analysis.special_functions.trigonometric.basic ⟷ Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic

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

@@ -163,21 +163,21 @@ scoped notation "π" => Real.pi
 #print Real.cos_pi_div_two /-
 @[simp]
 theorem cos_pi_div_two : cos (π / 2) = 0 := by
-  rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)] <;>
+  rw [Real.pi, mul_div_cancel_left₀ _ (two_ne_zero' ℝ)] <;>
     exact (Classical.choose_spec exists_cos_eq_zero).2
 #align real.cos_pi_div_two Real.cos_pi_div_two
 -/
 
 #print Real.one_le_pi_div_two /-
 theorem one_le_pi_div_two : (1 : ℝ) ≤ π / 2 := by
-  rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)] <;>
+  rw [Real.pi, mul_div_cancel_left₀ _ (two_ne_zero' ℝ)] <;>
     exact (Classical.choose_spec exists_cos_eq_zero).1.1
 #align real.one_le_pi_div_two Real.one_le_pi_div_two
 -/
 
 #print Real.pi_div_two_le_two /-
 theorem pi_div_two_le_two : π / 2 ≤ 2 := by
-  rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)] <;>
+  rw [Real.pi, mul_div_cancel_left₀ _ (two_ne_zero' ℝ)] <;>
     exact (Classical.choose_spec exists_cos_eq_zero).1.2
 #align real.pi_div_two_le_two Real.pi_div_two_le_two
 -/
@@ -263,14 +263,14 @@ open scoped Real
 #print Real.sin_pi /-
 @[simp]
 theorem sin_pi : sin π = 0 := by
-  rw [← mul_div_cancel_left π (two_ne_zero' ℝ), two_mul, add_div, sin_add, cos_pi_div_two] <;> simp
+  rw [← mul_div_cancel_left₀ π (two_ne_zero' ℝ), two_mul, add_div, sin_add, cos_pi_div_two] <;> simp
 #align real.sin_pi Real.sin_pi
 -/
 
 #print Real.cos_pi /-
 @[simp]
 theorem cos_pi : cos π = -1 := by
-  rw [← mul_div_cancel_left π (two_ne_zero' ℝ), mul_div_assoc, cos_two_mul, cos_pi_div_two] <;>
+  rw [← mul_div_cancel_left₀ π (two_ne_zero' ℝ), mul_div_assoc, cos_two_mul, cos_pi_div_two] <;>
     simp [bit0, pow_add]
 #align real.cos_pi Real.cos_pi
 -/
@@ -978,10 +978,10 @@ theorem cos_pi_over_two_pow : ∀ n : ℕ, cos (π / 2 ^ (n + 1)) = sqrtTwoAddSe
     have : (2 : ℝ) ≠ 0 := two_ne_zero
     symm; rw [div_eq_iff_mul_eq this]; symm
     rw [sqrt_two_add_series, sqrt_eq_iff_sq_eq, mul_pow, cos_sq, ← mul_div_assoc, Nat.add_succ,
-      pow_succ, mul_div_mul_left _ _ this, cos_pi_over_two_pow, add_mul]
+      pow_succ', mul_div_mul_left _ _ this, cos_pi_over_two_pow, add_mul]
     congr; · norm_num
-    rw [mul_comm, sq, mul_assoc, ← mul_div_assoc, mul_div_cancel_left, ← mul_div_assoc,
-        mul_div_cancel_left] <;>
+    rw [mul_comm, sq, mul_assoc, ← mul_div_assoc, mul_div_cancel_left₀, ← mul_div_assoc,
+        mul_div_cancel_left₀] <;>
       try exact this
     apply add_nonneg; norm_num; apply sqrt_two_add_series_zero_nonneg; norm_num
     apply le_of_lt; apply cos_pos_of_mem_Ioo ⟨_, _⟩
@@ -1016,7 +1016,7 @@ theorem sin_pi_over_two_pow_succ (n : ℕ) :
   by
   symm; rw [div_eq_iff_mul_eq]; symm
   rw [sqrt_eq_iff_sq_eq, mul_pow, sin_sq_pi_over_two_pow_succ, sub_mul]
-  · congr; norm_num; rw [mul_comm]; convert mul_div_cancel' _ _; norm_num; norm_num
+  · congr; norm_num; rw [mul_comm]; convert mul_div_cancel₀ _ _; norm_num; norm_num
   · rw [sub_nonneg]; apply le_of_lt; apply sqrt_two_add_series_lt_two
   apply le_of_lt; apply mul_pos; apply sin_pos_of_pos_of_lt_pi
   · apply div_pos pi_pos; apply pow_pos; norm_num

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

@@ -553,7 +553,7 @@ theorem sin_pos_of_mem_Ioo {x : ℝ} (hx : x ∈ Ioo 0 π) : 0 < sin x :=
 #print Real.sin_nonneg_of_mem_Icc /-
 theorem sin_nonneg_of_mem_Icc {x : ℝ} (hx : x ∈ Icc 0 π) : 0 ≤ sin x :=
   by
-  rw [← closure_Ioo pi_ne_zero.symm] at hx 
+  rw [← closure_Ioo pi_ne_zero.symm] at hx
   exact
     closure_lt_subset_le continuous_const continuous_sin
       (closure_mono (fun y => sin_pos_of_mem_Ioo) hx)
@@ -722,8 +722,8 @@ theorem cos_eq_one_iff (x : ℝ) : cos x = 1 ↔ ∃ n : ℤ, (n : ℝ) * (2 * 
             Int.ediv_mul_cancel ((Int.dvd_iff_emod_eq_zero _ _).2 hn0)])
         fun hn1 => by
         rw [← Int.emod_add_ediv n 2, hn1, Int.cast_add, Int.cast_one, add_mul, one_mul, add_comm,
-              mul_comm (2 : ℤ), Int.cast_mul, mul_assoc, Int.cast_two] at hn  <;>
-            rw [← hn, cos_int_mul_two_pi_add_pi] at h  <;>
+              mul_comm (2 : ℤ), Int.cast_mul, mul_assoc, Int.cast_two] at hn <;>
+            rw [← hn, cos_int_mul_two_pi_add_pi] at h <;>
           exact absurd h (by norm_num)⟩,
     fun ⟨n, hn⟩ => hn ▸ cos_int_mul_two_pi _⟩
 #align real.cos_eq_one_iff Real.cos_eq_one_iff
@@ -734,9 +734,9 @@ theorem cos_eq_one_iff_of_lt_of_lt {x : ℝ} (hx₁ : -(2 * π) < x) (hx₂ : x
     cos x = 1 ↔ x = 0 :=
   ⟨fun h => by
     rcases(cos_eq_one_iff _).1 h with ⟨n, rfl⟩
-    rw [mul_lt_iff_lt_one_left two_pi_pos] at hx₂ 
-    rw [neg_lt, neg_mul_eq_neg_mul, mul_lt_iff_lt_one_left two_pi_pos] at hx₁ 
-    norm_cast at hx₁ hx₂ 
+    rw [mul_lt_iff_lt_one_left two_pi_pos] at hx₂
+    rw [neg_lt, neg_mul_eq_neg_mul, mul_lt_iff_lt_one_left two_pi_pos] at hx₁
+    norm_cast at hx₁ hx₂
     obtain rfl : n = 0 := le_antisymm (by linarith) (by linarith)
     simp, fun h => by simp [h]⟩
 #align real.cos_eq_one_iff_of_lt_of_lt Real.cos_eq_one_iff_of_lt_of_lt

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

@@ -55,7 +55,8 @@ namespace Complex
 #print Complex.continuous_sin /-
 @[continuity]
 theorem continuous_sin : Continuous sin := by
-  change Continuous fun z => (exp (-z * I) - exp (z * I)) * I / 2; continuity
+  change Continuous fun z => (NormedSpace.exp (-z * I) - NormedSpace.exp (z * I)) * I / 2;
+  continuity
 #align complex.continuous_sin Complex.continuous_sin
 -/
 
@@ -68,7 +69,7 @@ theorem continuousOn_sin {s : Set ℂ} : ContinuousOn sin s :=
 #print Complex.continuous_cos /-
 @[continuity]
 theorem continuous_cos : Continuous cos := by
-  change Continuous fun z => (exp (z * I) + exp (-z * I)) / 2; continuity
+  change Continuous fun z => (NormedSpace.exp (z * I) + NormedSpace.exp (-z * I)) / 2; continuity
 #align complex.continuous_cos Complex.continuous_cos
 -/
 
@@ -80,15 +81,15 @@ theorem continuousOn_cos {s : Set ℂ} : ContinuousOn cos s :=
 
 #print Complex.continuous_sinh /-
 @[continuity]
-theorem continuous_sinh : Continuous sinh := by change Continuous fun z => (exp z - exp (-z)) / 2;
-  continuity
+theorem continuous_sinh : Continuous sinh := by
+  change Continuous fun z => (NormedSpace.exp z - NormedSpace.exp (-z)) / 2; continuity
 #align complex.continuous_sinh Complex.continuous_sinh
 -/
 
 #print Complex.continuous_cosh /-
 @[continuity]
-theorem continuous_cosh : Continuous cosh := by change Continuous fun z => (exp z + exp (-z)) / 2;
-  continuity
+theorem continuous_cosh : Continuous cosh := by
+  change Continuous fun z => (NormedSpace.exp z + NormedSpace.exp (-z)) / 2; continuity
 #align complex.continuous_cosh Complex.continuous_cosh
 -/
 
@@ -1797,7 +1798,8 @@ theorem tan_int_mul_pi_sub (x : ℂ) (n : ℤ) : tan (n * π - x) = -tan x :=
 -/
 
 #print Complex.exp_antiperiodic /-
-theorem exp_antiperiodic : Function.Antiperiodic exp (π * I) := by simp [exp_add, exp_mul_I]
+theorem exp_antiperiodic : Function.Antiperiodic exp (π * I) := by
+  simp [NormedSpace.exp_add, exp_mul_I]
 #align complex.exp_antiperiodic Complex.exp_antiperiodic
 -/
 

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

@@ -3,7 +3,7 @@ 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.Analysis.SpecialFunctions.Exp
+import Analysis.SpecialFunctions.Exp
 
 #align_import analysis.special_functions.trigonometric.basic from "leanprover-community/mathlib"@"50251fd6309cca5ca2e747882ffecd2729f38c5d"
 

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

@@ -2,14 +2,11 @@
 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.basic
-! leanprover-community/mathlib commit 50251fd6309cca5ca2e747882ffecd2729f38c5d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecialFunctions.Exp
 
+#align_import analysis.special_functions.trigonometric.basic from "leanprover-community/mathlib"@"50251fd6309cca5ca2e747882ffecd2729f38c5d"
+
 /-!
 # Trigonometric functions
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

@@ -1871,11 +1871,11 @@ $$\left|exp^{a\left(e^{z}+e^{-z}\right)}\right| \le e^{a\cos b \exp^{|re z|}}.$$
 -/
 theorem abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le {a b : ℝ} (ha : a ≤ 0) {z : ℂ} (hz : |z.im| ≤ b)
     (hb : b ≤ π / 2) :
-    abs (exp (a * (exp z + exp (-z)))) ≤ Real.exp (a * Real.cos b * Real.exp (|z.re|)) :=
+    abs (exp (a * (exp z + exp (-z)))) ≤ Real.exp (a * Real.cos b * Real.exp |z.re|) :=
   by
   simp only [abs_exp, Real.exp_le_exp, of_real_mul_re, add_re, exp_re, neg_im, Real.cos_neg, ←
     add_mul, mul_assoc, mul_comm (Real.cos b), neg_re, ← Real.cos_abs z.im]
-  have : Real.exp (|z.re|) ≤ Real.exp z.re + Real.exp (-z.re) :=
+  have : Real.exp |z.re| ≤ Real.exp z.re + Real.exp (-z.re) :=
     apply_abs_le_add_of_nonneg (fun x => (Real.exp_pos x).le) z.re
   refine' mul_le_mul_of_nonpos_left (mul_le_mul this _ _ ((Real.exp_pos _).le.trans this)) ha
   ·

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

@@ -55,33 +55,45 @@ open Set Filter
 
 namespace Complex
 
+#print Complex.continuous_sin /-
 @[continuity]
 theorem continuous_sin : Continuous sin := by
   change Continuous fun z => (exp (-z * I) - exp (z * I)) * I / 2; continuity
 #align complex.continuous_sin Complex.continuous_sin
+-/
 
+#print Complex.continuousOn_sin /-
 theorem continuousOn_sin {s : Set ℂ} : ContinuousOn sin s :=
   continuous_sin.ContinuousOn
 #align complex.continuous_on_sin Complex.continuousOn_sin
+-/
 
+#print Complex.continuous_cos /-
 @[continuity]
 theorem continuous_cos : Continuous cos := by
   change Continuous fun z => (exp (z * I) + exp (-z * I)) / 2; continuity
 #align complex.continuous_cos Complex.continuous_cos
+-/
 
+#print Complex.continuousOn_cos /-
 theorem continuousOn_cos {s : Set ℂ} : ContinuousOn cos s :=
   continuous_cos.ContinuousOn
 #align complex.continuous_on_cos Complex.continuousOn_cos
+-/
 
+#print Complex.continuous_sinh /-
 @[continuity]
 theorem continuous_sinh : Continuous sinh := by change Continuous fun z => (exp z - exp (-z)) / 2;
   continuity
 #align complex.continuous_sinh Complex.continuous_sinh
+-/
 
+#print Complex.continuous_cosh /-
 @[continuity]
 theorem continuous_cosh : Continuous cosh := by change Continuous fun z => (exp z + exp (-z)) / 2;
   continuity
 #align complex.continuous_cosh Complex.continuous_cosh
+-/
 
 end Complex
 
@@ -133,10 +145,12 @@ end Real
 
 namespace Real
 
+#print Real.exists_cos_eq_zero /-
 theorem exists_cos_eq_zero : 0 ∈ cos '' Icc (1 : ℝ) 2 :=
   intermediate_value_Icc' (by norm_num) continuousOn_cos
     ⟨le_of_lt cos_two_neg, le_of_lt cos_one_pos⟩
 #align real.exists_cos_eq_zero Real.exists_cos_eq_zero
+-/
 
 #print Real.pi /-
 /-- The number π = 3.14159265... Defined here using choice as twice a zero of cos in [1,2], from
@@ -146,7 +160,6 @@ protected noncomputable def pi : ℝ :=
 #align real.pi Real.pi
 -/
 
--- mathport name: real.pi
 scoped notation "π" => Real.pi
 
 #print Real.cos_pi_div_two /-
@@ -157,42 +170,58 @@ theorem cos_pi_div_two : cos (π / 2) = 0 := by
 #align real.cos_pi_div_two Real.cos_pi_div_two
 -/
 
+#print Real.one_le_pi_div_two /-
 theorem one_le_pi_div_two : (1 : ℝ) ≤ π / 2 := by
   rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)] <;>
     exact (Classical.choose_spec exists_cos_eq_zero).1.1
 #align real.one_le_pi_div_two Real.one_le_pi_div_two
+-/
 
+#print Real.pi_div_two_le_two /-
 theorem pi_div_two_le_two : π / 2 ≤ 2 := by
   rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)] <;>
     exact (Classical.choose_spec exists_cos_eq_zero).1.2
 #align real.pi_div_two_le_two Real.pi_div_two_le_two
+-/
 
+#print Real.two_le_pi /-
 theorem two_le_pi : (2 : ℝ) ≤ π :=
   (div_le_div_right (show (0 : ℝ) < 2 by norm_num)).1
     (by rw [div_self (two_ne_zero' ℝ)] <;> exact one_le_pi_div_two)
 #align real.two_le_pi Real.two_le_pi
+-/
 
+#print Real.pi_le_four /-
 theorem pi_le_four : π ≤ 4 :=
   (div_le_div_right (show (0 : ℝ) < 2 by norm_num)).1
     (calc
       π / 2 ≤ 2 := pi_div_two_le_two
       _ = 4 / 2 := by norm_num)
 #align real.pi_le_four Real.pi_le_four
+-/
 
+#print Real.pi_pos /-
 theorem pi_pos : 0 < π :=
   lt_of_lt_of_le (by norm_num) two_le_pi
 #align real.pi_pos Real.pi_pos
+-/
 
+#print Real.pi_ne_zero /-
 theorem pi_ne_zero : π ≠ 0 :=
   ne_of_gt pi_pos
 #align real.pi_ne_zero Real.pi_ne_zero
+-/
 
+#print Real.pi_div_two_pos /-
 theorem pi_div_two_pos : 0 < π / 2 :=
   half_pos pi_pos
 #align real.pi_div_two_pos Real.pi_div_two_pos
+-/
 
+#print Real.two_pi_pos /-
 theorem two_pi_pos : 0 < 2 * π := by linarith [pi_pos]
 #align real.two_pi_pos Real.two_pi_pos
+-/
 
 end Real
 
@@ -209,17 +238,23 @@ noncomputable def pi : ℝ≥0 :=
 #align nnreal.pi NNReal.pi
 -/
 
+#print NNReal.coe_real_pi /-
 @[simp]
 theorem coe_real_pi : (pi : ℝ) = π :=
   rfl
 #align nnreal.coe_real_pi NNReal.coe_real_pi
+-/
 
+#print NNReal.pi_pos /-
 theorem pi_pos : 0 < pi := by exact_mod_cast Real.pi_pos
 #align nnreal.pi_pos NNReal.pi_pos
+-/
 
+#print NNReal.pi_ne_zero /-
 theorem pi_ne_zero : pi ≠ 0 :=
   pi_pos.ne'
 #align nnreal.pi_ne_zero NNReal.pi_ne_zero
+-/
 
 end NNReal
 
@@ -227,16 +262,20 @@ namespace Real
 
 open scoped Real
 
+#print Real.sin_pi /-
 @[simp]
 theorem sin_pi : sin π = 0 := by
   rw [← mul_div_cancel_left π (two_ne_zero' ℝ), two_mul, add_div, sin_add, cos_pi_div_two] <;> simp
 #align real.sin_pi Real.sin_pi
+-/
 
+#print Real.cos_pi /-
 @[simp]
 theorem cos_pi : cos π = -1 := by
   rw [← mul_div_cancel_left π (two_ne_zero' ℝ), mul_div_assoc, cos_two_mul, cos_pi_div_two] <;>
     simp [bit0, pow_add]
 #align real.cos_pi Real.cos_pi
+-/
 
 #print Real.sin_two_pi /-
 @[simp]
@@ -496,6 +535,7 @@ theorem cos_int_mul_two_pi_sub_pi (n : ℤ) : cos (n * (2 * π) - π) = -1 := by
 #align real.cos_int_mul_two_pi_sub_pi Real.cos_int_mul_two_pi_sub_pi
 -/
 
+#print Real.sin_pos_of_pos_of_lt_pi /-
 theorem sin_pos_of_pos_of_lt_pi {x : ℝ} (h0x : 0 < x) (hxp : x < π) : 0 < sin x :=
   if hx2 : x ≤ 2 then sin_pos_of_pos_of_le_two h0x hx2
   else
@@ -504,11 +544,15 @@ theorem sin_pos_of_pos_of_lt_pi {x : ℝ} (h0x : 0 < x) (hxp : x < π) : 0 < sin
       sub_le_iff_le_add.2 (le_trans pi_le_four (this ▸ add_le_add_left (le_of_not_ge hx2) _))
     sin_pi_sub x ▸ sin_pos_of_pos_of_le_two (sub_pos.2 hxp) this
 #align real.sin_pos_of_pos_of_lt_pi Real.sin_pos_of_pos_of_lt_pi
+-/
 
+#print Real.sin_pos_of_mem_Ioo /-
 theorem sin_pos_of_mem_Ioo {x : ℝ} (hx : x ∈ Ioo 0 π) : 0 < sin x :=
   sin_pos_of_pos_of_lt_pi hx.1 hx.2
 #align real.sin_pos_of_mem_Ioo Real.sin_pos_of_mem_Ioo
+-/
 
+#print Real.sin_nonneg_of_mem_Icc /-
 theorem sin_nonneg_of_mem_Icc {x : ℝ} (hx : x ∈ Icc 0 π) : 0 ≤ sin x :=
   by
   rw [← closure_Ioo pi_ne_zero.symm] at hx 
@@ -516,18 +560,25 @@ theorem sin_nonneg_of_mem_Icc {x : ℝ} (hx : x ∈ Icc 0 π) : 0 ≤ sin x :=
     closure_lt_subset_le continuous_const continuous_sin
       (closure_mono (fun y => sin_pos_of_mem_Ioo) hx)
 #align real.sin_nonneg_of_mem_Icc Real.sin_nonneg_of_mem_Icc
+-/
 
