2 pi_div_two_pos.le) hx
   · rwa [← div_eq_inv_mul, div_le_one pi_div_two_pos]
 #align real.mul_le_sin Real.mul_le_sin
+-/
 
 end Real
 

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

@@ -102,7 +102,6 @@ theorem cos_eq_cos_iff {x y : ℂ} : cos x = cos y ↔ ∃ k : ℤ, y = 2 * k *
           sub_eq_iff_eq_add, mul_comm (2 : ℂ), mul_right_comm _ (2 : ℂ)]
       constructor <;> · rintro ⟨k, rfl⟩; use -k; simp
     _ ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = 2 * k * π - x := exists_or.symm
-    
 #align complex.cos_eq_cos_iff Complex.cos_eq_cos_iff
 
 theorem sin_eq_sin_iff {x y : ℂ} :

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

@@ -186,7 +186,7 @@ theorem cos_eq_iff_quadratic {z w : ℂ} :
   ring
 #align complex.cos_eq_iff_quadratic Complex.cos_eq_iff_quadratic
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (w «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (w «expr ≠ » 0) -/
 #print Complex.cos_surjective /-
 theorem cos_surjective : Function.Surjective cos :=
   by

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
 
 ! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.complex
-! leanprover-community/mathlib commit 8f9fea08977f7e450770933ee6abb20733b47c92
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.Convex.SpecificFunctions.Deriv
 /-!
 # Complex trigonometric functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Basic facts and derivatives for the complex trigonometric functions.
 
 Several facts about the real trigonometric functions have the proofs deferred here, rather than

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

@@ -80,9 +80,11 @@ theorem tan_ne_zero_iff {θ : ℂ} : tan θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π
   rw [← not_exists, not_iff_not, tan_eq_zero_iff]
 #align complex.tan_ne_zero_iff Complex.tan_ne_zero_iff
 
+#print Complex.tan_int_mul_pi_div_two /-
 theorem tan_int_mul_pi_div_two (n : ℤ) : tan (n * π / 2) = 0 :=
   tan_eq_zero_iff.mpr (by use n)
 #align complex.tan_int_mul_pi_div_two Complex.tan_int_mul_pi_div_two
+-/
 
 theorem cos_eq_cos_iff {x y : ℂ} : cos x = cos y ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = 2 * k * π - x :=
   calc
@@ -133,6 +135,7 @@ theorem tan_add' {x y : ℂ}
   tan_add (Or.inl h)
 #align complex.tan_add' Complex.tan_add'
 
+#print Complex.tan_two_mul /-
 theorem tan_two_mul {z : ℂ} : tan (2 * z) = 2 * tan z / (1 - tan z ^ 2) :=
   by
   by_cases h : ∀ k : ℤ, z ≠ (2 * k + 1) * π / 2
@@ -140,14 +143,15 @@ theorem tan_two_mul {z : ℂ} : tan (2 * z) = 2 * tan z / (1 - tan z ^ 2) :=
   · rw [not_forall_not] at h 
     rw [two_mul, two_mul, sq, tan_add (Or.inr ⟨h, h⟩)]
 #align complex.tan_two_mul Complex.tan_two_mul
+-/
 
-theorem tan_add_mul_i {x y : ℂ}
+theorem tan_add_mul_I {x y : ℂ}
     (h :
       ((∀ k : ℤ, x ≠ (2 * k + 1) * π / 2) ∧ ∀ l : ℤ, y * I ≠ (2 * l + 1) * π / 2) ∨
         (∃ k : ℤ, x = (2 * k + 1) * π / 2) ∧ ∃ l : ℤ, y * I = (2 * l + 1) * π / 2) :
     tan (x + y * I) = (tan x + tanh y * I) / (1 - tan x * tanh y * I) := by
   rw [tan_add h, tan_mul_I, mul_assoc]
-#align complex.tan_add_mul_I Complex.tan_add_mul_i
+#align complex.tan_add_mul_I Complex.tan_add_mul_I
 
 theorem tan_eq {z : ℂ}
     (h :
@@ -180,6 +184,7 @@ theorem cos_eq_iff_quadratic {z w : ℂ} :
 #align complex.cos_eq_iff_quadratic Complex.cos_eq_iff_quadratic
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (w «expr ≠ » 0) -/
+#print Complex.cos_surjective /-
 theorem cos_surjective : Function.Surjective cos :=
   by
   intro x
@@ -196,23 +201,30 @@ theorem cos_surjective : Function.Surjective cos :=
   convert hw
   ring
 #align complex.cos_surjective Complex.cos_surjective
+-/
 
+#print Complex.range_cos /-
 @[simp]
 theorem range_cos : range cos = Set.univ :=
   cos_surjective.range_eq
 #align complex.range_cos Complex.range_cos
+-/
 