+#print Real.sin_nonneg_of_nonneg_of_le_pi /-
 theorem sin_nonneg_of_nonneg_of_le_pi {x : ℝ} (h0x : 0 ≤ x) (hxp : x ≤ π) : 0 ≤ sin x :=
   sin_nonneg_of_mem_Icc ⟨h0x, hxp⟩
 #align real.sin_nonneg_of_nonneg_of_le_pi Real.sin_nonneg_of_nonneg_of_le_pi
+-/
 
+#print Real.sin_neg_of_neg_of_neg_pi_lt /-
 theorem sin_neg_of_neg_of_neg_pi_lt {x : ℝ} (hx0 : x < 0) (hpx : -π < x) : sin x < 0 :=
   neg_pos.1 <| sin_neg x ▸ sin_pos_of_pos_of_lt_pi (neg_pos.2 hx0) (neg_lt.1 hpx)
 #align real.sin_neg_of_neg_of_neg_pi_lt Real.sin_neg_of_neg_of_neg_pi_lt
+-/
 
+#print Real.sin_nonpos_of_nonnpos_of_neg_pi_le /-
 theorem sin_nonpos_of_nonnpos_of_neg_pi_le {x : ℝ} (hx0 : x ≤ 0) (hpx : -π ≤ x) : sin x ≤ 0 :=
   neg_nonneg.1 <| sin_neg x ▸ sin_nonneg_of_nonneg_of_le_pi (neg_nonneg.2 hx0) (neg_le.1 hpx)
 #align real.sin_nonpos_of_nonnpos_of_neg_pi_le Real.sin_nonpos_of_nonnpos_of_neg_pi_le
+-/
 
 #print Real.sin_pi_div_two /-
 @[simp]
@@ -571,39 +622,54 @@ theorem cos_pi_div_two_sub (x : ℝ) : cos (π / 2 - x) = sin x := by
 #align real.cos_pi_div_two_sub Real.cos_pi_div_two_sub
 -/
 
+#print Real.cos_pos_of_mem_Ioo /-
 theorem cos_pos_of_mem_Ioo {x : ℝ} (hx : x ∈ Ioo (-(π / 2)) (π / 2)) : 0 < cos x :=
   sin_add_pi_div_two x ▸ sin_pos_of_mem_Ioo ⟨by linarith [hx.1], by linarith [hx.2]⟩
 #align real.cos_pos_of_mem_Ioo Real.cos_pos_of_mem_Ioo
+-/
 
+#print Real.cos_nonneg_of_mem_Icc /-
 theorem cos_nonneg_of_mem_Icc {x : ℝ} (hx : x ∈ Icc (-(π / 2)) (π / 2)) : 0 ≤ cos x :=
   sin_add_pi_div_two x ▸ sin_nonneg_of_mem_Icc ⟨by linarith [hx.1], by linarith [hx.2]⟩
 #align real.cos_nonneg_of_mem_Icc Real.cos_nonneg_of_mem_Icc
+-/
 
+#print Real.cos_nonneg_of_neg_pi_div_two_le_of_le /-
 theorem cos_nonneg_of_neg_pi_div_two_le_of_le {x : ℝ} (hl : -(π / 2) ≤ x) (hu : x ≤ π / 2) :
     0 ≤ cos x :=
   cos_nonneg_of_mem_Icc ⟨hl, hu⟩
 #align real.cos_nonneg_of_neg_pi_div_two_le_of_le Real.cos_nonneg_of_neg_pi_div_two_le_of_le
+-/
 
+#print Real.cos_neg_of_pi_div_two_lt_of_lt /-
 theorem cos_neg_of_pi_div_two_lt_of_lt {x : ℝ} (hx₁ : π / 2 < x) (hx₂ : x < π + π / 2) :
     cos x < 0 :=
   neg_pos.1 <| cos_pi_sub x ▸ cos_pos_of_mem_Ioo ⟨by linarith, by linarith⟩
 #align real.cos_neg_of_pi_div_two_lt_of_lt Real.cos_neg_of_pi_div_two_lt_of_lt
+-/
 
+#print Real.cos_nonpos_of_pi_div_two_le_of_le /-
 theorem cos_nonpos_of_pi_div_two_le_of_le {x : ℝ} (hx₁ : π / 2 ≤ x) (hx₂ : x ≤ π + π / 2) :
     cos x ≤ 0 :=
   neg_nonneg.1 <| cos_pi_sub x ▸ cos_nonneg_of_mem_Icc ⟨by linarith, by linarith⟩
 #align real.cos_nonpos_of_pi_div_two_le_of_le Real.cos_nonpos_of_pi_div_two_le_of_le
+-/
 
+#print Real.sin_eq_sqrt_one_sub_cos_sq /-
 theorem sin_eq_sqrt_one_sub_cos_sq {x : ℝ} (hl : 0 ≤ x) (hu : x ≤ π) :
     sin x = sqrt (1 - cos x ^ 2) := by
   rw [← abs_sin_eq_sqrt_one_sub_cos_sq, abs_of_nonneg (sin_nonneg_of_nonneg_of_le_pi hl hu)]
 #align real.sin_eq_sqrt_one_sub_cos_sq Real.sin_eq_sqrt_one_sub_cos_sq
+-/
 
+#print Real.cos_eq_sqrt_one_sub_sin_sq /-
 theorem cos_eq_sqrt_one_sub_sin_sq {x : ℝ} (hl : -(π / 2) ≤ x) (hu : x ≤ π / 2) :
     cos x = sqrt (1 - sin x ^ 2) := by
   rw [← abs_cos_eq_sqrt_one_sub_sin_sq, abs_of_nonneg (cos_nonneg_of_mem_Icc ⟨hl, hu⟩)]
 #align real.cos_eq_sqrt_one_sub_sin_sq Real.cos_eq_sqrt_one_sub_sin_sq
+-/
 
+#print Real.sin_eq_zero_iff_of_lt_of_lt /-
 theorem sin_eq_zero_iff_of_lt_of_lt {x : ℝ} (hx₁ : -π < x) (hx₂ : x < π) : sin x = 0 ↔ x = 0 :=
   ⟨fun h =>
     le_antisymm
@@ -619,7 +685,9 @@ theorem sin_eq_zero_iff_of_lt_of_lt {x : ℝ} (hx₁ : -π < x) (hx₂ : x < π)
             _ < 0 := sin_neg_of_neg_of_neg_pi_lt h0 hx₁),
     fun h => by simp [h]⟩
 #align real.sin_eq_zero_iff_of_lt_of_lt Real.sin_eq_zero_iff_of_lt_of_lt
+-/
 
+#print Real.sin_eq_zero_iff /-
 theorem sin_eq_zero_iff {x : ℝ} : sin x = 0 ↔ ∃ n : ℤ, (n : ℝ) * π = x :=
   ⟨fun h =>
     ⟨⌊x / π⌋,
@@ -630,16 +698,22 @@ theorem sin_eq_zero_iff {x : ℝ} : sin x = 0 ↔ ∃ n : ℤ, (n : ℝ) * π =
               (by simp [sub_eq_add_neg, sin_add, h, sin_int_mul_pi]))⟩,
     fun ⟨n, hn⟩ => hn ▸ sin_int_mul_pi _⟩
 #align real.sin_eq_zero_iff Real.sin_eq_zero_iff
+-/
 
+#print Real.sin_ne_zero_iff /-
 theorem sin_ne_zero_iff {x : ℝ} : sin x ≠ 0 ↔ ∀ n : ℤ, (n : ℝ) * π ≠ x := by
   rw [← not_exists, not_iff_not, sin_eq_zero_iff]
 #align real.sin_ne_zero_iff Real.sin_ne_zero_iff
+-/
 
+#print Real.sin_eq_zero_iff_cos_eq /-
 theorem sin_eq_zero_iff_cos_eq {x : ℝ} : sin x = 0 ↔ cos x = 1 ∨ cos x = -1 := by
   rw [← mul_self_eq_one_iff, ← sin_sq_add_cos_sq x, sq, sq, ← sub_eq_iff_eq_add, sub_self] <;>
     exact ⟨fun h => by rw [h, MulZeroClass.mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
 #align real.sin_eq_zero_iff_cos_eq Real.sin_eq_zero_iff_cos_eq
+-/
 
+#print Real.cos_eq_one_iff /-
 theorem cos_eq_one_iff (x : ℝ) : cos x = 1 ↔ ∃ n : ℤ, (n : ℝ) * (2 * π) = x :=
   ⟨fun h =>
     let ⟨n, hn⟩ := sin_eq_zero_iff.1 (sin_eq_zero_iff_cos_eq.2 (Or.inl h))
@@ -655,7 +729,9 @@ theorem cos_eq_one_iff (x : ℝ) : cos x = 1 ↔ ∃ n : ℤ, (n : ℝ) * (2 * 
           exact absurd h (by norm_num)⟩,
     fun ⟨n, hn⟩ => hn ▸ cos_int_mul_two_pi _⟩
 #align real.cos_eq_one_iff Real.cos_eq_one_iff
+-/
 
+#print Real.cos_eq_one_iff_of_lt_of_lt /-
 theorem cos_eq_one_iff_of_lt_of_lt {x : ℝ} (hx₁ : -(2 * π) < x) (hx₂ : x < 2 * π) :
     cos x = 1 ↔ x = 0 :=
   ⟨fun h => by
@@ -666,7 +742,9 @@ theorem cos_eq_one_iff_of_lt_of_lt {x : ℝ} (hx₁ : -(2 * π) < x) (hx₂ : x
     obtain rfl : n = 0 := le_antisymm (by linarith) (by linarith)
     simp, fun h => by simp [h]⟩
 #align real.cos_eq_one_iff_of_lt_of_lt Real.cos_eq_one_iff_of_lt_of_lt
+-/
 
+#print Real.cos_lt_cos_of_nonneg_of_le_pi_div_two /-
 theorem cos_lt_cos_of_nonneg_of_le_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y ≤ π / 2)
     (hxy : x < y) : cos y < cos x :=
   by
@@ -675,7 +753,9 @@ theorem cos_lt_cos_of_nonneg_of_le_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy
   have : 0 < sin ((y - x) / 2) := by refine' sin_pos_of_pos_of_lt_pi _ _ <;> linarith
   nlinarith
 #align real.cos_lt_cos_of_nonneg_of_le_pi_div_two Real.cos_lt_cos_of_nonneg_of_le_pi_div_two
+-/
 
+#print Real.cos_lt_cos_of_nonneg_of_le_pi /-
 theorem cos_lt_cos_of_nonneg_of_le_pi {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y ≤ π) (hxy : x < y) :
     cos y < cos x :=
   match (le_total x (π / 2) : x ≤ π / 2 ∨ π / 2 ≤ x), le_total y (π / 2) with
@@ -697,80 +777,115 @@ theorem cos_lt_cos_of_nonneg_of_le_pi {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y 
         rw [← cos_pi_sub, ← cos_pi_sub] <;> apply cos_lt_cos_of_nonneg_of_le_pi_div_two <;>
           linarith)
 #align real.cos_lt_cos_of_nonneg_of_le_pi Real.cos_lt_cos_of_nonneg_of_le_pi
+-/
 
+#print Real.strictAntiOn_cos /-
 theorem strictAntiOn_cos : StrictAntiOn cos (Icc 0 π) := fun x hx y hy hxy =>
   cos_lt_cos_of_nonneg_of_le_pi hx.1 hy.2 hxy
 #align real.strict_anti_on_cos Real.strictAntiOn_cos
+-/
 
+#print Real.cos_le_cos_of_nonneg_of_le_pi /-
 theorem cos_le_cos_of_nonneg_of_le_pi {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y ≤ π) (hxy : x ≤ y) :
     cos y ≤ cos x :=
   (strictAntiOn_cos.le_iff_le ⟨hx₁.trans hxy, hy₂⟩ ⟨hx₁, hxy.trans hy₂⟩).2 hxy
 #align real.cos_le_cos_of_nonneg_of_le_pi Real.cos_le_cos_of_nonneg_of_le_pi
+-/
 
+#print Real.sin_lt_sin_of_lt_of_le_pi_div_two /-
 theorem sin_lt_sin_of_lt_of_le_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) ≤ x) (hy₂ : y ≤ π / 2)
     (hxy : x < y) : sin x < sin y := by
   rw [← cos_sub_pi_div_two, ← cos_sub_pi_div_two, ← cos_neg (x - _), ← cos_neg (y - _)] <;>
       apply cos_lt_cos_of_nonneg_of_le_pi <;>
     linarith
 #align real.sin_lt_sin_of_lt_of_le_pi_div_two Real.sin_lt_sin_of_lt_of_le_pi_div_two
+-/
 
+#print Real.strictMonoOn_sin /-
 theorem strictMonoOn_sin : StrictMonoOn sin (Icc (-(π / 2)) (π / 2)) := fun x hx y hy hxy =>
   sin_lt_sin_of_lt_of_le_pi_div_two hx.1 hy.2 hxy
 #align real.strict_mono_on_sin Real.strictMonoOn_sin
+-/
 
+#print Real.sin_le_sin_of_le_of_le_pi_div_two /-
 theorem sin_le_sin_of_le_of_le_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) ≤ x) (hy₂ : y ≤ π / 2)
     (hxy : x ≤ y) : sin x ≤ sin y :=
   (strictMonoOn_sin.le_iff_le ⟨hx₁, hxy.trans hy₂⟩ ⟨hx₁.trans hxy, hy₂⟩).2 hxy
 #align real.sin_le_sin_of_le_of_le_pi_div_two Real.sin_le_sin_of_le_of_le_pi_div_two
+-/
 
+#print Real.injOn_sin /-
 theorem injOn_sin : InjOn sin (Icc (-(π / 2)) (π / 2)) :=
   strictMonoOn_sin.InjOn
 #align real.inj_on_sin Real.injOn_sin
+-/
 
+#print Real.injOn_cos /-
 theorem injOn_cos : InjOn cos (Icc 0 π) :=
   strictAntiOn_cos.InjOn
 #align real.inj_on_cos Real.injOn_cos
+-/
 
+#print Real.surjOn_sin /-
 theorem surjOn_sin : SurjOn sin (Icc (-(π / 2)) (π / 2)) (Icc (-1) 1) := by
   simpa only [sin_neg, sin_pi_div_two] using
     intermediate_value_Icc (neg_le_self pi_div_two_pos.le) continuous_sin.continuous_on
 #align real.surj_on_sin Real.surjOn_sin
+-/
 
+#print Real.surjOn_cos /-
 theorem surjOn_cos : SurjOn cos (Icc 0 π) (Icc (-1) 1) := by
   simpa only [cos_zero, cos_pi] using intermediate_value_Icc' pi_pos.le continuous_cos.continuous_on
 #align real.surj_on_cos Real.surjOn_cos
+-/
 
+#print Real.sin_mem_Icc /-
 theorem sin_mem_Icc (x : ℝ) : sin x ∈ Icc (-1 : ℝ) 1 :=
   ⟨neg_one_le_sin x, sin_le_one x⟩
 #align real.sin_mem_Icc Real.sin_mem_Icc
+-/
 
+#print Real.cos_mem_Icc /-
 theorem cos_mem_Icc (x : ℝ) : cos x ∈ Icc (-1 : ℝ) 1 :=
   ⟨neg_one_le_cos x, cos_le_one x⟩
 #align real.cos_mem_Icc Real.cos_mem_Icc
+-/
 
+#print Real.mapsTo_sin /-
 theorem mapsTo_sin (s : Set ℝ) : MapsTo sin s (Icc (-1 : ℝ) 1) := fun x _ => sin_mem_Icc x
 #align real.maps_to_sin Real.mapsTo_sin
+-/
 
+#print Real.mapsTo_cos /-
 theorem mapsTo_cos (s : Set ℝ) : MapsTo cos s (Icc (-1 : ℝ) 1) := fun x _ => cos_mem_Icc x
 #align real.maps_to_cos Real.mapsTo_cos
+-/
 
+#print Real.bijOn_sin /-
 theorem bijOn_sin : BijOn sin (Icc (-(π / 2)) (π / 2)) (Icc (-1) 1) :=
   ⟨mapsTo_sin _, injOn_sin, surjOn_sin⟩
 #align real.bij_on_sin Real.bijOn_sin
+-/
 
+#print Real.bijOn_cos /-
 theorem bijOn_cos : BijOn cos (Icc 0 π) (Icc (-1) 1) :=
   ⟨mapsTo_cos _, injOn_cos, surjOn_cos⟩
 #align real.bij_on_cos Real.bijOn_cos
+-/
 
+#print Real.range_cos /-
 @[simp]
 theorem range_cos : range cos = (Icc (-1) 1 : Set ℝ) :=
   Subset.antisymm (range_subset_iff.2 cos_mem_Icc) surjOn_cos.subset_range
 #align real.range_cos Real.range_cos
+-/
 
+#print Real.range_sin /-
 @[simp]
 theorem range_sin : range sin = (Icc (-1) 1 : Set ℝ) :=
   Subset.antisymm (range_subset_iff.2 sin_mem_Icc) surjOn_sin.subset_range
 #align real.range_sin Real.range_sin
+-/
 
 #print Real.range_cos_infinite /-
 theorem range_cos_infinite : (range Real.cos).Infinite := by rw [Real.range_cos];
@@ -804,22 +919,31 @@ theorem sqrtTwoAddSeries_zero : sqrtTwoAddSeries x 0 = x := by simp
 #align real.sqrt_two_add_series_zero Real.sqrtTwoAddSeries_zero
 -/
 
+#print Real.sqrtTwoAddSeries_one /-
 theorem sqrtTwoAddSeries_one : sqrtTwoAddSeries 0 1 = sqrt 2 := by simp
 #align real.sqrt_two_add_series_one Real.sqrtTwoAddSeries_one
+-/
 
+#print Real.sqrtTwoAddSeries_two /-
 theorem sqrtTwoAddSeries_two : sqrtTwoAddSeries 0 2 = sqrt (2 + sqrt 2) := by simp
 #align real.sqrt_two_add_series_two Real.sqrtTwoAddSeries_two
+-/
 
+#print Real.sqrtTwoAddSeries_zero_nonneg /-
 theorem sqrtTwoAddSeries_zero_nonneg : ∀ n : ℕ, 0 ≤ sqrtTwoAddSeries 0 n
   | 0 => le_refl 0
   | n + 1 => sqrt_nonneg _
 #align real.sqrt_two_add_series_zero_nonneg Real.sqrtTwoAddSeries_zero_nonneg
+-/
 
+#print Real.sqrtTwoAddSeries_nonneg /-
 theorem sqrtTwoAddSeries_nonneg {x : ℝ} (h : 0 ≤ x) : ∀ n : ℕ, 0 ≤ sqrtTwoAddSeries x n
   | 0 => h
   | n + 1 => sqrt_nonneg _
 #align real.sqrt_two_add_series_nonneg Real.sqrtTwoAddSeries_nonneg
+-/
 
+#print Real.sqrtTwoAddSeries_lt_two /-
 theorem sqrtTwoAddSeries_lt_two : ∀ n : ℕ, sqrtTwoAddSeries 0 n < 2
   | 0 => by norm_num
   | n + 1 => by
@@ -828,13 +952,17 @@ theorem sqrtTwoAddSeries_lt_two : ∀ n : ℕ, sqrtTwoAddSeries 0 n < 2
     · refine' (sqrt_two_add_series_lt_two n).trans_le _; norm_num
     · exact add_nonneg zero_le_two (sqrt_two_add_series_zero_nonneg n)
 #align real.sqrt_two_add_series_lt_two Real.sqrtTwoAddSeries_lt_two
+-/
 
+#print Real.sqrtTwoAddSeries_succ /-
 theorem sqrtTwoAddSeries_succ (x : ℝ) :
     ∀ n : ℕ, sqrtTwoAddSeries x (n + 1) = sqrtTwoAddSeries (sqrt (2 + x)) n
   | 0 => rfl
   | n + 1 => by rw [sqrt_two_add_series, sqrt_two_add_series_succ, sqrt_two_add_series]
 #align real.sqrt_two_add_series_succ Real.sqrtTwoAddSeries_succ
+-/
 
+#print Real.sqrtTwoAddSeries_monotone_left /-
 theorem sqrtTwoAddSeries_monotone_left {x y : ℝ} (h : x ≤ y) :
     ∀ n : ℕ, sqrtTwoAddSeries x n ≤ sqrtTwoAddSeries y n
   | 0 => h
@@ -842,6 +970,7 @@ theorem sqrtTwoAddSeries_monotone_left {x y : ℝ} (h : x ≤ y) :
     rw [sqrt_two_add_series, sqrt_two_add_series]
     exact sqrt_le_sqrt (add_le_add_left (sqrt_two_add_series_monotone_left _) _)
 #align real.sqrt_two_add_series_monotone_left Real.sqrtTwoAddSeries_monotone_left
+-/
 
 #print Real.cos_pi_over_two_pow /-
 @[simp]
@@ -866,17 +995,21 @@ theorem cos_pi_over_two_pow : ∀ n : ℕ, cos (π / 2 ^ (n + 1)) = sqrtTwoAddSe
 #align real.cos_pi_over_two_pow Real.cos_pi_over_two_pow
 -/
 
+#print Real.sin_sq_pi_over_two_pow /-
 theorem sin_sq_pi_over_two_pow (n : ℕ) :
     sin (π / 2 ^ (n + 1)) ^ 2 = 1 - (sqrtTwoAddSeries 0 n / 2) ^ 2 := by
   rw [sin_sq, cos_pi_over_two_pow]
 #align real.sin_sq_pi_over_two_pow Real.sin_sq_pi_over_two_pow
+-/
 
+#print Real.sin_sq_pi_over_two_pow_succ /-
 theorem sin_sq_pi_over_two_pow_succ (n : ℕ) :
     sin (π / 2 ^ (n + 2)) ^ 2 = 1 / 2 - sqrtTwoAddSeries 0 n / 4 :=
   by
   rw [sin_sq_pi_over_two_pow, sqrt_two_add_series, div_pow, sq_sqrt, add_div, ← sub_sub]
   congr; norm_num; norm_num; apply add_nonneg; norm_num; apply sqrt_two_add_series_zero_nonneg
 #align real.sin_sq_pi_over_two_pow_succ Real.sin_sq_pi_over_two_pow_succ
+-/
 
 #print Real.sin_pi_over_two_pow_succ /-
 @[simp]
@@ -970,6 +1103,7 @@ theorem cos_pi_div_three : cos (π / 3) = 1 / 2 :=
 #align real.cos_pi_div_three Real.cos_pi_div_three
 -/
 
+#print Real.sq_cos_pi_div_six /-
 /-- The square of the cosine of `π / 6` is `3 / 4` (this is sometimes more convenient than the
 result for cosine itself). -/
 theorem sq_cos_pi_div_six : cos (π / 6) ^ 2 = 3 / 4 :=
@@ -983,6 +1117,7 @@ theorem sq_cos_pi_div_six : cos (π / 6) ^ 2 = 3 / 4 :=
   convert h1 using 1
   ring
 #align real.sq_cos_pi_div_six Real.sq_cos_pi_div_six
+-/
 
 #print Real.cos_pi_div_six /-
 /-- The cosine of `π / 6` is `√3 / 2`. -/
@@ -1012,6 +1147,7 @@ theorem sin_pi_div_six : sin (π / 6) = 1 / 2 :=
 #align real.sin_pi_div_six Real.sin_pi_div_six
 -/
 
+#print Real.sq_sin_pi_div_three /-
 /-- The square of the sine of `π / 3` is `3 / 4` (this is sometimes more convenient than the
 result for cosine itself). -/
 theorem sq_sin_pi_div_three : sin (π / 3) ^ 2 = 3 / 4 :=
@@ -1020,6 +1156,7 @@ theorem sq_sin_pi_div_three : sin (π / 3) ^ 2 = 3 / 4 :=
   congr
   ring
 #align real.sq_sin_pi_div_three Real.sq_sin_pi_div_three
+-/
 
 #print Real.sin_pi_div_three /-
 /-- The sine of `π / 3` is `√3 / 2`. -/
@@ -1034,19 +1171,25 @@ theorem sin_pi_div_three : sin (π / 3) = sqrt 3 / 2 :=
 
 end CosDivSq
 
+#print Real.sinOrderIso /-
 /-- `real.sin` as an `order_iso` between `[-(π / 2), π / 2]` and `[-1, 1]`. -/
 def sinOrderIso : Icc (-(π / 2)) (π / 2) ≃o Icc (-1 : ℝ) 1 :=
   (strictMonoOn_sin.OrderIso _ _).trans <| OrderIso.setCongr _ _ bijOn_sin.image_eq
 #align real.sin_order_iso Real.sinOrderIso
+-/
 
+#print Real.coe_sinOrderIso_apply /-
 @[simp]
 theorem coe_sinOrderIso_apply (x : Icc (-(π / 2)) (π / 2)) : (sinOrderIso x : ℝ) = sin x :=
   rfl
 #align real.coe_sin_order_iso_apply Real.coe_sinOrderIso_apply
+-/
 
+#print Real.sinOrderIso_apply /-
 theorem sinOrderIso_apply (x : Icc (-(π / 2)) (π / 2)) : sinOrderIso x = ⟨sin x, sin_mem_Icc x⟩ :=
   rfl
 #align real.sin_order_iso_apply Real.sinOrderIso_apply
+-/
 
 #print Real.tan_pi_div_four /-
 @[simp]
@@ -1064,28 +1207,37 @@ theorem tan_pi_div_two : tan (π / 2) = 0 := by simp [tan_eq_sin_div_cos]
 #align real.tan_pi_div_two Real.tan_pi_div_two
 -/
 
+#print Real.tan_pos_of_pos_of_lt_pi_div_two /-
 theorem tan_pos_of_pos_of_lt_pi_div_two {x : ℝ} (h0x : 0 < x) (hxp : x < π / 2) : 0 < tan x := by
   rw [tan_eq_sin_div_cos] <;>
     exact
       div_pos (sin_pos_of_pos_of_lt_pi h0x (by linarith)) (cos_pos_of_mem_Ioo ⟨by linarith, hxp⟩)
 #align real.tan_pos_of_pos_of_lt_pi_div_two Real.tan_pos_of_pos_of_lt_pi_div_two
+-/
 
+#print Real.tan_nonneg_of_nonneg_of_le_pi_div_two /-
 theorem tan_nonneg_of_nonneg_of_le_pi_div_two {x : ℝ} (h0x : 0 ≤ x) (hxp : x ≤ π / 2) : 0 ≤ tan x :=
   match lt_or_eq_of_le h0x, lt_or_eq_of_le hxp with
   | Or.inl hx0, Or.inl hxp => le_of_lt (tan_pos_of_pos_of_lt_pi_div_two hx0 hxp)
   | Or.inl hx0, Or.inr hxp => by simp [hxp, tan_eq_sin_div_cos]
   | Or.inr hx0, _ => by simp [hx0.symm]
 #align real.tan_nonneg_of_nonneg_of_le_pi_div_two Real.tan_nonneg_of_nonneg_of_le_pi_div_two
+-/
 
+#print Real.tan_neg_of_neg_of_pi_div_two_lt /-
 theorem tan_neg_of_neg_of_pi_div_two_lt {x : ℝ} (hx0 : x < 0) (hpx : -(π / 2) < x) : tan x < 0 :=
   neg_pos.1 (tan_neg x ▸ tan_pos_of_pos_of_lt_pi_div_two (by linarith) (by linarith [pi_pos]))
 #align real.tan_neg_of_neg_of_pi_div_two_lt Real.tan_neg_of_neg_of_pi_div_two_lt
+-/
 
+#print Real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le /-
 theorem tan_nonpos_of_nonpos_of_neg_pi_div_two_le {x : ℝ} (hx0 : x ≤ 0) (hpx : -(π / 2) ≤ x) :
     tan x ≤ 0 :=
   neg_nonneg.1 (tan_neg x ▸ tan_nonneg_of_nonneg_of_le_pi_div_two (by linarith) (by linarith))
 #align real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le Real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le
+-/
 
+#print Real.tan_lt_tan_of_nonneg_of_lt_pi_div_two /-
 theorem tan_lt_tan_of_nonneg_of_lt_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y < π / 2)
     (hxy : x < y) : tan x < tan y :=
   by
@@ -1096,7 +1248,9 @@ theorem tan_lt_tan_of_nonneg_of_lt_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy
       (sin_nonneg_of_nonneg_of_le_pi (by linarith) (by linarith))
       (cos_pos_of_mem_Ioo ⟨by linarith, hy₂⟩)
 #align real.tan_lt_tan_of_nonneg_of_lt_pi_div_two Real.tan_lt_tan_of_nonneg_of_lt_pi_div_two
+-/
 
+#print Real.tan_lt_tan_of_lt_of_lt_pi_div_two /-
 theorem tan_lt_tan_of_lt_of_lt_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) < x) (hy₂ : y < π / 2)
     (hxy : x < y) : tan x < tan y :=
   match le_total x 0, le_total y 0 with
@@ -1116,19 +1270,26 @@ theorem tan_lt_tan_of_lt_of_lt_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) < x) (h
   | Or.inr hx0, Or.inl hy0 => by linarith
   | Or.inr hx0, Or.inr hy0 => tan_lt_tan_of_nonneg_of_lt_pi_div_two hx0 hy₂ hxy
 #align real.tan_lt_tan_of_lt_of_lt_pi_div_two Real.tan_lt_tan_of_lt_of_lt_pi_div_two
+-/
 
+#print Real.strictMonoOn_tan /-
 theorem strictMonoOn_tan : StrictMonoOn tan (Ioo (-(π / 2)) (π / 2)) := fun x hx y hy =>
   tan_lt_tan_of_lt_of_lt_pi_div_two hx.1 hy.2
 #align real.strict_mono_on_tan Real.strictMonoOn_tan
+-/
 
+#print Real.injOn_tan /-
 theorem injOn_tan : InjOn tan (Ioo (-(π / 2)) (π / 2)) :=
   strictMonoOn_tan.InjOn
 #align real.inj_on_tan Real.injOn_tan
+-/
 
+#print Real.tan_inj_of_lt_of_lt_pi_div_two /-
 theorem tan_inj_of_lt_of_lt_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) < x) (hx₂ : x < π / 2)
     (hy₁ : -(π / 2) < y) (hy₂ : y < π / 2) (hxy : tan x = tan y) : x = y :=
   injOn_tan ⟨hx₁, hx₂⟩ ⟨hy₁, hy₂⟩ hxy
 #align real.tan_inj_of_lt_of_lt_pi_div_two Real.tan_inj_of_lt_of_lt_pi_div_two
+-/
 
 #print Real.tan_periodic /-
 theorem tan_periodic : Function.Periodic tan π := by
@@ -1208,10 +1369,13 @@ theorem tan_int_mul_pi_sub (x : ℝ) (n : ℤ) : tan (n * π - x) = -tan x :=
 #align real.tan_int_mul_pi_sub Real.tan_int_mul_pi_sub
 -/
 
+#print Real.tendsto_sin_pi_div_two /-
 theorem tendsto_sin_pi_div_two : Tendsto sin (𝓝[<] (π / 2)) (𝓝 1) := by
   convert continuous_sin.continuous_within_at; simp
 #align real.tendsto_sin_pi_div_two Real.tendsto_sin_pi_div_two
+-/
 
+#print Real.tendsto_cos_pi_div_two /-
 theorem tendsto_cos_pi_div_two : Tendsto cos (𝓝[<] (π / 2)) (𝓝[>] 0) :=
   by
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
@@ -1220,17 +1384,23 @@ theorem tendsto_cos_pi_div_two : Tendsto cos (𝓝[<] (π / 2)) (𝓝[>] 0) :=
     filter_upwards [Ioo_mem_nhdsWithin_Iio (right_mem_Ioc.mpr (neg_lt_self pi_div_two_pos))] with x
       hx using cos_pos_of_mem_Ioo hx
 #align real.tendsto_cos_pi_div_two Real.tendsto_cos_pi_div_two
+-/
 
+#print Real.tendsto_tan_pi_div_two /-
 theorem tendsto_tan_pi_div_two : Tendsto tan (𝓝[<] (π / 2)) atTop :=
   by
   convert tendsto_cos_pi_div_two.inv_tendsto_zero.at_top_mul zero_lt_one tendsto_sin_pi_div_two
   simp only [Pi.inv_apply, ← div_eq_inv_mul, ← tan_eq_sin_div_cos]
 #align real.tendsto_tan_pi_div_two Real.tendsto_tan_pi_div_two
+-/
 
+#print Real.tendsto_sin_neg_pi_div_two /-
 theorem tendsto_sin_neg_pi_div_two : Tendsto sin (𝓝[>] (-(π / 2))) (𝓝 (-1)) := by
   convert continuous_sin.continuous_within_at; simp
 #align real.tendsto_sin_neg_pi_div_two Real.tendsto_sin_neg_pi_div_two
+-/
 
+#print Real.tendsto_cos_neg_pi_div_two /-
 theorem tendsto_cos_neg_pi_div_two : Tendsto cos (𝓝[>] (-(π / 2))) (𝓝[>] 0) :=
   by
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
@@ -1239,7 +1409,9 @@ theorem tendsto_cos_neg_pi_div_two : Tendsto cos (𝓝[>] (-(π / 2))) (𝓝[>]
     filter_upwards [Ioo_mem_nhdsWithin_Ioi (left_mem_Ico.mpr (neg_lt_self pi_div_two_pos))] with x
       hx using cos_pos_of_mem_Ioo hx
 #align real.tendsto_cos_neg_pi_div_two Real.tendsto_cos_neg_pi_div_two
+-/
 
+#print Real.tendsto_tan_neg_pi_div_two /-
 theorem tendsto_tan_neg_pi_div_two : Tendsto tan (𝓝[>] (-(π / 2))) atBot :=
   by
   convert
@@ -1247,6 +1419,7 @@ theorem tendsto_tan_neg_pi_div_two : Tendsto tan (𝓝[>] (-(π / 2))) atBot :=
       tendsto_sin_neg_pi_div_two
   simp only [Pi.inv_apply, ← div_eq_inv_mul, ← tan_eq_sin_div_cos]
 #align real.tendsto_tan_neg_pi_div_two Real.tendsto_tan_neg_pi_div_two
+-/
 
 end Real
 
@@ -1254,10 +1427,12 @@ namespace Complex
 
 open scoped Real
 
+#print Complex.sin_eq_zero_iff_cos_eq /-
 theorem sin_eq_zero_iff_cos_eq {z : ℂ} : sin z = 0 ↔ cos z = 1 ∨ cos z = -1 := by
   rw [← mul_self_eq_one_iff, ← sin_sq_add_cos_sq, sq, sq, ← sub_eq_iff_eq_add, sub_self] <;>
     exact ⟨fun h => by rw [h, MulZeroClass.mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
 #align complex.sin_eq_zero_iff_cos_eq Complex.sin_eq_zero_iff_cos_eq
+-/
 
 #print Complex.cos_pi_div_two /-
 @[simp]
@@ -1624,51 +1799,72 @@ theorem tan_int_mul_pi_sub (x : ℂ) (n : ℤ) : tan (n * π - x) = -tan x :=
 #align complex.tan_int_mul_pi_sub Complex.tan_int_mul_pi_sub
 -/
 
+#print Complex.exp_antiperiodic /-
 theorem exp_antiperiodic : Function.Antiperiodic exp (π * I) := by simp [exp_add, exp_mul_I]
 #align complex.exp_antiperiodic Complex.exp_antiperiodic
+-/
 
+#print Complex.exp_periodic /-
 theorem exp_periodic : Function.Periodic exp (2 * π * I) :=
   (mul_assoc (2 : ℂ) π I).symm ▸ exp_antiperiodic.Periodic
 #align complex.exp_periodic Complex.exp_periodic
+-/
 
+#print Complex.exp_mul_I_antiperiodic /-
 theorem exp_mul_I_antiperiodic : Function.Antiperiodic (fun x => exp (x * I)) π := by
   simpa only [mul_inv_cancel_right₀ I_ne_zero] using exp_antiperiodic.mul_const I_ne_zero
 #align complex.exp_mul_I_antiperiodic Complex.exp_mul_I_antiperiodic
+-/
 
+#print Complex.exp_mul_I_periodic /-
 theorem exp_mul_I_periodic : Function.Periodic (fun x => exp (x * I)) (2 * π) :=
   exp_mul_I_antiperiodic.Periodic
 #align complex.exp_mul_I_periodic Complex.exp_mul_I_periodic
+-/
 
+#print Complex.exp_pi_mul_I /-
 @[simp]
 theorem exp_pi_mul_I : exp (π * I) = -1 :=
   exp_zero ▸ exp_antiperiodic.Eq
 #align complex.exp_pi_mul_I Complex.exp_pi_mul_I
+-/
 
+#print Complex.exp_two_pi_mul_I /-
 @[simp]
 theorem exp_two_pi_mul_I : exp (2 * π * I) = 1 :=
   exp_periodic.Eq.trans exp_zero
 #align complex.exp_two_pi_mul_I Complex.exp_two_pi_mul_I
+-/
 
+#print Complex.exp_nat_mul_two_pi_mul_I /-
 @[simp]
 theorem exp_nat_mul_two_pi_mul_I (n : ℕ) : exp (n * (2 * π * I)) = 1 :=
   (exp_periodic.nat_mul_eq n).trans exp_zero
 #align complex.exp_nat_mul_two_pi_mul_I Complex.exp_nat_mul_two_pi_mul_I
+-/
 
+#print Complex.exp_int_mul_two_pi_mul_I /-
 @[simp]
 theorem exp_int_mul_two_pi_mul_I (n : ℤ) : exp (n * (2 * π * I)) = 1 :=
   (exp_periodic.int_mul_eq n).trans exp_zero
 #align complex.exp_int_mul_two_pi_mul_I Complex.exp_int_mul_two_pi_mul_I
+-/
 
+#print Complex.exp_add_pi_mul_I /-
 @[simp]
 theorem exp_add_pi_mul_I (z : ℂ) : exp (z + π * I) = -exp z :=
   exp_antiperiodic z
 #align complex.exp_add_pi_mul_I Complex.exp_add_pi_mul_I
+-/
 
+#print Complex.exp_sub_pi_mul_I /-
 @[simp]
 theorem exp_sub_pi_mul_I (z : ℂ) : exp (z - π * I) = -exp z :=
   exp_antiperiodic.sub_eq z
 #align complex.exp_sub_pi_mul_I Complex.exp_sub_pi_mul_I
+-/
 
+#print Complex.abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le /-
 /-- A supporting lemma for the **Phragmen-Lindelöf principle** in a horizontal strip. If `z : ℂ`
 belongs to a horizontal strip `|complex.im z| ≤ b`, `b ≤ π / 2`, and `a ≤ 0`, then
 $$\left|exp^{a\left(e^{z}+e^{-z}\right)}\right| \le e^{a\cos b \exp^{|re z|}}.$$
@@ -1689,6 +1885,7 @@ theorem abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le {a b : ℝ} (ha : a ≤ 0) {
   · refine' Real.cos_nonneg_of_mem_Icc ⟨_, hb⟩
     exact (neg_nonpos.2 <| real.pi_div_two_pos.le).trans ((_root_.abs_nonneg _).trans hz)
 #align complex.abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le Complex.abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le
+-/
 
 end Complex
 

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

@@ -176,8 +176,7 @@ theorem pi_le_four : π ≤ 4 :=
   (div_le_div_right (show (0 : ℝ) < 2 by norm_num)).1
     (calc
       π / 2 ≤ 2 := pi_div_two_le_two
-      _ = 4 / 2 := by norm_num
-      )
+      _ = 4 / 2 := by norm_num)
 #align real.pi_le_four Real.pi_le_four
 
 theorem pi_pos : 0 < π :=
@@ -612,14 +611,12 @@ theorem sin_eq_zero_iff_of_lt_of_lt {x : ℝ} (hx₁ : -π < x) (hx₂ : x < π)
         lt_irrefl (0 : ℝ) <|
           calc
             0 < sin x := sin_pos_of_pos_of_lt_pi h0 hx₂
-            _ = 0 := h
-            )
+            _ = 0 := h)
       (le_of_not_gt fun h0 =>
         lt_irrefl (0 : ℝ) <|
           calc
             0 = sin x := h.symm
-            _ < 0 := sin_neg_of_neg_of_neg_pi_lt h0 hx₁
-            ),
+            _ < 0 := sin_neg_of_neg_of_neg_pi_lt h0 hx₁),
     fun h => by simp [h]⟩
 #align real.sin_eq_zero_iff_of_lt_of_lt Real.sin_eq_zero_iff_of_lt_of_lt
 