+#print Complex.sin_surjective /-
 theorem sin_surjective : Function.Surjective sin :=
   by
   intro x
   rcases cos_surjective x with ⟨z, rfl⟩
   exact ⟨z + π / 2, sin_add_pi_div_two z⟩
 #align complex.sin_surjective Complex.sin_surjective
+-/
 
+#print Complex.range_sin /-
 @[simp]
 theorem range_sin : range sin = Set.univ :=
   sin_surjective.range_eq
 #align complex.range_sin Complex.range_sin
+-/
 
 end Complex
 

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

@@ -161,12 +161,12 @@ theorem tan_eq {z : ℂ}
 
 open scoped Topology
 
-theorem continuousOn_tan : ContinuousOn tan { x | cos x ≠ 0 } :=
+theorem continuousOn_tan : ContinuousOn tan {x | cos x ≠ 0} :=
   continuousOn_sin.div continuousOn_cos fun x => id
 #align complex.continuous_on_tan Complex.continuousOn_tan
 
 @[continuity]
-theorem continuous_tan : Continuous fun x : { x | cos x ≠ 0 } => tan x :=
+theorem continuous_tan : Continuous fun x : {x | cos x ≠ 0} => tan x :=
   continuousOn_iff_continuous_restrict.1 continuousOn_tan
 #align complex.continuous_tan Complex.continuous_tan
 

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

@@ -69,7 +69,7 @@ theorem sin_ne_zero_iff {θ : ℂ} : sin θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π
 theorem tan_eq_zero_iff {θ : ℂ} : tan θ = 0 ↔ ∃ k : ℤ, θ = k * π / 2 :=
   by
   have h := (sin_two_mul θ).symm
-  rw [mul_assoc] at h
+  rw [mul_assoc] at h 
   rw [tan, div_eq_zero_iff, ← mul_eq_zero, ← MulZeroClass.zero_mul (1 / 2 : ℂ), mul_one_div,
     CancelDenoms.cancel_factors_eq_div h two_ne_zero, mul_comm]
   simpa only [zero_div, MulZeroClass.zero_mul, Ne.def, not_false_iff, field_simps] using
@@ -122,7 +122,7 @@ theorem tan_add {x y : ℂ}
       div_self (cos_ne_zero_iff.mpr h2)]
   · obtain ⟨t, hx, hy, hxy⟩ := tan_int_mul_pi_div_two, t (2 * k + 1), t (2 * l + 1),
       t (2 * k + 1 + (2 * l + 1))
-    simp only [Int.cast_add, Int.cast_bit0, Int.cast_mul, Int.cast_one, hx, hy] at hx hy hxy
+    simp only [Int.cast_add, Int.cast_bit0, Int.cast_mul, Int.cast_one, hx, hy] at hx hy hxy 
     rw [hx, hy, add_zero, zero_div, mul_div_assoc, mul_div_assoc, ←
       add_mul (2 * (k : ℂ) + 1) (2 * l + 1) (π / 2), ← mul_div_assoc, hxy]
 #align complex.tan_add Complex.tan_add
@@ -137,7 +137,7 @@ theorem tan_two_mul {z : ℂ} : tan (2 * z) = 2 * tan z / (1 - tan z ^ 2) :=
   by
   by_cases h : ∀ k : ℤ, z ≠ (2 * k + 1) * π / 2
   · rw [two_mul, two_mul, sq, tan_add (Or.inl ⟨h, h⟩)]
-  · rw [not_forall_not] at h
+  · rw [not_forall_not] at h 
     rw [two_mul, two_mul, sq, tan_add (Or.inr ⟨h, h⟩)]
 #align complex.tan_two_mul Complex.tan_two_mul
 
@@ -183,7 +183,7 @@ theorem cos_eq_iff_quadratic {z w : ℂ} :
 theorem cos_surjective : Function.Surjective cos :=
   by
   intro x
-  obtain ⟨w, w₀, hw⟩ : ∃ (w : _)(_ : w ≠ 0), 1 * w * w + -2 * x * w + 1 = 0 :=
+  obtain ⟨w, w₀, hw⟩ : ∃ (w : _) (_ : w ≠ 0), 1 * w * w + -2 * x * w + 1 = 0 :=
     by
     rcases exists_quadratic_eq_zero one_ne_zero
         ⟨_, (cpow_nat_inv_pow _ two_ne_zero).symm.trans <| pow_two _⟩ with

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

@@ -29,7 +29,7 @@ namespace Complex
 
 open Set Filter
 
-open Real
+open scoped Real
 
 theorem cos_eq_zero_iff {θ : ℂ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1) * π / 2 :=
   by
@@ -159,7 +159,7 @@ theorem tan_eq {z : ℂ}
   convert tan_add_mul_I h <;> exact (re_add_im z).symm
 #align complex.tan_eq Complex.tan_eq
 