@@ -688,13 +685,11 @@ theorem cos_lt_cos_of_nonneg_of_le_pi {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y 
       (fun hx =>
         calc
           cos y ≤ 0 := cos_nonpos_of_pi_div_two_le_of_le hy (by linarith [pi_pos])
-          _ < cos x := cos_pos_of_mem_Ioo ⟨by linarith, hx⟩
-          )
+          _ < cos x := cos_pos_of_mem_Ioo ⟨by linarith, hx⟩)
       fun hx =>
       calc
         cos y < 0 := cos_neg_of_pi_div_two_lt_of_lt (by linarith) (by linarith [pi_pos])
         _ = cos x := by rw [hx, cos_pi_div_two]
-        
   | Or.inr hx, Or.inl hy => by linarith
   | Or.inr hx, Or.inr hy =>
     neg_lt_neg_iff.1
@@ -1115,8 +1110,7 @@ theorem tan_lt_tan_of_lt_of_lt_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) < x) (h
       (fun hy0 =>
         calc
           tan x ≤ 0 := tan_nonpos_of_nonpos_of_neg_pi_div_two_le hx0 (le_of_lt hx₁)
-          _ < tan y := tan_pos_of_pos_of_lt_pi_div_two hy0 hy₂
-          )
+          _ < tan y := tan_pos_of_pos_of_lt_pi_div_two hy0 hy₂)
       fun hy0 => by
       rw [← hy0, tan_zero] <;> exact tan_neg_of_neg_of_pi_div_two_lt (hy0.symm ▸ hxy) hx₁
   | Or.inr hx0, Or.inl hy0 => by linarith
@@ -1271,7 +1265,6 @@ theorem cos_pi_div_two : cos (π / 2) = 0 :=
   calc
     cos (π / 2) = Real.cos (π / 2) := by rw [of_real_cos] <;> simp
     _ = 0 := by simp
-    
 #align complex.cos_pi_div_two Complex.cos_pi_div_two
 -/
 
@@ -1281,7 +1274,6 @@ theorem sin_pi_div_two : sin (π / 2) = 1 :=
   calc
     sin (π / 2) = Real.sin (π / 2) := by rw [of_real_sin] <;> simp
     _ = 1 := by simp
-    
 #align complex.sin_pi_div_two Complex.sin_pi_div_two
 -/
 

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

@@ -665,7 +665,7 @@ theorem cos_eq_one_iff_of_lt_of_lt {x : ℝ} (hx₁ : -(2 * π) < x) (hx₂ : x
     rcases(cos_eq_one_iff _).1 h with ⟨n, rfl⟩
     rw [mul_lt_iff_lt_one_left two_pi_pos] at hx₂ 
     rw [neg_lt, neg_mul_eq_neg_mul, mul_lt_iff_lt_one_left two_pi_pos] at hx₁ 
-    norm_cast  at hx₁ hx₂ 
+    norm_cast at hx₁ hx₂ 
     obtain rfl : n = 0 := le_antisymm (by linarith) (by linarith)
     simp, fun h => by simp [h]⟩
 #align real.cos_eq_one_iff_of_lt_of_lt Real.cos_eq_one_iff_of_lt_of_lt
@@ -1223,8 +1223,8 @@ theorem tendsto_cos_pi_div_two : Tendsto cos (𝓝[<] (π / 2)) (𝓝[>] 0) :=
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
   · convert continuous_cos.continuous_within_at; simp
   ·
-    filter_upwards [Ioo_mem_nhdsWithin_Iio
-        (right_mem_Ioc.mpr (neg_lt_self pi_div_two_pos))]with x hx using cos_pos_of_mem_Ioo hx
+    filter_upwards [Ioo_mem_nhdsWithin_Iio (right_mem_Ioc.mpr (neg_lt_self pi_div_two_pos))] with x
+      hx using cos_pos_of_mem_Ioo hx
 #align real.tendsto_cos_pi_div_two Real.tendsto_cos_pi_div_two
 
 theorem tendsto_tan_pi_div_two : Tendsto tan (𝓝[<] (π / 2)) atTop :=
@@ -1242,13 +1242,14 @@ theorem tendsto_cos_neg_pi_div_two : Tendsto cos (𝓝[>] (-(π / 2))) (𝓝[>]
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
   · convert continuous_cos.continuous_within_at; simp
   ·
-    filter_upwards [Ioo_mem_nhdsWithin_Ioi
-        (left_mem_Ico.mpr (neg_lt_self pi_div_two_pos))]with x hx using cos_pos_of_mem_Ioo hx
+    filter_upwards [Ioo_mem_nhdsWithin_Ioi (left_mem_Ico.mpr (neg_lt_self pi_div_two_pos))] with x
+      hx using cos_pos_of_mem_Ioo hx
 #align real.tendsto_cos_neg_pi_div_two Real.tendsto_cos_neg_pi_div_two
 
 theorem tendsto_tan_neg_pi_div_two : Tendsto tan (𝓝[>] (-(π / 2))) atBot :=
   by
-  convert tendsto_cos_neg_pi_div_two.inv_tendsto_zero.at_top_mul_neg (by norm_num)
+  convert
+    tendsto_cos_neg_pi_div_two.inv_tendsto_zero.at_top_mul_neg (by norm_num)
       tendsto_sin_neg_pi_div_two
   simp only [Pi.inv_apply, ← div_eq_inv_mul, ← tan_eq_sin_div_cos]
 #align real.tendsto_tan_neg_pi_div_two Real.tendsto_tan_neg_pi_div_two

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

@@ -512,7 +512,7 @@ theorem sin_pos_of_mem_Ioo {x : ℝ} (hx : x ∈ Ioo 0 π) : 0 < sin x :=
 
 theorem sin_nonneg_of_mem_Icc {x : ℝ} (hx : x ∈ Icc 0 π) : 0 ≤ sin x :=
   by
-  rw [← closure_Ioo pi_ne_zero.symm] at hx
+  rw [← closure_Ioo pi_ne_zero.symm] at hx 
   exact
     closure_lt_subset_le continuous_const continuous_sin
       (closure_mono (fun y => sin_pos_of_mem_Ioo) hx)
@@ -653,8 +653,8 @@ theorem cos_eq_one_iff (x : ℝ) : cos x = 1 ↔ ∃ n : ℤ, (n : ℝ) * (2 * 
             Int.ediv_mul_cancel ((Int.dvd_iff_emod_eq_zero _ _).2 hn0)])
         fun hn1 => by
         rw [← Int.emod_add_ediv n 2, hn1, Int.cast_add, Int.cast_one, add_mul, one_mul, add_comm,
-              mul_comm (2 : ℤ), Int.cast_mul, mul_assoc, Int.cast_two] at hn <;>
-            rw [← hn, cos_int_mul_two_pi_add_pi] at h <;>
+              mul_comm (2 : ℤ), Int.cast_mul, mul_assoc, Int.cast_two] at hn  <;>
+            rw [← hn, cos_int_mul_two_pi_add_pi] at h  <;>
           exact absurd h (by norm_num)⟩,
     fun ⟨n, hn⟩ => hn ▸ cos_int_mul_two_pi _⟩
 #align real.cos_eq_one_iff Real.cos_eq_one_iff
@@ -663,9 +663,9 @@ theorem cos_eq_one_iff_of_lt_of_lt {x : ℝ} (hx₁ : -(2 * π) < x) (hx₂ : x
     cos x = 1 ↔ x = 0 :=
   ⟨fun h => by
     rcases(cos_eq_one_iff _).1 h with ⟨n, rfl⟩
-    rw [mul_lt_iff_lt_one_left two_pi_pos] at hx₂
-    rw [neg_lt, neg_mul_eq_neg_mul, mul_lt_iff_lt_one_left two_pi_pos] at hx₁
-    norm_cast  at hx₁ hx₂
+    rw [mul_lt_iff_lt_one_left two_pi_pos] at hx₂ 
+    rw [neg_lt, neg_mul_eq_neg_mul, mul_lt_iff_lt_one_left two_pi_pos] at hx₁ 
+    norm_cast  at hx₁ hx₂ 
     obtain rfl : n = 0 := le_antisymm (by linarith) (by linarith)
     simp, fun h => by simp [h]⟩
 #align real.cos_eq_one_iff_of_lt_of_lt Real.cos_eq_one_iff_of_lt_of_lt
@@ -857,7 +857,7 @@ theorem cos_pi_over_two_pow : ∀ n : ℕ, cos (π / 2 ^ (n + 1)) = sqrtTwoAddSe
     symm; rw [div_eq_iff_mul_eq this]; symm
     rw [sqrt_two_add_series, sqrt_eq_iff_sq_eq, mul_pow, cos_sq, ← mul_div_assoc, Nat.add_succ,
       pow_succ, mul_div_mul_left _ _ this, cos_pi_over_two_pow, add_mul]
-    congr ; · norm_num
+    congr; · norm_num
     rw [mul_comm, sq, mul_assoc, ← mul_div_assoc, mul_div_cancel_left, ← mul_div_assoc,
         mul_div_cancel_left] <;>
       try exact this
@@ -880,7 +880,7 @@ theorem sin_sq_pi_over_two_pow_succ (n : ℕ) :
     sin (π / 2 ^ (n + 2)) ^ 2 = 1 / 2 - sqrtTwoAddSeries 0 n / 4 :=
   by
   rw [sin_sq_pi_over_two_pow, sqrt_two_add_series, div_pow, sq_sqrt, add_div, ← sub_sub]
-  congr ; norm_num; norm_num; apply add_nonneg; norm_num; apply sqrt_two_add_series_zero_nonneg
+  congr; norm_num; norm_num; apply add_nonneg; norm_num; apply sqrt_two_add_series_zero_nonneg
 #align real.sin_sq_pi_over_two_pow_succ Real.sin_sq_pi_over_two_pow_succ
 
 #print Real.sin_pi_over_two_pow_succ /-
@@ -890,7 +890,7 @@ theorem sin_pi_over_two_pow_succ (n : ℕ) :
   by
   symm; rw [div_eq_iff_mul_eq]; symm
   rw [sqrt_eq_iff_sq_eq, mul_pow, sin_sq_pi_over_two_pow_succ, sub_mul]
-  · congr ; norm_num; rw [mul_comm]; convert mul_div_cancel' _ _; norm_num; norm_num
+  · congr; norm_num; rw [mul_comm]; convert mul_div_cancel' _ _; norm_num; norm_num
   · rw [sub_nonneg]; apply le_of_lt; apply sqrt_two_add_series_lt_two
   apply le_of_lt; apply mul_pos; apply sin_pos_of_pos_of_lt_pi
   · apply div_pos pi_pos; apply pow_pos; norm_num
@@ -903,28 +903,28 @@ theorem sin_pi_over_two_pow_succ (n : ℕ) :
 
 #print Real.cos_pi_div_four /-
 @[simp]
-theorem cos_pi_div_four : cos (π / 4) = sqrt 2 / 2 := by trans cos (π / 2 ^ 2); congr ; norm_num;
+theorem cos_pi_div_four : cos (π / 4) = sqrt 2 / 2 := by trans cos (π / 2 ^ 2); congr; norm_num;
   simp
 #align real.cos_pi_div_four Real.cos_pi_div_four
 -/
 
 #print Real.sin_pi_div_four /-
 @[simp]
-theorem sin_pi_div_four : sin (π / 4) = sqrt 2 / 2 := by trans sin (π / 2 ^ 2); congr ; norm_num;
+theorem sin_pi_div_four : sin (π / 4) = sqrt 2 / 2 := by trans sin (π / 2 ^ 2); congr; norm_num;
   simp
 #align real.sin_pi_div_four Real.sin_pi_div_four
 -/
 
 #print Real.cos_pi_div_eight /-
 @[simp]
-theorem cos_pi_div_eight : cos (π / 8) = sqrt (2 + sqrt 2) / 2 := by trans cos (π / 2 ^ 3); congr ;
+theorem cos_pi_div_eight : cos (π / 8) = sqrt (2 + sqrt 2) / 2 := by trans cos (π / 2 ^ 3); congr;
   norm_num; simp
 #align real.cos_pi_div_eight Real.cos_pi_div_eight
 -/
 
 #print Real.sin_pi_div_eight /-
 @[simp]
-theorem sin_pi_div_eight : sin (π / 8) = sqrt (2 - sqrt 2) / 2 := by trans sin (π / 2 ^ 3); congr ;
+theorem sin_pi_div_eight : sin (π / 8) = sqrt (2 - sqrt 2) / 2 := by trans sin (π / 2 ^ 3); congr;
   norm_num; simp
 #align real.sin_pi_div_eight Real.sin_pi_div_eight
 -/
@@ -932,28 +932,28 @@ theorem sin_pi_div_eight : sin (π / 8) = sqrt (2 - sqrt 2) / 2 := by trans sin
 #print Real.cos_pi_div_sixteen /-
 @[simp]
 theorem cos_pi_div_sixteen : cos (π / 16) = sqrt (2 + sqrt (2 + sqrt 2)) / 2 := by
-  trans cos (π / 2 ^ 4); congr ; norm_num; simp
+  trans cos (π / 2 ^ 4); congr; norm_num; simp
 #align real.cos_pi_div_sixteen Real.cos_pi_div_sixteen
 -/
 
 #print Real.sin_pi_div_sixteen /-
 @[simp]
 theorem sin_pi_div_sixteen : sin (π / 16) = sqrt (2 - sqrt (2 + sqrt 2)) / 2 := by
-  trans sin (π / 2 ^ 4); congr ; norm_num; simp
+  trans sin (π / 2 ^ 4); congr; norm_num; simp
 #align real.sin_pi_div_sixteen Real.sin_pi_div_sixteen
 -/
 
 #print Real.cos_pi_div_thirty_two /-
 @[simp]
 theorem cos_pi_div_thirty_two : cos (π / 32) = sqrt (2 + sqrt (2 + sqrt (2 + sqrt 2))) / 2 := by
-  trans cos (π / 2 ^ 5); congr ; norm_num; simp
+  trans cos (π / 2 ^ 5); congr; norm_num; simp
 #align real.cos_pi_div_thirty_two Real.cos_pi_div_thirty_two
 -/
 
 #print Real.sin_pi_div_thirty_two /-
 @[simp]
 theorem sin_pi_div_thirty_two : sin (π / 32) = sqrt (2 - sqrt (2 + sqrt (2 + sqrt 2))) / 2 := by
-  trans sin (π / 2 ^ 5); congr ; norm_num; simp
+  trans sin (π / 2 ^ 5); congr; norm_num; simp
 #align real.sin_pi_div_thirty_two Real.sin_pi_div_thirty_two
 -/
 
@@ -984,7 +984,7 @@ theorem sq_cos_pi_div_six : cos (π / 6) ^ 2 = 3 / 4 :=
     convert cos_sq (π / 6)
     have h2 : 2 * (π / 6) = π / 3 := by cancel_denoms
     rw [h2, cos_pi_div_three]
-  rw [← sub_eq_zero] at h1⊢
+  rw [← sub_eq_zero] at h1 ⊢
   convert h1 using 1
   ring
 #align real.sq_cos_pi_div_six Real.sq_cos_pi_div_six
@@ -994,10 +994,10 @@ theorem sq_cos_pi_div_six : cos (π / 6) ^ 2 = 3 / 4 :=
 @[simp]
 theorem cos_pi_div_six : cos (π / 6) = sqrt 3 / 2 :=
   by
-  suffices sqrt 3 = cos (π / 6) * 2 by field_simp [(by norm_num : 0 ≠ 2)] ; exact this.symm
+  suffices sqrt 3 = cos (π / 6) * 2 by field_simp [(by norm_num : 0 ≠ 2)]; exact this.symm
   rw [sqrt_eq_iff_sq_eq]
   · have h1 := (mul_right_inj' (by norm_num : (4 : ℝ) ≠ 0)).mpr sq_cos_pi_div_six
-    rw [← sub_eq_zero] at h1⊢
+    rw [← sub_eq_zero] at h1 ⊢
     convert h1 using 1
     ring
   · norm_num

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

@@ -49,7 +49,7 @@ sin, cos, tan, angle
 
 noncomputable section
 
-open Classical Topology Filter
+open scoped Classical Topology Filter
 
 open Set Filter
 
@@ -201,7 +201,7 @@ namespace NNReal
 
 open Real
 
-open Real NNReal
+open scoped Real NNReal
 
 #print NNReal.pi /-
 /-- `π` considered as a nonnegative real. -/
@@ -226,7 +226,7 @@ end NNReal
 
 namespace Real
 
-open Real
+open scoped Real
 
 @[simp]
 theorem sin_pi : sin π = 0 := by
@@ -1257,7 +1257,7 @@ end Real
 
 namespace Complex
 
-open Real
+open scoped Real
 
 theorem sin_eq_zero_iff_cos_eq {z : ℂ} : sin z = 0 ↔ cos z = 1 ∨ cos z = -1 := by
   rw [← mul_self_eq_one_iff, ← sin_sq_add_cos_sq, sq, sq, ← sub_eq_iff_eq_add, sub_self] <;>

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

@@ -55,65 +55,29 @@ open Set Filter
 
 namespace Complex
 
-/- warning: complex.continuous_sin -> Complex.continuous_sin is a dubious translation:
-lean 3 declaration is
-  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Complex.sin
-but is expected to have type
-  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.sin
-Case conversion may be inaccurate. Consider using '#align complex.continuous_sin Complex.continuous_sinₓ'. -/
 @[continuity]
 theorem continuous_sin : Continuous sin := by
   change Continuous fun z => (exp (-z * I) - exp (z * I)) * I / 2; continuity
 #align complex.continuous_sin Complex.continuous_sin
 
-/- warning: complex.continuous_on_sin -> Complex.continuousOn_sin is a dubious translation:
-lean 3 declaration is
-  forall {s : Set.{0} Complex}, ContinuousOn.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Complex.sin s
-but is expected to have type
-  forall {s : Set.{0} Complex}, ContinuousOn.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.sin s
-Case conversion may be inaccurate. Consider using '#align complex.continuous_on_sin Complex.continuousOn_sinₓ'. -/
 theorem continuousOn_sin {s : Set ℂ} : ContinuousOn sin s :=
   continuous_sin.ContinuousOn
 #align complex.continuous_on_sin Complex.continuousOn_sin
 
-/- warning: complex.continuous_cos -> Complex.continuous_cos is a dubious translation:
-lean 3 declaration is
-  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Complex.cos
-but is expected to have type
-  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.cos
-Case conversion may be inaccurate. Consider using '#align complex.continuous_cos Complex.continuous_cosₓ'. -/
 @[continuity]
 theorem continuous_cos : Continuous cos := by
   change Continuous fun z => (exp (z * I) + exp (-z * I)) / 2; continuity
 #align complex.continuous_cos Complex.continuous_cos
 
-/- warning: complex.continuous_on_cos -> Complex.continuousOn_cos is a dubious translation:
-lean 3 declaration is
-  forall {s : Set.{0} Complex}, ContinuousOn.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Complex.cos s
-but is expected to have type
-  forall {s : Set.{0} Complex}, ContinuousOn.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.cos s
-Case conversion may be inaccurate. Consider using '#align complex.continuous_on_cos Complex.continuousOn_cosₓ'. -/
 theorem continuousOn_cos {s : Set ℂ} : ContinuousOn cos s :=
   continuous_cos.ContinuousOn
 #align complex.continuous_on_cos Complex.continuousOn_cos
 
-/- warning: complex.continuous_sinh -> Complex.continuous_sinh is a dubious translation:
-lean 3 declaration is
-  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Complex.sinh
-but is expected to have type
-  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.sinh
-Case conversion may be inaccurate. Consider using '#align complex.continuous_sinh Complex.continuous_sinhₓ'. -/
 @[continuity]
 theorem continuous_sinh : Continuous sinh := by change Continuous fun z => (exp z - exp (-z)) / 2;
   continuity
 #align complex.continuous_sinh Complex.continuous_sinh
 
-/- warning: complex.continuous_cosh -> Complex.continuous_cosh is a dubious translation:
-lean 3 declaration is
-  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Complex.cosh
-but is expected to have type
-  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.cosh
-Case conversion may be inaccurate. Consider using '#align complex.continuous_cosh Complex.continuous_coshₓ'. -/
 @[continuity]
 theorem continuous_cosh : Continuous cosh := by change Continuous fun z => (exp z + exp (-z)) / 2;
   continuity
@@ -169,12 +133,6 @@ end Real
 
 namespace Real
 
-/- warning: real.exists_cos_eq_zero -> Real.exists_cos_eq_zero is a dubious translation:
-lean 3 declaration is
-  Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.image.{0, 0} Real Real Real.cos (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))
-but is expected to have type
-  Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.image.{0, 0} Real Real Real.cos (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
-Case conversion may be inaccurate. Consider using '#align real.exists_cos_eq_zero Real.exists_cos_eq_zeroₓ'. -/
 theorem exists_cos_eq_zero : 0 ∈ cos '' Icc (1 : ℝ) 2 :=
   intermediate_value_Icc' (by norm_num) continuousOn_cos
     ⟨le_of_lt cos_two_neg, le_of_lt cos_one_pos⟩
@@ -199,45 +157,21 @@ theorem cos_pi_div_two : cos (π / 2) = 0 := by
 #align real.cos_pi_div_two Real.cos_pi_div_two
 -/
 
-/- warning: real.one_le_pi_div_two -> Real.one_le_pi_div_two is a dubious translation:
-lean 3 declaration is
-  LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))
-but is expected to have type
-  LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
-Case conversion may be inaccurate. Consider using '#align real.one_le_pi_div_two Real.one_le_pi_div_twoₓ'. -/
 theorem one_le_pi_div_two : (1 : ℝ) ≤ π / 2 := by
   rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)] <;>
     exact (Classical.choose_spec exists_cos_eq_zero).1.1
 #align real.one_le_pi_div_two Real.one_le_pi_div_two
 
-/- warning: real.pi_div_two_le_two -> Real.pi_div_two_le_two is a dubious translation:
-lean 3 declaration is
-  LE.le.{0} Real Real.hasLe (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
-but is expected to have type
-  LE.le.{0} Real Real.instLEReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
-Case conversion may be inaccurate. Consider using '#align real.pi_div_two_le_two Real.pi_div_two_le_twoₓ'. -/
 theorem pi_div_two_le_two : π / 2 ≤ 2 := by
   rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)] <;>
     exact (Classical.choose_spec exists_cos_eq_zero).1.2
 #align real.pi_div_two_le_two Real.pi_div_two_le_two
 
-/- warning: real.two_le_pi -> Real.two_le_pi is a dubious translation:
-lean 3 declaration is
-  LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) Real.pi
-but is expected to have type
-  LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi
-Case conversion may be inaccurate. Consider using '#align real.two_le_pi Real.two_le_piₓ'. -/
 theorem two_le_pi : (2 : ℝ) ≤ π :=
   (div_le_div_right (show (0 : ℝ) < 2 by norm_num)).1
     (by rw [div_self (two_ne_zero' ℝ)] <;> exact one_le_pi_div_two)
 #align real.two_le_pi Real.two_le_pi
 
-/- warning: real.pi_le_four -> Real.pi_le_four is a dubious translation:
-lean 3 declaration is
-  LE.le.{0} Real Real.hasLe Real.pi (OfNat.ofNat.{0} Real 4 (OfNat.mk.{0} Real 4 (bit0.{0} Real Real.hasAdd (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))
-but is expected to have type
-  LE.le.{0} Real Real.instLEReal Real.pi (OfNat.ofNat.{0} Real 4 (instOfNat.{0} Real 4 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
-Case conversion may be inaccurate. Consider using '#align real.pi_le_four Real.pi_le_fourₓ'. -/
 theorem pi_le_four : π ≤ 4 :=
   (div_le_div_right (show (0 : ℝ) < 2 by norm_num)).1
     (calc
@@ -246,42 +180,18 @@ theorem pi_le_four : π ≤ 4 :=
       )
 #align real.pi_le_four Real.pi_le_four
 
-/- warning: real.pi_pos -> Real.pi_pos is a dubious translation:
-lean 3 declaration is
-  LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) Real.pi
-but is expected to have type
-  LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) Real.pi
-Case conversion may be inaccurate. Consider using '#align real.pi_pos Real.pi_posₓ'. -/
 theorem pi_pos : 0 < π :=
   lt_of_lt_of_le (by norm_num) two_le_pi
 #align real.pi_pos Real.pi_pos
 
-/- warning: real.pi_ne_zero -> Real.pi_ne_zero is a dubious translation:
-lean 3 declaration is
-  Ne.{1} Real Real.pi (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
-but is expected to have type
-  Ne.{1} Real Real.pi (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
-Case conversion may be inaccurate. Consider using '#align real.pi_ne_zero Real.pi_ne_zeroₓ'. -/
 theorem pi_ne_zero : π ≠ 0 :=
   ne_of_gt pi_pos
 #align real.pi_ne_zero Real.pi_ne_zero
 
-/- warning: real.pi_div_two_pos -> Real.pi_div_two_pos is a dubious translation:
-lean 3 declaration is
-  LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))
-but is expected to have type
-  LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
-Case conversion may be inaccurate. Consider using '#align real.pi_div_two_pos Real.pi_div_two_posₓ'. -/
 theorem pi_div_two_pos : 0 < π / 2 :=
   half_pos pi_pos
 #align real.pi_div_two_pos Real.pi_div_two_pos
 
-/- warning: real.two_pi_pos -> Real.two_pi_pos is a dubious translation:
-lean 3 declaration is
-  LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) Real.pi)
-but is expected to have type
-  LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)
-Case conversion may be inaccurate. Consider using '#align real.two_pi_pos Real.two_pi_posₓ'. -/
 theorem two_pi_pos : 0 < 2 * π := by linarith [pi_pos]
 #align real.two_pi_pos Real.two_pi_pos
 
@@ -300,32 +210,14 @@ noncomputable def pi : ℝ≥0 :=
 #align nnreal.pi NNReal.pi
 -/
 
-/- warning: nnreal.coe_real_pi -> NNReal.coe_real_pi is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) NNReal.pi) Real.pi
-but is expected to have type
-  Eq.{1} Real (NNReal.toReal NNReal.pi) Real.pi
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_real_pi NNReal.coe_real_piₓ'. -/
 @[simp]
 theorem coe_real_pi : (pi : ℝ) = π :=
   rfl
 #align nnreal.coe_real_pi NNReal.coe_real_pi
 
-/- warning: nnreal.pi_pos -> NNReal.pi_pos is a dubious translation:
-lean 3 declaration is
-  LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) NNReal.pi
-but is expected to have type
-  LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) NNReal.pi
-Case conversion may be inaccurate. Consider using '#align nnreal.pi_pos NNReal.pi_posₓ'. -/
 theorem pi_pos : 0 < pi := by exact_mod_cast Real.pi_pos
 #align nnreal.pi_pos NNReal.pi_pos
 
-/- warning: nnreal.pi_ne_zero -> NNReal.pi_ne_zero is a dubious translation:
-lean 3 declaration is
-  Ne.{1} NNReal NNReal.pi (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
-but is expected to have type
-  Ne.{1} NNReal NNReal.pi (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
-Case conversion may be inaccurate. Consider using '#align nnreal.pi_ne_zero NNReal.pi_ne_zeroₓ'. -/
 theorem pi_ne_zero : pi ≠ 0 :=
   pi_pos.ne'
 #align nnreal.pi_ne_zero NNReal.pi_ne_zero
@@ -336,23 +228,11 @@ namespace Real
 
 open Real
 
-/- warning: real.sin_pi -> Real.sin_pi is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (Real.sin Real.pi) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
-but is expected to have type
-  Eq.{1} Real (Real.sin Real.pi) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
-Case conversion may be inaccurate. Consider using '#align real.sin_pi Real.sin_piₓ'. -/
 @[simp]
 theorem sin_pi : sin π = 0 := by
   rw [← mul_div_cancel_left π (two_ne_zero' ℝ), two_mul, add_div, sin_add, cos_pi_div_two] <;> simp
 #align real.sin_pi Real.sin_pi
 
-/- warning: real.cos_pi -> Real.cos_pi is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (Real.cos Real.pi) (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
-but is expected to have type
-  Eq.{1} Real (Real.cos Real.pi) (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
-Case conversion may be inaccurate. Consider using '#align real.cos_pi Real.cos_piₓ'. -/
 @[simp]
 theorem cos_pi : cos π = -1 := by
   rw [← mul_div_cancel_left π (two_ne_zero' ℝ), mul_div_assoc, cos_two_mul, cos_pi_div_two] <;>
@@ -617,12 +497,6 @@ theorem cos_int_mul_two_pi_sub_pi (n : ℤ) : cos (n * (2 * π) - π) = -1 := by
 #align real.cos_int_mul_two_pi_sub_pi Real.cos_int_mul_two_pi_sub_pi
 -/
 
-/- warning: real.sin_pos_of_pos_of_lt_pi -> Real.sin_pos_of_pos_of_lt_pi is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LT.lt.{0} Real Real.hasLt x Real.pi) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.sin x))
-but is expected to have type
-  forall {x : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LT.lt.{0} Real Real.instLTReal x Real.pi) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.sin x))
-Case conversion may be inaccurate. Consider using '#align real.sin_pos_of_pos_of_lt_pi Real.sin_pos_of_pos_of_lt_piₓ'. -/
 theorem sin_pos_of_pos_of_lt_pi {x : ℝ} (h0x : 0 < x) (hxp : x < π) : 0 < sin x :=
   if hx2 : x ≤ 2 then sin_pos_of_pos_of_le_two h0x hx2
   else
@@ -632,22 +506,10 @@ theorem sin_pos_of_pos_of_lt_pi {x : ℝ} (h0x : 0 < x) (hxp : x < π) : 0 < sin
     sin_pi_sub x ▸ sin_pos_of_pos_of_le_two (sub_pos.2 hxp) this
 #align real.sin_pos_of_pos_of_lt_pi Real.sin_pos_of_pos_of_lt_pi
 
-/- warning: real.sin_pos_of_mem_Ioo -> Real.sin_pos_of_mem_Ioo is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Ioo.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) Real.pi)) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.sin x))
-but is expected to have type
-  forall {x : Real}, (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioo.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) Real.pi)) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.sin x))
-Case conversion may be inaccurate. Consider using '#align real.sin_pos_of_mem_Ioo Real.sin_pos_of_mem_Iooₓ'. -/
 theorem sin_pos_of_mem_Ioo {x : ℝ} (hx : x ∈ Ioo 0 π) : 0 < sin x :=
   sin_pos_of_pos_of_lt_pi hx.1 hx.2
 #align real.sin_pos_of_mem_Ioo Real.sin_pos_of_mem_Ioo
 
-/- warning: real.sin_nonneg_of_mem_Icc -> Real.sin_nonneg_of_mem_Icc is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) Real.pi)) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.sin x))
-but is expected to have type
-  forall {x : Real}, (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) Real.pi)) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.sin x))
-Case conversion may be inaccurate. Consider using '#align real.sin_nonneg_of_mem_Icc Real.sin_nonneg_of_mem_Iccₓ'. -/
 theorem sin_nonneg_of_mem_Icc {x : ℝ} (hx : x ∈ Icc 0 π) : 0 ≤ sin x :=
   by
   rw [← closure_Ioo pi_ne_zero.symm] at hx
@@ -656,32 +518,14 @@ theorem sin_nonneg_of_mem_Icc {x : ℝ} (hx : x ∈ Icc 0 π) : 0 ≤ sin x :=
       (closure_mono (fun y => sin_pos_of_mem_Ioo) hx)
 #align real.sin_nonneg_of_mem_Icc Real.sin_nonneg_of_mem_Icc
 
-/- warning: real.sin_nonneg_of_nonneg_of_le_pi -> Real.sin_nonneg_of_nonneg_of_le_pi is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LE.le.{0} Real Real.hasLe x Real.pi) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.sin x))
-but is expected to have type
-  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LE.le.{0} Real Real.instLEReal x Real.pi) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.sin x))
-Case conversion may be inaccurate. Consider using '#align real.sin_nonneg_of_nonneg_of_le_pi Real.sin_nonneg_of_nonneg_of_le_piₓ'. -/
 theorem sin_nonneg_of_nonneg_of_le_pi {x : ℝ} (h0x : 0 ≤ x) (hxp : x ≤ π) : 0 ≤ sin x :=
   sin_nonneg_of_mem_Icc ⟨h0x, hxp⟩
 #align real.sin_nonneg_of_nonneg_of_le_pi Real.sin_nonneg_of_nonneg_of_le_pi
 
-/- warning: real.sin_neg_of_neg_of_neg_pi_lt -> Real.sin_neg_of_neg_of_neg_pi_lt is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, (LT.lt.{0} Real Real.hasLt x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Real Real.hasLt (Neg.neg.{0} Real Real.hasNeg Real.pi) x) -> (LT.lt.{0} Real Real.hasLt (Real.sin x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {x : Real}, (LT.lt.{0} Real Real.instLTReal x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LT.lt.{0} Real Real.instLTReal (Neg.neg.{0} Real Real.instNegReal Real.pi) x) -> (LT.lt.{0} Real Real.instLTReal (Real.sin x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align real.sin_neg_of_neg_of_neg_pi_lt Real.sin_neg_of_neg_of_neg_pi_ltₓ'. -/
 theorem sin_neg_of_neg_of_neg_pi_lt {x : ℝ} (hx0 : x < 0) (hpx : -π < x) : sin x < 0 :=
   neg_pos.1 <| sin_neg x ▸ sin_pos_of_pos_of_lt_pi (neg_pos.2 hx0) (neg_lt.1 hpx)
 #align real.sin_neg_of_neg_of_neg_pi_lt Real.sin_neg_of_neg_of_neg_pi_lt
 
-/- warning: real.sin_nonpos_of_nonnpos_of_neg_pi_le -> Real.sin_nonpos_of_nonnpos_of_neg_pi_le is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, (LE.le.{0} Real Real.hasLe x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LE.le.{0} Real Real.hasLe (Neg.neg.{0} Real Real.hasNeg Real.pi) x) -> (LE.le.{0} Real Real.hasLe (Real.sin x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {x : Real}, (LE.le.{0} Real Real.instLEReal x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LE.le.{0} Real Real.instLEReal (Neg.neg.{0} Real Real.instNegReal Real.pi) x) -> (LE.le.{0} Real Real.instLEReal (Real.sin x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align real.sin_nonpos_of_nonnpos_of_neg_pi_le Real.sin_nonpos_of_nonnpos_of_neg_pi_leₓ'. -/
 theorem sin_nonpos_of_nonnpos_of_neg_pi_le {x : ℝ} (hx0 : x ≤ 0) (hpx : -π ≤ x) : sin x ≤ 0 :=
   neg_nonneg.1 <| sin_neg x ▸ sin_nonneg_of_nonneg_of_le_pi (neg_nonneg.2 hx0) (neg_le.1 hpx)
 #align real.sin_nonpos_of_nonnpos_of_neg_pi_le Real.sin_nonpos_of_nonnpos_of_neg_pi_le
@@ -728,87 +572,39 @@ theorem cos_pi_div_two_sub (x : ℝ) : cos (π / 2 - x) = sin x := by
 #align real.cos_pi_div_two_sub Real.cos_pi_div_two_sub
 -/
 
-/- warning: real.cos_pos_of_mem_Ioo -> Real.cos_pos_of_mem_Ioo is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Ioo.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.cos x))
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-  forall {x : Real}, (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioo.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.cos x))
-Case conversion may be inaccurate. Consider using '#align real.cos_pos_of_mem_Ioo Real.cos_pos_of_mem_Iooₓ'. -/
 theorem cos_pos_of_mem_Ioo {x : ℝ} (hx : x ∈ Ioo (-(π / 2)) (π / 2)) : 0 < cos x :=
   sin_add_pi_div_two x ▸ sin_pos_of_mem_Ioo ⟨by linarith [hx.1], by linarith [hx.2]⟩
 #align real.cos_pos_of_mem_Ioo Real.cos_pos_of_mem_Ioo
 
-/- warning: real.cos_nonneg_of_mem_Icc -> Real.cos_nonneg_of_mem_Icc is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.cos x))
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-  forall {x : Real}, (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.cos x))
-Case conversion may be inaccurate. Consider using '#align real.cos_nonneg_of_mem_Icc Real.cos_nonneg_of_mem_Iccₓ'. -/
 theorem cos_nonneg_of_mem_Icc {x : ℝ} (hx : x ∈ Icc (-(π / 2)) (π / 2)) : 0 ≤ cos x :=
   sin_add_pi_div_two x ▸ sin_nonneg_of_mem_Icc ⟨by linarith [hx.1], by linarith [hx.2]⟩
 #align real.cos_nonneg_of_mem_Icc Real.cos_nonneg_of_mem_Icc
 
-/- warning: real.cos_nonneg_of_neg_pi_div_two_le_of_le -> Real.cos_nonneg_of_neg_pi_div_two_le_of_le is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, (LE.le.{0} Real Real.hasLe (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) x) -> (LE.le.{0} Real Real.hasLe x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.cos x))
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-  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) x) -> (LE.le.{0} Real Real.instLEReal x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.cos x))
-Case conversion may be inaccurate. Consider using '#align real.cos_nonneg_of_neg_pi_div_two_le_of_le Real.cos_nonneg_of_neg_pi_div_two_le_of_leₓ'. -/
 theorem cos_nonneg_of_neg_pi_div_two_le_of_le {x : ℝ} (hl : -(π / 2) ≤ x) (hu : x ≤ π / 2) :
     0 ≤ cos x :=
   cos_nonneg_of_mem_Icc ⟨hl, hu⟩
 #align real.cos_nonneg_of_neg_pi_div_two_le_of_le Real.cos_nonneg_of_neg_pi_div_two_le_of_le
 
-/- warning: real.cos_neg_of_pi_div_two_lt_of_lt -> Real.cos_neg_of_pi_div_two_lt_of_lt is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.cos_neg_of_pi_div_two_lt_of_lt Real.cos_neg_of_pi_div_two_lt_of_ltₓ'. -/
 theorem cos_neg_of_pi_div_two_lt_of_lt {x : ℝ} (hx₁ : π / 2 < x) (hx₂ : x < π + π / 2) :
     cos x < 0 :=
   neg_pos.1 <| cos_pi_sub x ▸ cos_pos_of_mem_Ioo ⟨by linarith, by linarith⟩
 #align real.cos_neg_of_pi_div_two_lt_of_lt Real.cos_neg_of_pi_div_two_lt_of_lt
 
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-Case conversion may be inaccurate. Consider using '#align real.cos_nonpos_of_pi_div_two_le_of_le Real.cos_nonpos_of_pi_div_two_le_of_leₓ'. -/
 theorem cos_nonpos_of_pi_div_two_le_of_le {x : ℝ} (hx₁ : π / 2 ≤ x) (hx₂ : x ≤ π + π / 2) :
     cos x ≤ 0 :=
   neg_nonneg.1 <| cos_pi_sub x ▸ cos_nonneg_of_mem_Icc ⟨by linarith, by linarith⟩
 #align real.cos_nonpos_of_pi_div_two_le_of_le Real.cos_nonpos_of_pi_div_two_le_of_le
 
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-Case conversion may be inaccurate. Consider using '#align real.sin_eq_sqrt_one_sub_cos_sq Real.sin_eq_sqrt_one_sub_cos_sqₓ'. -/
 theorem sin_eq_sqrt_one_sub_cos_sq {x : ℝ} (hl : 0 ≤ x) (hu : x ≤ π) :
     sin x = sqrt (1 - cos x ^ 2) := by
   rw [← abs_sin_eq_sqrt_one_sub_cos_sq, abs_of_nonneg (sin_nonneg_of_nonneg_of_le_pi hl hu)]
 #align real.sin_eq_sqrt_one_sub_cos_sq Real.sin_eq_sqrt_one_sub_cos_sq
 
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-Case conversion may be inaccurate. Consider using '#align real.cos_eq_sqrt_one_sub_sin_sq Real.cos_eq_sqrt_one_sub_sin_sqₓ'. -/
 theorem cos_eq_sqrt_one_sub_sin_sq {x : ℝ} (hl : -(π / 2) ≤ x) (hu : x ≤ π / 2) :
     cos x = sqrt (1 - sin x ^ 2) := by
   rw [← abs_cos_eq_sqrt_one_sub_sin_sq, abs_of_nonneg (cos_nonneg_of_mem_Icc ⟨hl, hu⟩)]
 #align real.cos_eq_sqrt_one_sub_sin_sq Real.cos_eq_sqrt_one_sub_sin_sq
 
-/- warning: real.sin_eq_zero_iff_of_lt_of_lt -> Real.sin_eq_zero_iff_of_lt_of_lt is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, (LT.lt.{0} Real Real.hasLt (Neg.neg.{0} Real Real.hasNeg Real.pi) x) -> (LT.lt.{0} Real Real.hasLt x Real.pi) -> (Iff (Eq.{1} Real (Real.sin x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
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-Case conversion may be inaccurate. Consider using '#align real.sin_eq_zero_iff_of_lt_of_lt Real.sin_eq_zero_iff_of_lt_of_ltₓ'. -/
 theorem sin_eq_zero_iff_of_lt_of_lt {x : ℝ} (hx₁ : -π < x) (hx₂ : x < π) : sin x = 0 ↔ x = 0 :=
   ⟨fun h =>
     le_antisymm
@@ -827,12 +623,6 @@ theorem sin_eq_zero_iff_of_lt_of_lt {x : ℝ} (hx₁ : -π < x) (hx₂ : x < π)
     fun h => by simp [h]⟩
 #align real.sin_eq_zero_iff_of_lt_of_lt Real.sin_eq_zero_iff_of_lt_of_lt
 