-open Topology
+open scoped Topology
 
 theorem continuousOn_tan : ContinuousOn tan { x | cos x ≠ 0 } :=
   continuousOn_sin.div continuousOn_cos fun x => id
@@ -218,7 +218,7 @@ end Complex
 
 namespace Real
 
-open Real
+open scoped Real
 
 theorem cos_eq_zero_iff {θ : ℝ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1) * π / 2 := by
   exact_mod_cast @Complex.cos_eq_zero_iff θ

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

@@ -37,14 +37,11 @@ theorem cos_eq_zero_iff {θ : ℂ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1
     by
     rw [@div_eq_iff _ _ (exp (θ * I) + exp (-θ * I)) 2 0 two_ne_zero, MulZeroClass.zero_mul,
       add_eq_zero_iff_eq_neg, neg_eq_neg_one_mul, ← div_eq_iff (exp_ne_zero _), ← exp_sub]
-    field_simp only
-    congr 3
-    ring
+    field_simp only; congr 3; ring
   rw [cos, h, ← exp_pi_mul_I, exp_eq_exp_iff_exists_int, mul_right_comm]
   refine' exists_congr fun x => _
   refine' (iff_of_eq <| congr_arg _ _).trans (mul_right_inj' <| mul_ne_zero two_ne_zero I_ne_zero)
-  field_simp
-  ring
+  field_simp; ring
 #align complex.cos_eq_zero_iff Complex.cos_eq_zero_iff
 
 theorem cos_ne_zero_iff {θ : ℂ} : cos θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ (2 * k + 1) * π / 2 := by
@@ -98,10 +95,7 @@ theorem cos_eq_cos_iff {x y : ℂ} : cos x = cos y ↔ ∃ k : ℤ, y = 2 * k *
       apply or_congr <;>
         field_simp [sin_eq_zero_iff, (by norm_num : -(2 : ℂ) ≠ 0), eq_sub_iff_add_eq',
           sub_eq_iff_eq_add, mul_comm (2 : ℂ), mul_right_comm _ (2 : ℂ)]
-      constructor <;>
-        · rintro ⟨k, rfl⟩
-          use -k
-          simp
+      constructor <;> · rintro ⟨k, rfl⟩; use -k; simp
     _ ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = 2 * k * π - x := exists_or.symm
     
 #align complex.cos_eq_cos_iff Complex.cos_eq_cos_iff

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

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
 
 ! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.complex
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
+! leanprover-community/mathlib commit 8f9fea08977f7e450770933ee6abb20733b47c92
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.QuadraticDiscriminant
-import Mathbin.Analysis.Convex.SpecificFunctions
+import Mathbin.Analysis.Convex.SpecificFunctions.Deriv
 
 /-!
 # Complex trigonometric functions

mathlib commit https://github.com/leanprover-community/mathlib/commit/3905fa80e62c0898131285baab35559fbc4e5cda

@@ -74,7 +74,7 @@ theorem tan_eq_zero_iff {θ : ℂ} : tan θ = 0 ↔ ∃ k : ℤ, θ = k * π / 2
   have h := (sin_two_mul θ).symm
   rw [mul_assoc] at h
   rw [tan, div_eq_zero_iff, ← mul_eq_zero, ← MulZeroClass.zero_mul (1 / 2 : ℂ), mul_one_div,
-    CancelFactors.cancel_factors_eq_div h two_ne_zero, mul_comm]
+    CancelDenoms.cancel_factors_eq_div h two_ne_zero, mul_comm]
   simpa only [zero_div, MulZeroClass.zero_mul, Ne.def, not_false_iff, field_simps] using
     sin_eq_zero_iff
 #align complex.tan_eq_zero_iff Complex.tan_eq_zero_iff

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -4,12 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
 
 ! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.complex
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.QuadraticDiscriminant
-import Mathbin.Analysis.SpecialFunctions.Trigonometric.Basic
 import Mathbin.Analysis.Convex.SpecificFunctions
 
 /-!