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-Case conversion may be inaccurate. Consider using '#align real.sin_eq_zero_iff Real.sin_eq_zero_iffₓ'. -/
 theorem sin_eq_zero_iff {x : ℝ} : sin x = 0 ↔ ∃ n : ℤ, (n : ℝ) * π = x :=
   ⟨fun h =>
     ⟨⌊x / π⌋,
@@ -844,33 +634,15 @@ theorem sin_eq_zero_iff {x : ℝ} : sin x = 0 ↔ ∃ n : ℤ, (n : ℝ) * π =
     fun ⟨n, hn⟩ => hn ▸ sin_int_mul_pi _⟩
 #align real.sin_eq_zero_iff Real.sin_eq_zero_iff
 
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-Case conversion may be inaccurate. Consider using '#align real.sin_ne_zero_iff Real.sin_ne_zero_iffₓ'. -/
 theorem sin_ne_zero_iff {x : ℝ} : sin x ≠ 0 ↔ ∀ n : ℤ, (n : ℝ) * π ≠ x := by
   rw [← not_exists, not_iff_not, sin_eq_zero_iff]
 #align real.sin_ne_zero_iff Real.sin_ne_zero_iff
 
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-Case conversion may be inaccurate. Consider using '#align real.sin_eq_zero_iff_cos_eq Real.sin_eq_zero_iff_cos_eqₓ'. -/
 theorem sin_eq_zero_iff_cos_eq {x : ℝ} : sin x = 0 ↔ cos x = 1 ∨ cos x = -1 := by
   rw [← mul_self_eq_one_iff, ← sin_sq_add_cos_sq x, sq, sq, ← sub_eq_iff_eq_add, sub_self] <;>
     exact ⟨fun h => by rw [h, MulZeroClass.mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
 #align real.sin_eq_zero_iff_cos_eq Real.sin_eq_zero_iff_cos_eq
 
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-Case conversion may be inaccurate. Consider using '#align real.cos_eq_one_iff Real.cos_eq_one_iffₓ'. -/
 theorem cos_eq_one_iff (x : ℝ) : cos x = 1 ↔ ∃ n : ℤ, (n : ℝ) * (2 * π) = x :=
   ⟨fun h =>
     let ⟨n, hn⟩ := sin_eq_zero_iff.1 (sin_eq_zero_iff_cos_eq.2 (Or.inl h))
@@ -887,12 +659,6 @@ theorem cos_eq_one_iff (x : ℝ) : cos x = 1 ↔ ∃ n : ℤ, (n : ℝ) * (2 * 
     fun ⟨n, hn⟩ => hn ▸ cos_int_mul_two_pi _⟩
 #align real.cos_eq_one_iff Real.cos_eq_one_iff
 
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-Case conversion may be inaccurate. Consider using '#align real.cos_eq_one_iff_of_lt_of_lt Real.cos_eq_one_iff_of_lt_of_ltₓ'. -/
 theorem cos_eq_one_iff_of_lt_of_lt {x : ℝ} (hx₁ : -(2 * π) < x) (hx₂ : x < 2 * π) :
     cos x = 1 ↔ x = 0 :=
   ⟨fun h => by
@@ -904,12 +670,6 @@ theorem cos_eq_one_iff_of_lt_of_lt {x : ℝ} (hx₁ : -(2 * π) < x) (hx₂ : x
     simp, fun h => by simp [h]⟩
 #align real.cos_eq_one_iff_of_lt_of_lt Real.cos_eq_one_iff_of_lt_of_lt
 
-/- warning: real.cos_lt_cos_of_nonneg_of_le_pi_div_two -> Real.cos_lt_cos_of_nonneg_of_le_pi_div_two is a dubious translation:
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-but is expected to have type
-  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LE.le.{0} Real Real.instLEReal y (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LT.lt.{0} Real Real.instLTReal x y) -> (LT.lt.{0} Real Real.instLTReal (Real.cos y) (Real.cos x))
-Case conversion may be inaccurate. Consider using '#align real.cos_lt_cos_of_nonneg_of_le_pi_div_two Real.cos_lt_cos_of_nonneg_of_le_pi_div_twoₓ'. -/
 theorem cos_lt_cos_of_nonneg_of_le_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y ≤ π / 2)
     (hxy : x < y) : cos y < cos x :=
   by
@@ -919,12 +679,6 @@ theorem cos_lt_cos_of_nonneg_of_le_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy
   nlinarith
 #align real.cos_lt_cos_of_nonneg_of_le_pi_div_two Real.cos_lt_cos_of_nonneg_of_le_pi_div_two
 
-/- warning: real.cos_lt_cos_of_nonneg_of_le_pi -> Real.cos_lt_cos_of_nonneg_of_le_pi is a dubious translation:
-lean 3 declaration is
-  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LE.le.{0} Real Real.hasLe y Real.pi) -> (LT.lt.{0} Real Real.hasLt x y) -> (LT.lt.{0} Real Real.hasLt (Real.cos y) (Real.cos x))
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-Case conversion may be inaccurate. Consider using '#align real.cos_lt_cos_of_nonneg_of_le_pi Real.cos_lt_cos_of_nonneg_of_le_piₓ'. -/
 theorem cos_lt_cos_of_nonneg_of_le_pi {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y ≤ π) (hxy : x < y) :
     cos y < cos x :=
   match (le_total x (π / 2) : x ≤ π / 2 ∨ π / 2 ≤ x), le_total y (π / 2) with
@@ -949,33 +703,15 @@ theorem cos_lt_cos_of_nonneg_of_le_pi {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y 
           linarith)
 #align real.cos_lt_cos_of_nonneg_of_le_pi Real.cos_lt_cos_of_nonneg_of_le_pi
 
-/- warning: real.strict_anti_on_cos -> Real.strictAntiOn_cos is a dubious translation:
-lean 3 declaration is
-  StrictAntiOn.{0, 0} Real Real Real.preorder Real.preorder Real.cos (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) Real.pi)
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-Case conversion may be inaccurate. Consider using '#align real.strict_anti_on_cos Real.strictAntiOn_cosₓ'. -/
 theorem strictAntiOn_cos : StrictAntiOn cos (Icc 0 π) := fun x hx y hy hxy =>
   cos_lt_cos_of_nonneg_of_le_pi hx.1 hy.2 hxy
 #align real.strict_anti_on_cos Real.strictAntiOn_cos
 
-/- warning: real.cos_le_cos_of_nonneg_of_le_pi -> Real.cos_le_cos_of_nonneg_of_le_pi is a dubious translation:
-lean 3 declaration is
-  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LE.le.{0} Real Real.hasLe y Real.pi) -> (LE.le.{0} Real Real.hasLe x y) -> (LE.le.{0} Real Real.hasLe (Real.cos y) (Real.cos x))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align real.cos_le_cos_of_nonneg_of_le_pi Real.cos_le_cos_of_nonneg_of_le_piₓ'. -/
 theorem cos_le_cos_of_nonneg_of_le_pi {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y ≤ π) (hxy : x ≤ y) :
     cos y ≤ cos x :=
   (strictAntiOn_cos.le_iff_le ⟨hx₁.trans hxy, hy₂⟩ ⟨hx₁, hxy.trans hy₂⟩).2 hxy
 #align real.cos_le_cos_of_nonneg_of_le_pi Real.cos_le_cos_of_nonneg_of_le_pi
 
-/- warning: real.sin_lt_sin_of_lt_of_le_pi_div_two -> Real.sin_lt_sin_of_lt_of_le_pi_div_two is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align real.sin_lt_sin_of_lt_of_le_pi_div_two Real.sin_lt_sin_of_lt_of_le_pi_div_twoₓ'. -/
 theorem sin_lt_sin_of_lt_of_le_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) ≤ x) (hy₂ : y ≤ π / 2)
     (hxy : x < y) : sin x < sin y := by
   rw [← cos_sub_pi_div_two, ← cos_sub_pi_div_two, ← cos_neg (x - _), ← cos_neg (y - _)] <;>
@@ -983,143 +719,59 @@ theorem sin_lt_sin_of_lt_of_le_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) ≤ x)
     linarith
 #align real.sin_lt_sin_of_lt_of_le_pi_div_two Real.sin_lt_sin_of_lt_of_le_pi_div_two
 
-/- warning: real.strict_mono_on_sin -> Real.strictMonoOn_sin is a dubious translation:
-lean 3 declaration is
-  StrictMonoOn.{0, 0} Real Real Real.preorder Real.preorder Real.sin (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))
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-  StrictMonoOn.{0, 0} Real Real Real.instPreorderReal Real.instPreorderReal Real.sin (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
-Case conversion may be inaccurate. Consider using '#align real.strict_mono_on_sin Real.strictMonoOn_sinₓ'. -/
 theorem strictMonoOn_sin : StrictMonoOn sin (Icc (-(π / 2)) (π / 2)) := fun x hx y hy hxy =>
   sin_lt_sin_of_lt_of_le_pi_div_two hx.1 hy.2 hxy
 #align real.strict_mono_on_sin Real.strictMonoOn_sin
 
-/- warning: real.sin_le_sin_of_le_of_le_pi_div_two -> Real.sin_le_sin_of_le_of_le_pi_div_two is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.sin_le_sin_of_le_of_le_pi_div_two Real.sin_le_sin_of_le_of_le_pi_div_twoₓ'. -/
 theorem sin_le_sin_of_le_of_le_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) ≤ x) (hy₂ : y ≤ π / 2)
     (hxy : x ≤ y) : sin x ≤ sin y :=
   (strictMonoOn_sin.le_iff_le ⟨hx₁, hxy.trans hy₂⟩ ⟨hx₁.trans hxy, hy₂⟩).2 hxy
 #align real.sin_le_sin_of_le_of_le_pi_div_two Real.sin_le_sin_of_le_of_le_pi_div_two
 
-/- warning: real.inj_on_sin -> Real.injOn_sin is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.inj_on_sin Real.injOn_sinₓ'. -/
 theorem injOn_sin : InjOn sin (Icc (-(π / 2)) (π / 2)) :=
   strictMonoOn_sin.InjOn
 #align real.inj_on_sin Real.injOn_sin
 
-/- warning: real.inj_on_cos -> Real.injOn_cos is a dubious translation:
-lean 3 declaration is
-  Set.InjOn.{0, 0} Real Real Real.cos (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) Real.pi)
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-Case conversion may be inaccurate. Consider using '#align real.inj_on_cos Real.injOn_cosₓ'. -/
 theorem injOn_cos : InjOn cos (Icc 0 π) :=
   strictAntiOn_cos.InjOn
 #align real.inj_on_cos Real.injOn_cos
 
-/- warning: real.surj_on_sin -> Real.surjOn_sin is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.surj_on_sin Real.surjOn_sinₓ'. -/
 theorem surjOn_sin : SurjOn sin (Icc (-(π / 2)) (π / 2)) (Icc (-1) 1) := by
   simpa only [sin_neg, sin_pi_div_two] using
     intermediate_value_Icc (neg_le_self pi_div_two_pos.le) continuous_sin.continuous_on
 #align real.surj_on_sin Real.surjOn_sin
 
-/- warning: real.surj_on_cos -> Real.surjOn_cos is a dubious translation:
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-  Set.SurjOn.{0, 0} Real Real Real.cos (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) Real.pi) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
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-Case conversion may be inaccurate. Consider using '#align real.surj_on_cos Real.surjOn_cosₓ'. -/
 theorem surjOn_cos : SurjOn cos (Icc 0 π) (Icc (-1) 1) := by
   simpa only [cos_zero, cos_pi] using intermediate_value_Icc' pi_pos.le continuous_cos.continuous_on
 #align real.surj_on_cos Real.surjOn_cos
 
-/- warning: real.sin_mem_Icc -> Real.sin_mem_Icc is a dubious translation:
-lean 3 declaration is
-  forall (x : Real), Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (Real.sin x) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
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-Case conversion may be inaccurate. Consider using '#align real.sin_mem_Icc Real.sin_mem_Iccₓ'. -/
 theorem sin_mem_Icc (x : ℝ) : sin x ∈ Icc (-1 : ℝ) 1 :=
   ⟨neg_one_le_sin x, sin_le_one x⟩
 #align real.sin_mem_Icc Real.sin_mem_Icc
 
-/- warning: real.cos_mem_Icc -> Real.cos_mem_Icc is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align real.cos_mem_Icc Real.cos_mem_Iccₓ'. -/
 theorem cos_mem_Icc (x : ℝ) : cos x ∈ Icc (-1 : ℝ) 1 :=
   ⟨neg_one_le_cos x, cos_le_one x⟩
 #align real.cos_mem_Icc Real.cos_mem_Icc
 
-/- warning: real.maps_to_sin -> Real.mapsTo_sin is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.maps_to_sin Real.mapsTo_sinₓ'. -/
 theorem mapsTo_sin (s : Set ℝ) : MapsTo sin s (Icc (-1 : ℝ) 1) := fun x _ => sin_mem_Icc x
 #align real.maps_to_sin Real.mapsTo_sin
 
-/- warning: real.maps_to_cos -> Real.mapsTo_cos is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.maps_to_cos Real.mapsTo_cosₓ'. -/
 theorem mapsTo_cos (s : Set ℝ) : MapsTo cos s (Icc (-1 : ℝ) 1) := fun x _ => cos_mem_Icc x
 #align real.maps_to_cos Real.mapsTo_cos
 
-/- warning: real.bij_on_sin -> Real.bijOn_sin is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.bij_on_sin Real.bijOn_sinₓ'. -/
 theorem bijOn_sin : BijOn sin (Icc (-(π / 2)) (π / 2)) (Icc (-1) 1) :=
   ⟨mapsTo_sin _, injOn_sin, surjOn_sin⟩
 #align real.bij_on_sin Real.bijOn_sin
 
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-Case conversion may be inaccurate. Consider using '#align real.bij_on_cos Real.bijOn_cosₓ'. -/
 theorem bijOn_cos : BijOn cos (Icc 0 π) (Icc (-1) 1) :=
   ⟨mapsTo_cos _, injOn_cos, surjOn_cos⟩
 #align real.bij_on_cos Real.bijOn_cos
 
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-Case conversion may be inaccurate. Consider using '#align real.range_cos Real.range_cosₓ'. -/
 @[simp]
 theorem range_cos : range cos = (Icc (-1) 1 : Set ℝ) :=
   Subset.antisymm (range_subset_iff.2 cos_mem_Icc) surjOn_cos.subset_range
 #align real.range_cos Real.range_cos
 
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-Case conversion may be inaccurate. Consider using '#align real.range_sin Real.range_sinₓ'. -/
 @[simp]
 theorem range_sin : range sin = (Icc (-1) 1 : Set ℝ) :=
   Subset.antisymm (range_subset_iff.2 sin_mem_Icc) surjOn_sin.subset_range
@@ -1157,52 +809,22 @@ theorem sqrtTwoAddSeries_zero : sqrtTwoAddSeries x 0 = x := by simp
 #align real.sqrt_two_add_series_zero Real.sqrtTwoAddSeries_zero
 -/
 
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-Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_one Real.sqrtTwoAddSeries_oneₓ'. -/
 theorem sqrtTwoAddSeries_one : sqrtTwoAddSeries 0 1 = sqrt 2 := by simp
 #align real.sqrt_two_add_series_one Real.sqrtTwoAddSeries_one
 
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-Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_two Real.sqrtTwoAddSeries_twoₓ'. -/
 theorem sqrtTwoAddSeries_two : sqrtTwoAddSeries 0 2 = sqrt (2 + sqrt 2) := by simp
 #align real.sqrt_two_add_series_two Real.sqrtTwoAddSeries_two
 
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-Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_zero_nonneg Real.sqrtTwoAddSeries_zero_nonnegₓ'. -/
 theorem sqrtTwoAddSeries_zero_nonneg : ∀ n : ℕ, 0 ≤ sqrtTwoAddSeries 0 n
   | 0 => le_refl 0
   | n + 1 => sqrt_nonneg _
 #align real.sqrt_two_add_series_zero_nonneg Real.sqrtTwoAddSeries_zero_nonneg
 
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-Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_nonneg Real.sqrtTwoAddSeries_nonnegₓ'. -/
 theorem sqrtTwoAddSeries_nonneg {x : ℝ} (h : 0 ≤ x) : ∀ n : ℕ, 0 ≤ sqrtTwoAddSeries x n
   | 0 => h
   | n + 1 => sqrt_nonneg _
 #align real.sqrt_two_add_series_nonneg Real.sqrtTwoAddSeries_nonneg
 
-/- warning: real.sqrt_two_add_series_lt_two -> Real.sqrtTwoAddSeries_lt_two is a dubious translation:
-lean 3 declaration is
-  forall (n : Nat), LT.lt.{0} Real Real.hasLt (Real.sqrtTwoAddSeries (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) n) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
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-Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_lt_two Real.sqrtTwoAddSeries_lt_twoₓ'. -/
 theorem sqrtTwoAddSeries_lt_two : ∀ n : ℕ, sqrtTwoAddSeries 0 n < 2
   | 0 => by norm_num
   | n + 1 => by
@@ -1212,24 +834,12 @@ theorem sqrtTwoAddSeries_lt_two : ∀ n : ℕ, sqrtTwoAddSeries 0 n < 2
     · exact add_nonneg zero_le_two (sqrt_two_add_series_zero_nonneg n)
 #align real.sqrt_two_add_series_lt_two Real.sqrtTwoAddSeries_lt_two
 
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-Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_succ Real.sqrtTwoAddSeries_succₓ'. -/
 theorem sqrtTwoAddSeries_succ (x : ℝ) :
     ∀ n : ℕ, sqrtTwoAddSeries x (n + 1) = sqrtTwoAddSeries (sqrt (2 + x)) n
   | 0 => rfl
   | n + 1 => by rw [sqrt_two_add_series, sqrt_two_add_series_succ, sqrt_two_add_series]
 #align real.sqrt_two_add_series_succ Real.sqrtTwoAddSeries_succ
 
-/- warning: real.sqrt_two_add_series_monotone_left -> Real.sqrtTwoAddSeries_monotone_left is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_monotone_left Real.sqrtTwoAddSeries_monotone_leftₓ'. -/
 theorem sqrtTwoAddSeries_monotone_left {x y : ℝ} (h : x ≤ y) :
     ∀ n : ℕ, sqrtTwoAddSeries x n ≤ sqrtTwoAddSeries y n
   | 0 => h
@@ -1261,23 +871,11 @@ theorem cos_pi_over_two_pow : ∀ n : ℕ, cos (π / 2 ^ (n + 1)) = sqrtTwoAddSe
 #align real.cos_pi_over_two_pow Real.cos_pi_over_two_pow
 -/
 
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-Case conversion may be inaccurate. Consider using '#align real.sin_sq_pi_over_two_pow Real.sin_sq_pi_over_two_powₓ'. -/
 theorem sin_sq_pi_over_two_pow (n : ℕ) :
     sin (π / 2 ^ (n + 1)) ^ 2 = 1 - (sqrtTwoAddSeries 0 n / 2) ^ 2 := by
   rw [sin_sq, cos_pi_over_two_pow]
 #align real.sin_sq_pi_over_two_pow Real.sin_sq_pi_over_two_pow
 
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-Case conversion may be inaccurate. Consider using '#align real.sin_sq_pi_over_two_pow_succ Real.sin_sq_pi_over_two_pow_succₓ'. -/
 theorem sin_sq_pi_over_two_pow_succ (n : ℕ) :
     sin (π / 2 ^ (n + 2)) ^ 2 = 1 / 2 - sqrtTwoAddSeries 0 n / 4 :=
   by
@@ -1377,12 +975,6 @@ theorem cos_pi_div_three : cos (π / 3) = 1 / 2 :=
 #align real.cos_pi_div_three Real.cos_pi_div_three
 -/
 
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 /-- The square of the cosine of `π / 6` is `3 / 4` (this is sometimes more convenient than the
 result for cosine itself). -/
 theorem sq_cos_pi_div_six : cos (π / 6) ^ 2 = 3 / 4 :=
@@ -1425,12 +1017,6 @@ theorem sin_pi_div_six : sin (π / 6) = 1 / 2 :=
 #align real.sin_pi_div_six Real.sin_pi_div_six
 -/
 
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 /-- The square of the sine of `π / 3` is `3 / 4` (this is sometimes more convenient than the
 result for cosine itself). -/
 theorem sq_sin_pi_div_three : sin (π / 3) ^ 2 = 3 / 4 :=
@@ -1453,28 +1039,16 @@ theorem sin_pi_div_three : sin (π / 3) = sqrt 3 / 2 :=
 
 end CosDivSq
 
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 /-- `real.sin` as an `order_iso` between `[-(π / 2), π / 2]` and `[-1, 1]`. -/
 def sinOrderIso : Icc (-(π / 2)) (π / 2) ≃o Icc (-1 : ℝ) 1 :=
   (strictMonoOn_sin.OrderIso _ _).trans <| OrderIso.setCongr _ _ bijOn_sin.image_eq
 #align real.sin_order_iso Real.sinOrderIso
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align real.coe_sin_order_iso_apply Real.coe_sinOrderIso_applyₓ'. -/
 @[simp]
 theorem coe_sinOrderIso_apply (x : Icc (-(π / 2)) (π / 2)) : (sinOrderIso x : ℝ) = sin x :=
   rfl
 #align real.coe_sin_order_iso_apply Real.coe_sinOrderIso_apply
 
-/- warning: real.sin_order_iso_apply -> Real.sinOrderIso_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align real.sin_order_iso_apply Real.sinOrderIso_applyₓ'. -/
 theorem sinOrderIso_apply (x : Icc (-(π / 2)) (π / 2)) : sinOrderIso x = ⟨sin x, sin_mem_Icc x⟩ :=
   rfl
 #align real.sin_order_iso_apply Real.sinOrderIso_apply
@@ -1495,24 +1069,12 @@ theorem tan_pi_div_two : tan (π / 2) = 0 := by simp [tan_eq_sin_div_cos]
 #align real.tan_pi_div_two Real.tan_pi_div_two
 -/
 
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 theorem tan_pos_of_pos_of_lt_pi_div_two {x : ℝ} (h0x : 0 < x) (hxp : x < π / 2) : 0 < tan x := by
   rw [tan_eq_sin_div_cos] <;>
     exact
       div_pos (sin_pos_of_pos_of_lt_pi h0x (by linarith)) (cos_pos_of_mem_Ioo ⟨by linarith, hxp⟩)
 #align real.tan_pos_of_pos_of_lt_pi_div_two Real.tan_pos_of_pos_of_lt_pi_div_two
 
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-Case conversion may be inaccurate. Consider using '#align real.tan_nonneg_of_nonneg_of_le_pi_div_two Real.tan_nonneg_of_nonneg_of_le_pi_div_twoₓ'. -/
 theorem tan_nonneg_of_nonneg_of_le_pi_div_two {x : ℝ} (h0x : 0 ≤ x) (hxp : x ≤ π / 2) : 0 ≤ tan x :=
   match lt_or_eq_of_le h0x, lt_or_eq_of_le hxp with
   | Or.inl hx0, Or.inl hxp => le_of_lt (tan_pos_of_pos_of_lt_pi_div_two hx0 hxp)
@@ -1520,33 +1082,15 @@ theorem tan_nonneg_of_nonneg_of_le_pi_div_two {x : ℝ} (h0x : 0 ≤ x) (hxp : x
   | Or.inr hx0, _ => by simp [hx0.symm]
 #align real.tan_nonneg_of_nonneg_of_le_pi_div_two Real.tan_nonneg_of_nonneg_of_le_pi_div_two
 
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-Case conversion may be inaccurate. Consider using '#align real.tan_neg_of_neg_of_pi_div_two_lt Real.tan_neg_of_neg_of_pi_div_two_ltₓ'. -/
 theorem tan_neg_of_neg_of_pi_div_two_lt {x : ℝ} (hx0 : x < 0) (hpx : -(π / 2) < x) : tan x < 0 :=
   neg_pos.1 (tan_neg x ▸ tan_pos_of_pos_of_lt_pi_div_two (by linarith) (by linarith [pi_pos]))
 #align real.tan_neg_of_neg_of_pi_div_two_lt Real.tan_neg_of_neg_of_pi_div_two_lt
 
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-Case conversion may be inaccurate. Consider using '#align real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le Real.tan_nonpos_of_nonpos_of_neg_pi_div_two_leₓ'. -/
 theorem tan_nonpos_of_nonpos_of_neg_pi_div_two_le {x : ℝ} (hx0 : x ≤ 0) (hpx : -(π / 2) ≤ x) :
     tan x ≤ 0 :=
   neg_nonneg.1 (tan_neg x ▸ tan_nonneg_of_nonneg_of_le_pi_div_two (by linarith) (by linarith))
 #align real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le Real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le
 
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-Case conversion may be inaccurate. Consider using '#align real.tan_lt_tan_of_nonneg_of_lt_pi_div_two Real.tan_lt_tan_of_nonneg_of_lt_pi_div_twoₓ'. -/
 theorem tan_lt_tan_of_nonneg_of_lt_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y < π / 2)
     (hxy : x < y) : tan x < tan y :=
   by
@@ -1558,12 +1102,6 @@ theorem tan_lt_tan_of_nonneg_of_lt_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy
       (cos_pos_of_mem_Ioo ⟨by linarith, hy₂⟩)
 #align real.tan_lt_tan_of_nonneg_of_lt_pi_div_two Real.tan_lt_tan_of_nonneg_of_lt_pi_div_two
 
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-Case conversion may be inaccurate. Consider using '#align real.tan_lt_tan_of_lt_of_lt_pi_div_two Real.tan_lt_tan_of_lt_of_lt_pi_div_twoₓ'. -/
 theorem tan_lt_tan_of_lt_of_lt_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) < x) (hy₂ : y < π / 2)
     (hxy : x < y) : tan x < tan y :=
   match le_total x 0, le_total y 0 with
@@ -1585,32 +1123,14 @@ theorem tan_lt_tan_of_lt_of_lt_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) < x) (h
   | Or.inr hx0, Or.inr hy0 => tan_lt_tan_of_nonneg_of_lt_pi_div_two hx0 hy₂ hxy
 #align real.tan_lt_tan_of_lt_of_lt_pi_div_two Real.tan_lt_tan_of_lt_of_lt_pi_div_two
 
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-Case conversion may be inaccurate. Consider using '#align real.strict_mono_on_tan Real.strictMonoOn_tanₓ'. -/
 theorem strictMonoOn_tan : StrictMonoOn tan (Ioo (-(π / 2)) (π / 2)) := fun x hx y hy =>
   tan_lt_tan_of_lt_of_lt_pi_div_two hx.1 hy.2
 #align real.strict_mono_on_tan Real.strictMonoOn_tan
 
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-Case conversion may be inaccurate. Consider using '#align real.inj_on_tan Real.injOn_tanₓ'. -/
 theorem injOn_tan : InjOn tan (Ioo (-(π / 2)) (π / 2)) :=
   strictMonoOn_tan.InjOn
 #align real.inj_on_tan Real.injOn_tan
 
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-Case conversion may be inaccurate. Consider using '#align real.tan_inj_of_lt_of_lt_pi_div_two Real.tan_inj_of_lt_of_lt_pi_div_twoₓ'. -/
 theorem tan_inj_of_lt_of_lt_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) < x) (hx₂ : x < π / 2)
     (hy₁ : -(π / 2) < y) (hy₂ : y < π / 2) (hxy : tan x = tan y) : x = y :=
   injOn_tan ⟨hx₁, hx₂⟩ ⟨hy₁, hy₂⟩ hxy
@@ -1694,22 +1214,10 @@ theorem tan_int_mul_pi_sub (x : ℝ) (n : ℤ) : tan (n * π - x) = -tan x :=
 #align real.tan_int_mul_pi_sub Real.tan_int_mul_pi_sub
 -/
 
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-Case conversion may be inaccurate. Consider using '#align real.tendsto_sin_pi_div_two Real.tendsto_sin_pi_div_twoₓ'. -/
 theorem tendsto_sin_pi_div_two : Tendsto sin (𝓝[<] (π / 2)) (𝓝 1) := by
   convert continuous_sin.continuous_within_at; simp
 #align real.tendsto_sin_pi_div_two Real.tendsto_sin_pi_div_two
 
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-Case conversion may be inaccurate. Consider using '#align real.tendsto_cos_pi_div_two Real.tendsto_cos_pi_div_twoₓ'. -/
 theorem tendsto_cos_pi_div_two : Tendsto cos (𝓝[<] (π / 2)) (𝓝[>] 0) :=
   by
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
@@ -1719,34 +1227,16 @@ theorem tendsto_cos_pi_div_two : Tendsto cos (𝓝[<] (π / 2)) (𝓝[>] 0) :=
         (right_mem_Ioc.mpr (neg_lt_self pi_div_two_pos))]with x hx using cos_pos_of_mem_Ioo hx
 #align real.tendsto_cos_pi_div_two Real.tendsto_cos_pi_div_two
 
-/- warning: real.tendsto_tan_pi_div_two -> Real.tendsto_tan_pi_div_two is a dubious translation:
-lean 3 declaration is
-  Filter.Tendsto.{0, 0} Real Real Real.tan (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (Set.Iio.{0} Real Real.preorder (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (Filter.atTop.{0} Real Real.preorder)
-but is expected to have type
-  Filter.Tendsto.{0, 0} Real Real Real.tan (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Set.Iio.{0} Real Real.instPreorderReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Filter.atTop.{0} Real Real.instPreorderReal)
-Case conversion may be inaccurate. Consider using '#align real.tendsto_tan_pi_div_two Real.tendsto_tan_pi_div_twoₓ'. -/
 theorem tendsto_tan_pi_div_two : Tendsto tan (𝓝[<] (π / 2)) atTop :=
   by
   convert tendsto_cos_pi_div_two.inv_tendsto_zero.at_top_mul zero_lt_one tendsto_sin_pi_div_two
   simp only [Pi.inv_apply, ← div_eq_inv_mul, ← tan_eq_sin_div_cos]
 #align real.tendsto_tan_pi_div_two Real.tendsto_tan_pi_div_two
 
-/- warning: real.tendsto_sin_neg_pi_div_two -> Real.tendsto_sin_neg_pi_div_two is a dubious translation:
-lean 3 declaration is
-  Filter.Tendsto.{0, 0} Real Real Real.sin (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Set.Ioi.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
-but is expected to have type
-  Filter.Tendsto.{0, 0} Real Real Real.sin (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Set.Ioi.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
-Case conversion may be inaccurate. Consider using '#align real.tendsto_sin_neg_pi_div_two Real.tendsto_sin_neg_pi_div_twoₓ'. -/
 theorem tendsto_sin_neg_pi_div_two : Tendsto sin (𝓝[>] (-(π / 2))) (𝓝 (-1)) := by
   convert continuous_sin.continuous_within_at; simp
 #align real.tendsto_sin_neg_pi_div_two Real.tendsto_sin_neg_pi_div_two
 
-/- warning: real.tendsto_cos_neg_pi_div_two -> Real.tendsto_cos_neg_pi_div_two is a dubious translation:
-lean 3 declaration is
-  Filter.Tendsto.{0, 0} Real Real Real.cos (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Set.Ioi.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))))) (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
-but is expected to have type
-  Filter.Tendsto.{0, 0} Real Real Real.cos (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Set.Ioi.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
-Case conversion may be inaccurate. Consider using '#align real.tendsto_cos_neg_pi_div_two Real.tendsto_cos_neg_pi_div_twoₓ'. -/
 theorem tendsto_cos_neg_pi_div_two : Tendsto cos (𝓝[>] (-(π / 2))) (𝓝[>] 0) :=
   by
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
@@ -1756,12 +1246,6 @@ theorem tendsto_cos_neg_pi_div_two : Tendsto cos (𝓝[>] (-(π / 2))) (𝓝[>]
         (left_mem_Ico.mpr (neg_lt_self pi_div_two_pos))]with x hx using cos_pos_of_mem_Ioo hx
 #align real.tendsto_cos_neg_pi_div_two Real.tendsto_cos_neg_pi_div_two
 
-/- warning: real.tendsto_tan_neg_pi_div_two -> Real.tendsto_tan_neg_pi_div_two is a dubious translation:
-lean 3 declaration is
-  Filter.Tendsto.{0, 0} Real Real Real.tan (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Set.Ioi.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))))) (Filter.atBot.{0} Real Real.preorder)
-but is expected to have type
-  Filter.Tendsto.{0, 0} Real Real Real.tan (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Set.Ioi.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) (Filter.atBot.{0} Real Real.instPreorderReal)
-Case conversion may be inaccurate. Consider using '#align real.tendsto_tan_neg_pi_div_two Real.tendsto_tan_neg_pi_div_twoₓ'. -/
 theorem tendsto_tan_neg_pi_div_two : Tendsto tan (𝓝[>] (-(π / 2))) atBot :=
   by
   convert tendsto_cos_neg_pi_div_two.inv_tendsto_zero.at_top_mul_neg (by norm_num)
@@ -1775,12 +1259,6 @@ namespace Complex
 
 open Real
 
-/- warning: complex.sin_eq_zero_iff_cos_eq -> Complex.sin_eq_zero_iff_cos_eq is a dubious translation:
-lean 3 declaration is
-  forall {z : Complex}, Iff (Eq.{1} Complex (Complex.sin z) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (Or (Eq.{1} Complex (Complex.cos z) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (Eq.{1} Complex (Complex.cos z) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))))
-but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} Complex (Complex.sin z) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (Or (Eq.{1} Complex (Complex.cos z) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (Eq.{1} Complex (Complex.cos z) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))))
-Case conversion may be inaccurate. Consider using '#align complex.sin_eq_zero_iff_cos_eq Complex.sin_eq_zero_iff_cos_eqₓ'. -/
 theorem sin_eq_zero_iff_cos_eq {z : ℂ} : sin z = 0 ↔ cos z = 1 ∨ cos z = -1 := by
   rw [← mul_self_eq_one_iff, ← sin_sq_add_cos_sq, sq, sq, ← sub_eq_iff_eq_add, sub_self] <;>
     exact ⟨fun h => by rw [h, MulZeroClass.mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
@@ -2153,117 +1631,51 @@ theorem tan_int_mul_pi_sub (x : ℂ) (n : ℤ) : tan (n * π - x) = -tan x :=
 #align complex.tan_int_mul_pi_sub Complex.tan_int_mul_pi_sub
 -/
 
-/- warning: complex.exp_antiperiodic -> Complex.exp_antiperiodic is a dubious translation:
-lean 3 declaration is
-  Function.Antiperiodic.{0, 0} Complex Complex Complex.hasAdd Complex.hasNeg Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi) Complex.I)
-but is expected to have type
-  Function.Antiperiodic.{0, 0} Complex Complex Complex.instAddComplex Complex.instNegComplex Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' Real.pi) Complex.I)
-Case conversion may be inaccurate. Consider using '#align complex.exp_antiperiodic Complex.exp_antiperiodicₓ'. -/
 theorem exp_antiperiodic : Function.Antiperiodic exp (π * I) := by simp [exp_add, exp_mul_I]
 #align complex.exp_antiperiodic Complex.exp_antiperiodic
 
-/- warning: complex.exp_periodic -> Complex.exp_periodic 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 complex.exp_periodic Complex.exp_periodicₓ'. -/
 theorem exp_periodic : Function.Periodic exp (2 * π * I) :=
   (mul_assoc (2 : ℂ) π I).symm ▸ exp_antiperiodic.Periodic
 #align complex.exp_periodic Complex.exp_periodic
 
-/- warning: complex.exp_mul_I_antiperiodic -> Complex.exp_mul_I_antiperiodic is a dubious translation:
-lean 3 declaration is
-  Function.Antiperiodic.{0, 0} Complex Complex Complex.hasAdd Complex.hasNeg (fun (x : Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) x Complex.I)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi)
-but is expected to have type
-  Function.Antiperiodic.{0, 0} Complex Complex Complex.instAddComplex Complex.instNegComplex (fun (x : Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) x Complex.I)) (Complex.ofReal' Real.pi)
-Case conversion may be inaccurate. Consider using '#align complex.exp_mul_I_antiperiodic Complex.exp_mul_I_antiperiodicₓ'. -/
 theorem exp_mul_I_antiperiodic : Function.Antiperiodic (fun x => exp (x * I)) π := by
   simpa only [mul_inv_cancel_right₀ I_ne_zero] using exp_antiperiodic.mul_const I_ne_zero
 #align complex.exp_mul_I_antiperiodic Complex.exp_mul_I_antiperiodic
 
-/- warning: complex.exp_mul_I_periodic -> Complex.exp_mul_I_periodic is a dubious translation:
-lean 3 declaration is
-  Function.Periodic.{0, 0} Complex Complex Complex.hasAdd (fun (x : Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) x Complex.I)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi))
-but is expected to have type
-  Function.Periodic.{0, 0} Complex Complex Complex.instAddComplex (fun (x : Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) x Complex.I)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.ofReal' Real.pi))
-Case conversion may be inaccurate. Consider using '#align complex.exp_mul_I_periodic Complex.exp_mul_I_periodicₓ'. -/
 theorem exp_mul_I_periodic : Function.Periodic (fun x => exp (x * I)) (2 * π) :=
   exp_mul_I_antiperiodic.Periodic
 #align complex.exp_mul_I_periodic Complex.exp_mul_I_periodic
 
-/- warning: complex.exp_pi_mul_I -> Complex.exp_pi_mul_I is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' Real.pi) Complex.I)) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
-Case conversion may be inaccurate. Consider using '#align complex.exp_pi_mul_I Complex.exp_pi_mul_Iₓ'. -/
 @[simp]
 theorem exp_pi_mul_I : exp (π * I) = -1 :=
   exp_zero ▸ exp_antiperiodic.Eq
 #align complex.exp_pi_mul_I Complex.exp_pi_mul_I
 
-/- warning: complex.exp_two_pi_mul_I -> Complex.exp_two_pi_mul_I is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi)) Complex.I)) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align complex.exp_two_pi_mul_I Complex.exp_two_pi_mul_Iₓ'. -/
 @[simp]
 theorem exp_two_pi_mul_I : exp (2 * π * I) = 1 :=
   exp_periodic.Eq.trans exp_zero
 #align complex.exp_two_pi_mul_I Complex.exp_two_pi_mul_I
 
-/- warning: complex.exp_nat_mul_two_pi_mul_I -> Complex.exp_nat_mul_two_pi_mul_I is a dubious translation:
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-but is expected to have type
-  forall (n : Nat), Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.ofReal' Real.pi)) Complex.I))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))
-Case conversion may be inaccurate. Consider using '#align complex.exp_nat_mul_two_pi_mul_I Complex.exp_nat_mul_two_pi_mul_Iₓ'. -/
 @[simp]
 theorem exp_nat_mul_two_pi_mul_I (n : ℕ) : exp (n * (2 * π * I)) = 1 :=
   (exp_periodic.nat_mul_eq n).trans exp_zero
 #align complex.exp_nat_mul_two_pi_mul_I Complex.exp_nat_mul_two_pi_mul_I
 
-/- warning: complex.exp_int_mul_two_pi_mul_I -> Complex.exp_int_mul_two_pi_mul_I is a dubious translation:
-lean 3 declaration is
-  forall (n : Int), Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi)) Complex.I))) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))
-but is expected to have type
-  forall (n : Int), Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.ofReal' Real.pi)) Complex.I))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))
-Case conversion may be inaccurate. Consider using '#align complex.exp_int_mul_two_pi_mul_I Complex.exp_int_mul_two_pi_mul_Iₓ'. -/
 @[simp]
 theorem exp_int_mul_two_pi_mul_I (n : ℤ) : exp (n * (2 * π * I)) = 1 :=
   (exp_periodic.int_mul_eq n).trans exp_zero
 #align complex.exp_int_mul_two_pi_mul_I Complex.exp_int_mul_two_pi_mul_I
 
-/- warning: complex.exp_add_pi_mul_I -> Complex.exp_add_pi_mul_I is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Complex (Complex.exp (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi) Complex.I))) (Neg.neg.{0} Complex Complex.hasNeg (Complex.exp z))
-but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (Complex.exp (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' Real.pi) Complex.I))) (Neg.neg.{0} Complex Complex.instNegComplex (Complex.exp z))
-Case conversion may be inaccurate. Consider using '#align complex.exp_add_pi_mul_I Complex.exp_add_pi_mul_Iₓ'. -/
 @[simp]
 theorem exp_add_pi_mul_I (z : ℂ) : exp (z + π * I) = -exp z :=
   exp_antiperiodic z
 #align complex.exp_add_pi_mul_I Complex.exp_add_pi_mul_I
 
-/- warning: complex.exp_sub_pi_mul_I -> Complex.exp_sub_pi_mul_I is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Complex (Complex.exp (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi) Complex.I))) (Neg.neg.{0} Complex Complex.hasNeg (Complex.exp z))
-but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (Complex.exp (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' Real.pi) Complex.I))) (Neg.neg.{0} Complex Complex.instNegComplex (Complex.exp z))
-Case conversion may be inaccurate. Consider using '#align complex.exp_sub_pi_mul_I Complex.exp_sub_pi_mul_Iₓ'. -/
 @[simp]
 theorem exp_sub_pi_mul_I (z : ℂ) : exp (z - π * I) = -exp z :=
   exp_antiperiodic.sub_eq z
 #align complex.exp_sub_pi_mul_I Complex.exp_sub_pi_mul_I
 