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

@@ -36,7 +36,7 @@ theorem cos_eq_zero_iff {θ : ℂ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1
   by
   have h : (exp (θ * I) + exp (-θ * I)) / 2 = 0 ↔ exp (2 * θ * I) = -1 :=
     by
-    rw [@div_eq_iff _ _ (exp (θ * I) + exp (-θ * I)) 2 0 two_ne_zero, zero_mul,
+    rw [@div_eq_iff _ _ (exp (θ * I) + exp (-θ * I)) 2 0 two_ne_zero, MulZeroClass.zero_mul,
       add_eq_zero_iff_eq_neg, neg_eq_neg_one_mul, ← div_eq_iff (exp_ne_zero _), ← exp_sub]
     field_simp only
     congr 3
@@ -74,9 +74,10 @@ theorem tan_eq_zero_iff {θ : ℂ} : tan θ = 0 ↔ ∃ k : ℤ, θ = k * π / 2
   by
   have h := (sin_two_mul θ).symm
   rw [mul_assoc] at h
-  rw [tan, div_eq_zero_iff, ← mul_eq_zero, ← zero_mul (1 / 2 : ℂ), mul_one_div,
+  rw [tan, div_eq_zero_iff, ← mul_eq_zero, ← MulZeroClass.zero_mul (1 / 2 : ℂ), mul_one_div,
     CancelFactors.cancel_factors_eq_div h two_ne_zero, mul_comm]
-  simpa only [zero_div, zero_mul, Ne.def, not_false_iff, field_simps] using sin_eq_zero_iff
+  simpa only [zero_div, MulZeroClass.zero_mul, Ne.def, not_false_iff, field_simps] using
+    sin_eq_zero_iff
 #align complex.tan_eq_zero_iff Complex.tan_eq_zero_iff
 
 theorem tan_ne_zero_iff {θ : ℂ} : tan θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π / 2 := by
@@ -196,7 +197,7 @@ theorem cos_surjective : Function.Surjective cos :=
       ⟨w, hw⟩
     refine' ⟨w, _, hw⟩
     rintro rfl
-    simpa only [zero_add, one_ne_zero, mul_zero] using hw
+    simpa only [zero_add, one_ne_zero, MulZeroClass.mul_zero] using hw
   refine' ⟨log w / I, cos_eq_iff_quadratic.2 _⟩
   rw [div_mul_cancel _ I_ne_zero, exp_log w₀]
   convert hw

mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba

@@ -149,19 +149,19 @@ theorem tan_two_mul {z : ℂ} : tan (2 * z) = 2 * tan z / (1 - tan z ^ 2) :=
 
 theorem tan_add_mul_i {x y : ℂ}
     (h :
-      ((∀ k : ℤ, x ≠ (2 * k + 1) * π / 2) ∧ ∀ l : ℤ, y * i ≠ (2 * l + 1) * π / 2) ∨
-        (∃ k : ℤ, x = (2 * k + 1) * π / 2) ∧ ∃ l : ℤ, y * i = (2 * l + 1) * π / 2) :
-    tan (x + y * i) = (tan x + tanh y * i) / (1 - tan x * tanh y * i) := by
+      ((∀ k : ℤ, x ≠ (2 * k + 1) * π / 2) ∧ ∀ l : ℤ, y * I ≠ (2 * l + 1) * π / 2) ∨
+        (∃ k : ℤ, x = (2 * k + 1) * π / 2) ∧ ∃ l : ℤ, y * I = (2 * l + 1) * π / 2) :
+    tan (x + y * I) = (tan x + tanh y * I) / (1 - tan x * tanh y * I) := by
   rw [tan_add h, tan_mul_I, mul_assoc]
 #align complex.tan_add_mul_I Complex.tan_add_mul_i
 
 theorem tan_eq {z : ℂ}
     (h :
       ((∀ k : ℤ, (z.re : ℂ) ≠ (2 * k + 1) * π / 2) ∧
-          ∀ l : ℤ, (z.im : ℂ) * i ≠ (2 * l + 1) * π / 2) ∨
+          ∀ l : ℤ, (z.im : ℂ) * I ≠ (2 * l + 1) * π / 2) ∨
         (∃ k : ℤ, (z.re : ℂ) = (2 * k + 1) * π / 2) ∧
-          ∃ l : ℤ, (z.im : ℂ) * i = (2 * l + 1) * π / 2) :
-    tan z = (tan z.re + tanh z.im * i) / (1 - tan z.re * tanh z.im * i) := by
+          ∃ l : ℤ, (z.im : ℂ) * I = (2 * l + 1) * π / 2) :
+    tan z = (tan z.re + tanh z.im * I) / (1 - tan z.re * tanh z.im * I) := by
   convert tan_add_mul_I h <;> exact (re_add_im z).symm
 #align complex.tan_eq Complex.tan_eq
 
@@ -177,7 +177,7 @@ theorem continuous_tan : Continuous fun x : { x | cos x ≠ 0 } => tan x :=
 #align complex.continuous_tan Complex.continuous_tan
 
 theorem cos_eq_iff_quadratic {z w : ℂ} :
-    cos z = w ↔ exp (z * i) ^ 2 - 2 * w * exp (z * i) + 1 = 0 :=
+    cos z = w ↔ exp (z * I) ^ 2 - 2 * w * exp (z * I) + 1 = 0 :=
   by
   rw [← sub_eq_zero]
   field_simp [cos, exp_neg, exp_ne_zero]

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

@@ -185,7 +185,7 @@ theorem cos_eq_iff_quadratic {z w : ℂ} :
   ring
 #align complex.cos_eq_iff_quadratic Complex.cos_eq_iff_quadratic
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (w «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (w «expr ≠ » 0) -/
 theorem cos_surjective : Function.Surjective cos :=
   by
   intro x

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

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

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

| Statement | New name | Old name | |

@@ -202,7 +202,7 @@ theorem cos_surjective : Function.Surjective cos := by
     rintro rfl
     simp only [zero_add, one_ne_zero, mul_zero] at hw
   refine' ⟨log w / I, cos_eq_iff_quadratic.2 _⟩
-  rw [div_mul_cancel _ I_ne_zero, exp_log w₀]
+  rw [div_mul_cancel₀ _ I_ne_zero, exp_log w₀]
   convert hw using 1
   ring
 #align complex.cos_surjective Complex.cos_surjective

I removed some of the tactics that were not used and are hopefully uncontroversial arising from the linter at #11308.

As the commit messages should convey, the removed tactics are, essentially,

push_cast
norm_cast
congr
norm_num
dsimp
funext
intro
infer_instance

@@ -33,7 +33,7 @@ theorem cos_eq_zero_iff {θ : ℂ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1
   have h : (exp (θ * I) + exp (-θ * I)) / 2 = 0 ↔ exp (2 * θ * I) = -1 := by
     rw [@div_eq_iff _ _ (exp (θ * I) + exp (-θ * I)) 2 0 two_ne_zero, zero_mul,
       add_eq_zero_iff_eq_neg, neg_eq_neg_one_mul, ← div_eq_iff (exp_ne_zero _), ← exp_sub]
-    congr 3; ring_nf
+    ring_nf
   rw [cos, h, ← exp_pi_mul_I, exp_eq_exp_iff_exists_int, mul_right_comm]
   refine' exists_congr fun x => _
   refine' (iff_of_eq <| congr_arg _ _).trans (mul_right_inj' <| mul_ne_zero two_ne_zero I_ne_zero)

This version assumes that the cosine is not zero.

@@ -61,16 +61,18 @@ theorem sin_ne_zero_iff {θ : ℂ} : sin θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π
   rw [← not_exists, not_iff_not, sin_eq_zero_iff]
 #align complex.sin_ne_zero_iff Complex.sin_ne_zero_iff
 
-theorem tan_eq_zero_iff {θ : ℂ} : tan θ = 0 ↔ ∃ k : ℤ, θ = k * π / 2 := by
-  have h := (sin_two_mul θ).symm
-  rw [mul_assoc] at h
-  rw [tan, div_eq_zero_iff, ← mul_eq_zero, ← zero_mul (1 / 2 : ℂ), mul_one_div,
-    CancelDenoms.cancel_factors_eq_div h two_ne_zero, mul_comm]
-  simpa only [zero_div, zero_mul, Ne.def, not_false_iff, field_simps] using
-    sin_eq_zero_iff
+/-- The tangent of a complex number is equal to zero
+iff this number is equal to `k * π / 2` for an integer `k`.
+
+Note that this lemma takes into account that we use zero as the junk value for division by zero.
+See also `Complex.tan_eq_zero_iff'`.  -/
+theorem tan_eq_zero_iff {θ : ℂ} : tan θ = 0 ↔ ∃ k : ℤ, k * π / 2 = θ := by
+  rw [tan, div_eq_zero_iff, ← mul_eq_zero, ← mul_right_inj' two_ne_zero, mul_zero,
+    ← mul_assoc, ← sin_two_mul, sin_eq_zero_iff]
+  field_simp [mul_comm, eq_comm]
 #align complex.tan_eq_zero_iff Complex.tan_eq_zero_iff
 
-theorem tan_ne_zero_iff {θ : ℂ} : tan θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π / 2 := by
+theorem tan_ne_zero_iff {θ : ℂ} : tan θ ≠ 0 ↔ ∀ k : ℤ, (k * π / 2 : ℂ) ≠ θ := by
   rw [← not_exists, not_iff_not, tan_eq_zero_iff]
 #align complex.tan_ne_zero_iff Complex.tan_ne_zero_iff
 
@@ -78,6 +80,13 @@ theorem tan_int_mul_pi_div_two (n : ℤ) : tan (n * π / 2) = 0 :=
   tan_eq_zero_iff.mpr (by use n)
 #align complex.tan_int_mul_pi_div_two Complex.tan_int_mul_pi_div_two
 
+/-- If the tangent of a complex number is well-defined,
+then it is equal to zero iff the number is equal to `k * π` for an integer `k`.
+
+See also `Complex.tan_eq_zero_iff` for a version that takes into account junk values of `θ`. -/
+theorem tan_eq_zero_iff' {θ : ℂ} (hθ : cos θ ≠ 0) : tan θ = 0 ↔ ∃ k : ℤ, k * π = θ := by
+  simp only [tan, hθ, div_eq_zero_iff, sin_eq_zero_iff]; simp [eq_comm]
+
 theorem cos_eq_cos_iff {x y : ℂ} : cos x = cos y ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = 2 * k * π - x :=
   calc
     cos x = cos y ↔ cos x - cos y = 0 := sub_eq_zero.symm
@@ -246,6 +255,18 @@ theorem sin_eq_one_iff {x : ℝ} : sin x = 1 ↔ ∃ k : ℤ, π / 2 + k * (2 *
 theorem sin_eq_neg_one_iff {x : ℝ} : sin x = -1 ↔ ∃ k : ℤ, -(π / 2) + k * (2 * π) = x :=
   mod_cast @Complex.sin_eq_neg_one_iff x
 
+theorem tan_eq_zero_iff {θ : ℝ} : tan θ = 0 ↔ ∃ k : ℤ, k * π / 2 = θ :=
+  mod_cast @Complex.tan_eq_zero_iff θ
+#align real.tan_eq_zero_iff Real.tan_eq_zero_iff
+
+theorem tan_eq_zero_iff' {θ : ℝ} (hθ : cos θ ≠ 0) : tan θ = 0 ↔ ∃ k : ℤ, k * π = θ := by
+  revert hθ
+  exact_mod_cast @Complex.tan_eq_zero_iff' θ
+
+theorem tan_ne_zero_iff {θ : ℝ} : tan θ ≠ 0 ↔ ∀ k : ℤ, k * π / 2 ≠ θ :=
+  mod_cast @Complex.tan_ne_zero_iff θ
+#align real.tan_ne_zero_iff Real.tan_ne_zero_iff
+
 theorem lt_sin_mul {x : ℝ} (hx : 0 < x) (hx' : x < 1) : x < sin (π / 2 * x) := by
   simpa [mul_comm x] using
     strictConcaveOn_sin_Icc.2 ⟨le_rfl, pi_pos.le⟩ ⟨pi_div_two_pos.le, half_le_self pi_pos.le⟩

@@ -98,6 +98,22 @@ theorem sin_eq_sin_iff {x y : ℂ} :
   refine' exists_congr fun k => or_congr _ _ <;> refine' Eq.congr rfl _ <;> field_simp <;> ring
 #align complex.sin_eq_sin_iff Complex.sin_eq_sin_iff
 
+theorem cos_eq_one_iff {x : ℂ} : cos x = 1 ↔ ∃ k : ℤ, k * (2 * π) = x := by
+  rw [← cos_zero, eq_comm, cos_eq_cos_iff]
+  simp [mul_assoc, mul_left_comm, eq_comm]
+
+theorem cos_eq_neg_one_iff {x : ℂ} : cos x = -1 ↔ ∃ k : ℤ, π + k * (2 * π) = x := by
+  rw [← neg_eq_iff_eq_neg, ← cos_sub_pi, cos_eq_one_iff]
+  simp only [eq_sub_iff_add_eq']
+
+theorem sin_eq_one_iff {x : ℂ} : sin x = 1 ↔ ∃ k : ℤ, π / 2 + k * (2 * π) = x := by
+  rw [← cos_sub_pi_div_two, cos_eq_one_iff]
+  simp only [eq_sub_iff_add_eq']
+
+theorem sin_eq_neg_one_iff {x : ℂ} : sin x = -1 ↔ ∃ k : ℤ, -(π / 2) + k * (2 * π) = x := by
+  rw [← neg_eq_iff_eq_neg, ← cos_add_pi_div_two, cos_eq_one_iff]
+  simp only [← sub_eq_neg_add, sub_eq_iff_eq_add]
+
 theorem tan_add {x y : ℂ}
     (h : ((∀ k : ℤ, x ≠ (2 * k + 1) * π / 2) ∧ ∀ l : ℤ, y ≠ (2 * l + 1) * π / 2) ∨
       (∃ k : ℤ, x = (2 * k + 1) * π / 2) ∧ ∃ l : ℤ, y = (2 * l + 1) * π / 2) :
@@ -208,8 +224,8 @@ theorem cos_eq_zero_iff {θ : ℝ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1
   mod_cast @Complex.cos_eq_zero_iff θ
 #align real.cos_eq_zero_iff Real.cos_eq_zero_iff
 
-theorem cos_ne_zero_iff {θ : ℝ} : cos θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ (2 * k + 1) * π / 2 := by
-  rw [← not_exists, not_iff_not, cos_eq_zero_iff]
+theorem cos_ne_zero_iff {θ : ℝ} : cos θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ (2 * k + 1) * π / 2 :=
+  mod_cast @Complex.cos_ne_zero_iff θ
 #align real.cos_ne_zero_iff Real.cos_ne_zero_iff
 
 theorem cos_eq_cos_iff {x y : ℝ} : cos x = cos y ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = 2 * k * π - x :=
@@ -221,6 +237,15 @@ theorem sin_eq_sin_iff {x y : ℝ} :
   mod_cast @Complex.sin_eq_sin_iff x y
 #align real.sin_eq_sin_iff Real.sin_eq_sin_iff
 
+theorem cos_eq_neg_one_iff {x : ℝ} : cos x = -1 ↔ ∃ k : ℤ, π + k * (2 * π) = x :=
+  mod_cast @Complex.cos_eq_neg_one_iff x
+
+theorem sin_eq_one_iff {x : ℝ} : sin x = 1 ↔ ∃ k : ℤ, π / 2 + k * (2 * π) = x :=
+  mod_cast @Complex.sin_eq_one_iff x
+
+theorem sin_eq_neg_one_iff {x : ℝ} : sin x = -1 ↔ ∃ k : ℤ, -(π / 2) + k * (2 * π) = x :=
+  mod_cast @Complex.sin_eq_neg_one_iff x
+
 theorem lt_sin_mul {x : ℝ} (hx : 0 < x) (hx' : x < 1) : x < sin (π / 2 * x) := by
   simpa [mul_comm x] using
     strictConcaveOn_sin_Icc.2 ⟨le_rfl, pi_pos.le⟩ ⟨pi_div_two_pos.le, half_le_self pi_pos.le⟩

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

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

@@ -5,6 +5,7 @@ Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin
 -/
 import Mathlib.Algebra.QuadraticDiscriminant
 import Mathlib.Analysis.Convex.SpecificFunctions.Deriv
+import Mathlib.Analysis.SpecialFunctions.Pow.Complex
 
 #align_import analysis.special_functions.trigonometric.complex from "leanprover-community/mathlib"@"8f9fea08977f7e450770933ee6abb20733b47c92"
 

Follow-up #9184

@@ -168,7 +168,7 @@ theorem cos_eq_iff_quadratic {z w : ℂ} :
 
 theorem cos_surjective : Function.Surjective cos := by
   intro x
-  obtain ⟨w, w₀, hw⟩ : ∃ (w : _) (_ : w ≠ 0), 1 * w * w + -2 * x * w + 1 = 0 := by
+  obtain ⟨w, w₀, hw⟩ : ∃ w ≠ 0, 1 * w * w + -2 * x * w + 1 = 0 := by
     rcases exists_quadratic_eq_zero one_ne_zero
         ⟨_, (cpow_nat_inv_pow _ two_ne_zero).symm.trans <| pow_two _⟩ with
       ⟨w, hw⟩

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

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

@@ -203,8 +203,8 @@ namespace Real
 
 open scoped Real
 
-theorem cos_eq_zero_iff {θ : ℝ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1) * π / 2 := by
-  exact_mod_cast @Complex.cos_eq_zero_iff θ
+theorem cos_eq_zero_iff {θ : ℝ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1) * π / 2 :=
+  mod_cast @Complex.cos_eq_zero_iff θ
 #align real.cos_eq_zero_iff Real.cos_eq_zero_iff
 
 theorem cos_ne_zero_iff {θ : ℝ} : cos θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ (2 * k + 1) * π / 2 := by
@@ -212,12 +212,12 @@ theorem cos_ne_zero_iff {θ : ℝ} : cos θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ (2 * k
 #align real.cos_ne_zero_iff Real.cos_ne_zero_iff
 
 theorem cos_eq_cos_iff {x y : ℝ} : cos x = cos y ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = 2 * k * π - x :=
-  by exact_mod_cast @Complex.cos_eq_cos_iff x y
+  mod_cast @Complex.cos_eq_cos_iff x y
 #align real.cos_eq_cos_iff Real.cos_eq_cos_iff
 
 theorem sin_eq_sin_iff {x y : ℝ} :
-    sin x = sin y ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = (2 * k + 1) * π - x := by
-  exact_mod_cast @Complex.sin_eq_sin_iff x y
+    sin x = sin y ↔ ∃ k : ℤ, y = 2 * k * π + x ∨ y = (2 * k + 1) * π - x :=
+  mod_cast @Complex.sin_eq_sin_iff x y
 #align real.sin_eq_sin_iff Real.sin_eq_sin_iff
 
 theorem lt_sin_mul {x : ℝ} (hx : 0 < x) (hx' : x < 1) : x < sin (π / 2 * x) := by

PR contents

This is the supremum of

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

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

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

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

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

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

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

leanprover/lean4#2722

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

leanprover/lean4#2783

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

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

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

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

@@ -121,8 +121,6 @@ theorem tan_add' {x y : ℂ}
   tan_add (Or.inl h)
 #align complex.tan_add' Complex.tan_add'
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 theorem tan_two_mul {z : ℂ} : tan (2 * z) = (2 : ℂ) * tan z / ((1 : ℂ) - tan z ^ 2) := by
   by_cases h : ∀ k : ℤ, z ≠ (2 * k + 1) * π / 2
   · rw [two_mul, two_mul, sq, tan_add (Or.inl ⟨h, h⟩)]

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).

@@ -30,7 +30,7 @@ open scoped Real
 
 theorem cos_eq_zero_iff {θ : ℂ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1) * π / 2 := by
   have h : (exp (θ * I) + exp (-θ * I)) / 2 = 0 ↔ exp (2 * θ * I) = -1 := by
-    rw [@div_eq_iff _ _ (exp (θ * I) + exp (-θ * I)) 2 0 two_ne_zero, MulZeroClass.zero_mul,
+    rw [@div_eq_iff _ _ (exp (θ * I) + exp (-θ * I)) 2 0 two_ne_zero, zero_mul,
       add_eq_zero_iff_eq_neg, neg_eq_neg_one_mul, ← div_eq_iff (exp_ne_zero _), ← exp_sub]
     congr 3; ring_nf
   rw [cos, h, ← exp_pi_mul_I, exp_eq_exp_iff_exists_int, mul_right_comm]
@@ -63,9 +63,9 @@ theorem sin_ne_zero_iff {θ : ℂ} : sin θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π
 theorem tan_eq_zero_iff {θ : ℂ} : tan θ = 0 ↔ ∃ k : ℤ, θ = k * π / 2 := by
   have h := (sin_two_mul θ).symm
   rw [mul_assoc] at h
-  rw [tan, div_eq_zero_iff, ← mul_eq_zero, ← MulZeroClass.zero_mul (1 / 2 : ℂ), mul_one_div,
+  rw [tan, div_eq_zero_iff, ← mul_eq_zero, ← zero_mul (1 / 2 : ℂ), mul_one_div,
     CancelDenoms.cancel_factors_eq_div h two_ne_zero, mul_comm]
-  simpa only [zero_div, MulZeroClass.zero_mul, Ne.def, not_false_iff, field_simps] using
+  simpa only [zero_div, zero_mul, Ne.def, not_false_iff, field_simps] using
     sin_eq_zero_iff
 #align complex.tan_eq_zero_iff Complex.tan_eq_zero_iff
 
@@ -176,7 +176,7 @@ theorem cos_surjective : Function.Surjective cos := by
       ⟨w, hw⟩
     refine' ⟨w, _, hw⟩
     rintro rfl
-    simp only [zero_add, one_ne_zero, MulZeroClass.mul_zero] at hw
+    simp only [zero_add, one_ne_zero, mul_zero] at hw
   refine' ⟨log w / I, cos_eq_iff_quadratic.2 _⟩
   rw [div_mul_cancel _ I_ne_zero, exp_log w₀]
   convert hw using 1

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

@@ -32,7 +32,7 @@ theorem cos_eq_zero_iff {θ : ℂ} : cos θ = 0 ↔ ∃ k : ℤ, θ = (2 * k + 1
   have h : (exp (θ * I) + exp (-θ * I)) / 2 = 0 ↔ exp (2 * θ * I) = -1 := by
     rw [@div_eq_iff _ _ (exp (θ * I) + exp (-θ * I)) 2 0 two_ne_zero, MulZeroClass.zero_mul,
       add_eq_zero_iff_eq_neg, neg_eq_neg_one_mul, ← div_eq_iff (exp_ne_zero _), ← exp_sub]
-    field_simp only; congr 3; ring_nf
+    congr 3; ring_nf
   rw [cos, h, ← exp_pi_mul_I, exp_eq_exp_iff_exists_int, mul_right_comm]
   refine' exists_congr fun x => _
   refine' (iff_of_eq <| congr_arg _ _).trans (mul_right_inj' <| mul_ne_zero two_ne_zero I_ne_zero)

@@ -121,8 +121,7 @@ theorem tan_add' {x y : ℂ}
   tan_add (Or.inl h)
 #align complex.tan_add' Complex.tan_add'
 
-local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y)
--- porting note: lean4#2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 theorem tan_two_mul {z : ℂ} : tan (2 * z) = (2 : ℂ) * tan z / ((1 : ℂ) - tan z ^ 2) := by
   by_cases h : ∀ k : ℤ, z ≠ (2 * k + 1) * π / 2

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-
-! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.complex
-! leanprover-community/mathlib commit 8f9fea08977f7e450770933ee6abb20733b47c92
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.QuadraticDiscriminant
 import Mathlib.Analysis.Convex.SpecificFunctions.Deriv
 
+#align_import analysis.special_functions.trigonometric.complex from "leanprover-community/mathlib"@"8f9fea08977f7e450770933ee6abb20733b47c92"
+
 /-!
 # Complex trigonometric functions