-/- warning: complex.abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le -> Complex.abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le is a dubious translation:
-lean 3 declaration is
-  forall {a : Real} {b : Real}, (LE.le.{0} Real Real.hasLe a (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall {z : Complex}, (LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)) b) -> (LE.le.{0} Real Real.hasLe b (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (LE.le.{0} Real Real.hasLe (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) a) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) (Complex.exp z) (Complex.exp (Neg.neg.{0} Complex Complex.hasNeg z)))))) (Real.exp (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) a (Real.cos b)) (Real.exp (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)))))))
-but is expected to have type
-  forall {a : Real} {b : Real}, (LE.le.{0} Real Real.instLEReal a (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall {z : Complex}, (LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) b) -> (LE.le.{0} Real Real.instLEReal b (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' a) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.exp z) (Complex.exp (Neg.neg.{0} Complex Complex.instNegComplex z)))))) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' a) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.exp z) (Complex.exp (Neg.neg.{0} Complex Complex.instNegComplex z)))))) (Real.exp (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) a (Real.cos b)) (Real.exp (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)))))))
-Case conversion may be inaccurate. Consider using '#align complex.abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le Complex.abs_exp_mul_exp_add_exp_neg_le_of_abs_im_leₓ'. -/
 /-- A supporting lemma for the **Phragmen-Lindelöf principle** in a horizontal strip. If `z : ℂ`
 belongs to a horizontal strip `|complex.im z| ≤ b`, `b ≤ π / 2`, and `a ≤ 0`, then
 $$\left|exp^{a\left(e^{z}+e^{-z}\right)}\right| \le e^{a\cos b \exp^{|re z|}}.$$

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

@@ -62,10 +62,8 @@ but is expected to have type
   Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.sin
 Case conversion may be inaccurate. Consider using '#align complex.continuous_sin Complex.continuous_sinₓ'. -/
 @[continuity]
-theorem continuous_sin : Continuous sin :=
-  by
-  change Continuous fun z => (exp (-z * I) - exp (z * I)) * I / 2
-  continuity
+theorem continuous_sin : Continuous sin := by
+  change Continuous fun z => (exp (-z * I) - exp (z * I)) * I / 2; continuity
 #align complex.continuous_sin Complex.continuous_sin
 
 /- warning: complex.continuous_on_sin -> Complex.continuousOn_sin is a dubious translation:
@@ -85,10 +83,8 @@ but is expected to have type
   Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.cos
 Case conversion may be inaccurate. Consider using '#align complex.continuous_cos Complex.continuous_cosₓ'. -/
 @[continuity]
-theorem continuous_cos : Continuous cos :=
-  by
-  change Continuous fun z => (exp (z * I) + exp (-z * I)) / 2
-  continuity
+theorem continuous_cos : Continuous cos := by
+  change Continuous fun z => (exp (z * I) + exp (-z * I)) / 2; continuity
 #align complex.continuous_cos Complex.continuous_cos
 
 /- warning: complex.continuous_on_cos -> Complex.continuousOn_cos is a dubious translation:
@@ -108,9 +104,7 @@ but is expected to have type
   Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.sinh
 Case conversion may be inaccurate. Consider using '#align complex.continuous_sinh Complex.continuous_sinhₓ'. -/
 @[continuity]
-theorem continuous_sinh : Continuous sinh :=
-  by
-  change Continuous fun z => (exp z - exp (-z)) / 2
+theorem continuous_sinh : Continuous sinh := by change Continuous fun z => (exp z - exp (-z)) / 2;
   continuity
 #align complex.continuous_sinh Complex.continuous_sinh
 
@@ -121,9 +115,7 @@ but is expected to have type
   Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.cosh
 Case conversion may be inaccurate. Consider using '#align complex.continuous_cosh Complex.continuous_coshₓ'. -/
 @[continuity]
-theorem continuous_cosh : Continuous cosh :=
-  by
-  change Continuous fun z => (exp z + exp (-z)) / 2
+theorem continuous_cosh : Continuous cosh := by change Continuous fun z => (exp z + exp (-z)) / 2;
   continuity
 #align complex.continuous_cosh Complex.continuous_cosh
 
@@ -1134,17 +1126,13 @@ theorem range_sin : range sin = (Icc (-1) 1 : Set ℝ) :=
 #align real.range_sin Real.range_sin
 
 #print Real.range_cos_infinite /-
-theorem range_cos_infinite : (range Real.cos).Infinite :=
-  by
-  rw [Real.range_cos]
+theorem range_cos_infinite : (range Real.cos).Infinite := by rw [Real.range_cos];
   exact Icc_infinite (by norm_num)
 #align real.range_cos_infinite Real.range_cos_infinite
 -/
 
 #print Real.range_sin_infinite /-
-theorem range_sin_infinite : (range Real.sin).Infinite :=
-  by
-  rw [Real.range_sin]
+theorem range_sin_infinite : (range Real.sin).Infinite := by rw [Real.range_sin];
   exact Icc_infinite (by norm_num)
 #align real.range_sin_infinite Real.range_sin_infinite
 -/
@@ -1220,8 +1208,7 @@ theorem sqrtTwoAddSeries_lt_two : ∀ n : ℕ, sqrtTwoAddSeries 0 n < 2
   | n + 1 => by
     refine' lt_of_lt_of_le _ (sqrt_sq zero_lt_two.le).le
     rw [sqrt_two_add_series, sqrt_lt_sqrt_iff, ← lt_sub_iff_add_lt']
-    · refine' (sqrt_two_add_series_lt_two n).trans_le _
-      norm_num
+    · refine' (sqrt_two_add_series_lt_two n).trans_le _; norm_num
     · exact add_nonneg zero_le_two (sqrt_two_add_series_zero_nonneg n)
 #align real.sqrt_two_add_series_lt_two Real.sqrtTwoAddSeries_lt_two
 
@@ -1266,12 +1253,8 @@ theorem cos_pi_over_two_pow : ∀ n : ℕ, cos (π / 2 ^ (n + 1)) = sqrtTwoAddSe
       try exact this
     apply add_nonneg; norm_num; apply sqrt_two_add_series_zero_nonneg; norm_num
     apply le_of_lt; apply cos_pos_of_mem_Ioo ⟨_, _⟩
-    · trans (0 : ℝ)
-      rw [neg_lt_zero]
-      apply pi_div_two_pos
-      apply div_pos pi_pos
-      apply pow_pos
-      norm_num
+    · trans (0 : ℝ); rw [neg_lt_zero]; apply pi_div_two_pos
+      apply div_pos pi_pos; apply pow_pos; norm_num
     apply div_lt_div' (le_refl π) _ pi_pos _
     refine' lt_of_le_of_lt (le_of_eq (pow_one _).symm) _
     apply pow_lt_pow; norm_num; apply Nat.succ_lt_succ; apply Nat.succ_pos; all_goals norm_num
@@ -1309,19 +1292,10 @@ theorem sin_pi_over_two_pow_succ (n : ℕ) :
   by
   symm; rw [div_eq_iff_mul_eq]; symm
   rw [sqrt_eq_iff_sq_eq, mul_pow, sin_sq_pi_over_two_pow_succ, sub_mul]
-  · congr
-    norm_num
-    rw [mul_comm]
-    convert mul_div_cancel' _ _
-    norm_num
-    norm_num
-  · rw [sub_nonneg]
-    apply le_of_lt
-    apply sqrt_two_add_series_lt_two
+  · congr ; norm_num; rw [mul_comm]; convert mul_div_cancel' _ _; norm_num; norm_num
+  · rw [sub_nonneg]; apply le_of_lt; apply sqrt_two_add_series_lt_two
   apply le_of_lt; apply mul_pos; apply sin_pos_of_pos_of_lt_pi
-  · apply div_pos pi_pos
-    apply pow_pos
-    norm_num
+  · apply div_pos pi_pos; apply pow_pos; norm_num
   refine' lt_of_lt_of_le _ (le_of_eq (div_one _)); rw [div_lt_div_left]
   refine' lt_of_le_of_lt (le_of_eq (pow_zero 2).symm) _
   apply pow_lt_pow; norm_num; apply Nat.succ_pos; apply pi_pos
@@ -1331,89 +1305,57 @@ theorem sin_pi_over_two_pow_succ (n : ℕ) :
 
 #print Real.cos_pi_div_four /-
 @[simp]
-theorem cos_pi_div_four : cos (π / 4) = sqrt 2 / 2 :=
-  by
-  trans cos (π / 2 ^ 2)
-  congr
-  norm_num
+theorem cos_pi_div_four : cos (π / 4) = sqrt 2 / 2 := by trans cos (π / 2 ^ 2); congr ; norm_num;
   simp
 #align real.cos_pi_div_four Real.cos_pi_div_four
 -/
 
 #print Real.sin_pi_div_four /-
 @[simp]
-theorem sin_pi_div_four : sin (π / 4) = sqrt 2 / 2 :=
-  by
-  trans sin (π / 2 ^ 2)
-  congr
-  norm_num
+theorem sin_pi_div_four : sin (π / 4) = sqrt 2 / 2 := by trans sin (π / 2 ^ 2); congr ; norm_num;
   simp
 #align real.sin_pi_div_four Real.sin_pi_div_four
 -/
 
 #print Real.cos_pi_div_eight /-
 @[simp]
-theorem cos_pi_div_eight : cos (π / 8) = sqrt (2 + sqrt 2) / 2 :=
-  by
-  trans cos (π / 2 ^ 3)
-  congr
-  norm_num
-  simp
+theorem cos_pi_div_eight : cos (π / 8) = sqrt (2 + sqrt 2) / 2 := by trans cos (π / 2 ^ 3); congr ;
+  norm_num; simp
 #align real.cos_pi_div_eight Real.cos_pi_div_eight
 -/
 
 #print Real.sin_pi_div_eight /-
 @[simp]
-theorem sin_pi_div_eight : sin (π / 8) = sqrt (2 - sqrt 2) / 2 :=
-  by
-  trans sin (π / 2 ^ 3)
-  congr
-  norm_num
-  simp
+theorem sin_pi_div_eight : sin (π / 8) = sqrt (2 - sqrt 2) / 2 := by trans sin (π / 2 ^ 3); congr ;
+  norm_num; simp
 #align real.sin_pi_div_eight Real.sin_pi_div_eight
 -/
 
 #print Real.cos_pi_div_sixteen /-
 @[simp]
-theorem cos_pi_div_sixteen : cos (π / 16) = sqrt (2 + sqrt (2 + sqrt 2)) / 2 :=
-  by
-  trans cos (π / 2 ^ 4)
-  congr
-  norm_num
-  simp
+theorem cos_pi_div_sixteen : cos (π / 16) = sqrt (2 + sqrt (2 + sqrt 2)) / 2 := by
+  trans cos (π / 2 ^ 4); congr ; norm_num; simp
 #align real.cos_pi_div_sixteen Real.cos_pi_div_sixteen
 -/
 
 #print Real.sin_pi_div_sixteen /-
 @[simp]
-theorem sin_pi_div_sixteen : sin (π / 16) = sqrt (2 - sqrt (2 + sqrt 2)) / 2 :=
-  by
-  trans sin (π / 2 ^ 4)
-  congr
-  norm_num
-  simp
+theorem sin_pi_div_sixteen : sin (π / 16) = sqrt (2 - sqrt (2 + sqrt 2)) / 2 := by
+  trans sin (π / 2 ^ 4); congr ; norm_num; simp
 #align real.sin_pi_div_sixteen Real.sin_pi_div_sixteen
 -/
 
 #print Real.cos_pi_div_thirty_two /-
 @[simp]
-theorem cos_pi_div_thirty_two : cos (π / 32) = sqrt (2 + sqrt (2 + sqrt (2 + sqrt 2))) / 2 :=
-  by
-  trans cos (π / 2 ^ 5)
-  congr
-  norm_num
-  simp
+theorem cos_pi_div_thirty_two : cos (π / 32) = sqrt (2 + sqrt (2 + sqrt (2 + sqrt 2))) / 2 := by
+  trans cos (π / 2 ^ 5); congr ; norm_num; simp
 #align real.cos_pi_div_thirty_two Real.cos_pi_div_thirty_two
 -/
 
 #print Real.sin_pi_div_thirty_two /-
 @[simp]
-theorem sin_pi_div_thirty_two : sin (π / 32) = sqrt (2 - sqrt (2 + sqrt (2 + sqrt 2))) / 2 :=
-  by
-  trans sin (π / 2 ^ 5)
-  congr
-  norm_num
-  simp
+theorem sin_pi_div_thirty_two : sin (π / 32) = sqrt (2 - sqrt (2 + sqrt (2 + sqrt 2))) / 2 := by
+  trans sin (π / 2 ^ 5); congr ; norm_num; simp
 #align real.sin_pi_div_thirty_two Real.sin_pi_div_thirty_two
 -/
 
@@ -1425,9 +1367,7 @@ theorem cos_pi_div_three : cos (π / 3) = 1 / 2 :=
   by
   have h₁ : (2 * cos (π / 3) - 1) ^ 2 * (2 * cos (π / 3) + 2) = 0 :=
     by
-    have : cos (3 * (π / 3)) = cos π := by
-      congr 1
-      ring
+    have : cos (3 * (π / 3)) = cos π := by congr 1; ring
     linarith [cos_pi, cos_three_mul (π / 3)]
   cases' mul_eq_zero.mp h₁ with h h
   · linarith [pow_eq_zero h]
@@ -1462,10 +1402,7 @@ theorem sq_cos_pi_div_six : cos (π / 6) ^ 2 = 3 / 4 :=
 @[simp]
 theorem cos_pi_div_six : cos (π / 6) = sqrt 3 / 2 :=
   by
-  suffices sqrt 3 = cos (π / 6) * 2
-    by
-    field_simp [(by norm_num : 0 ≠ 2)]
-    exact this.symm
+  suffices sqrt 3 = cos (π / 6) * 2 by field_simp [(by norm_num : 0 ≠ 2)] ; exact this.symm
   rw [sqrt_eq_iff_sq_eq]
   · have h1 := (mul_right_inj' (by norm_num : (4 : ℝ) ≠ 0)).mpr sq_cos_pi_div_six
     rw [← sub_eq_zero] at h1⊢
@@ -1763,10 +1700,8 @@ lean 3 declaration is
 but is expected to have type
   Filter.Tendsto.{0, 0} Real Real Real.sin (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Set.Iio.{0} Real Real.instPreorderReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
 Case conversion may be inaccurate. Consider using '#align real.tendsto_sin_pi_div_two Real.tendsto_sin_pi_div_twoₓ'. -/
-theorem tendsto_sin_pi_div_two : Tendsto sin (𝓝[<] (π / 2)) (𝓝 1) :=
-  by
-  convert continuous_sin.continuous_within_at
-  simp
+theorem tendsto_sin_pi_div_two : Tendsto sin (𝓝[<] (π / 2)) (𝓝 1) := by
+  convert continuous_sin.continuous_within_at; simp
 #align real.tendsto_sin_pi_div_two Real.tendsto_sin_pi_div_two
 
 /- warning: real.tendsto_cos_pi_div_two -> Real.tendsto_cos_pi_div_two is a dubious translation:
@@ -1778,8 +1713,7 @@ Case conversion may be inaccurate. Consider using '#align real.tendsto_cos_pi_di
 theorem tendsto_cos_pi_div_two : Tendsto cos (𝓝[<] (π / 2)) (𝓝[>] 0) :=
   by
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
-  · convert continuous_cos.continuous_within_at
-    simp
+  · convert continuous_cos.continuous_within_at; simp
   ·
     filter_upwards [Ioo_mem_nhdsWithin_Iio
         (right_mem_Ioc.mpr (neg_lt_self pi_div_two_pos))]with x hx using cos_pos_of_mem_Ioo hx
@@ -1803,10 +1737,8 @@ lean 3 declaration is
 but is expected to have type
   Filter.Tendsto.{0, 0} Real Real Real.sin (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Set.Ioi.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
 Case conversion may be inaccurate. Consider using '#align real.tendsto_sin_neg_pi_div_two Real.tendsto_sin_neg_pi_div_twoₓ'. -/
-theorem tendsto_sin_neg_pi_div_two : Tendsto sin (𝓝[>] (-(π / 2))) (𝓝 (-1)) :=
-  by
-  convert continuous_sin.continuous_within_at
-  simp
+theorem tendsto_sin_neg_pi_div_two : Tendsto sin (𝓝[>] (-(π / 2))) (𝓝 (-1)) := by
+  convert continuous_sin.continuous_within_at; simp
 #align real.tendsto_sin_neg_pi_div_two Real.tendsto_sin_neg_pi_div_two
 
 /- warning: real.tendsto_cos_neg_pi_div_two -> Real.tendsto_cos_neg_pi_div_two is a dubious translation:
@@ -1818,8 +1750,7 @@ Case conversion may be inaccurate. Consider using '#align real.tendsto_cos_neg_p
 theorem tendsto_cos_neg_pi_div_two : Tendsto cos (𝓝[>] (-(π / 2))) (𝓝[>] 0) :=
   by
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
-  · convert continuous_cos.continuous_within_at
-    simp
+  · convert continuous_cos.continuous_within_at; simp
   ·
     filter_upwards [Ioo_mem_nhdsWithin_Ioi
         (left_mem_Ico.mpr (neg_lt_self pi_div_two_pos))]with x hx using cos_pos_of_mem_Ioo hx

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

@@ -1528,10 +1528,7 @@ def sinOrderIso : Icc (-(π / 2)) (π / 2) ≃o Icc (-1 : ℝ) 1 :=
 #align real.sin_order_iso Real.sinOrderIso
 
 /- warning: real.coe_sin_order_iso_apply -> Real.coe_sinOrderIso_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align real.coe_sin_order_iso_apply Real.coe_sinOrderIso_applyₓ'. -/
 @[simp]
 theorem coe_sinOrderIso_apply (x : Icc (-(π / 2)) (π / 2)) : (sinOrderIso x : ℝ) = sin x :=
@@ -1539,10 +1536,7 @@ theorem coe_sinOrderIso_apply (x : Icc (-(π / 2)) (π / 2)) : (sinOrderIso x :
 #align real.coe_sin_order_iso_apply Real.coe_sinOrderIso_apply
 
 /- warning: real.sin_order_iso_apply -> Real.sinOrderIso_apply is a dubious translation:
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(Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) Real.sinOrderIso x) (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Real.sin (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) x)) (Real.sin_mem_Icc (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) x)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align real.sin_order_iso_apply Real.sinOrderIso_applyₓ'. -/
 theorem sinOrderIso_apply (x : Icc (-(π / 2)) (π / 2)) : sinOrderIso x = ⟨sin x, sin_mem_Icc x⟩ :=
   rfl

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

@@ -1531,7 +1531,7 @@ def sinOrderIso : Icc (-(π / 2)) (π / 2) ≃o Icc (-1 : ℝ) 1 :=
 lean 3 declaration is
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(One.one.{0} Real Real.hasOne))))) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) Real (coeSubtype.{1} Real (fun (x : 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(HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))))))) x))
 but is expected to have type
-  forall (x : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))), Eq.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (fun (_x : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real 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(x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Set.Elem.{0} Real 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Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) Real.sinOrderIso x)) (Real.sin (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) x))
+  forall (x : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))), Eq.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : 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(One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) Real.sinOrderIso x)) (Real.sin (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) x))
 Case conversion may be inaccurate. Consider using '#align real.coe_sin_order_iso_apply Real.coe_sinOrderIso_applyₓ'. -/
 @[simp]
 theorem coe_sinOrderIso_apply (x : Icc (-(π / 2)) (π / 2)) : (sinOrderIso x : ℝ) = sin x :=
@@ -1542,7 +1542,7 @@ theorem coe_sinOrderIso_apply (x : Icc (-(π / 2)) (π / 2)) : (sinOrderIso x :
 lean 3 declaration is
   forall (x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))), Eq.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeFn.{1, 1} (OrderIso.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))))) (fun (_x : RelIso.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) (RelIso.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))) Real.sinOrderIso x) (Subtype.mk.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Real.sin ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))))))) x)) (Real.sin_mem_Icc ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))))))) x)))
 but is expected to have type
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2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 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(Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) Real.sinOrderIso x) (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Real.sin (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) x)) (Real.sin_mem_Icc (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) x)))
+  forall (x : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))), Eq.{1} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (fun (_x : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 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(Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} 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(One.toOfNat1.{0} Real Real.instOneReal)))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) Real.sinOrderIso x) (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Real.sin (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) x)) (Real.sin_mem_Icc (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) x)))
 Case conversion may be inaccurate. Consider using '#align real.sin_order_iso_apply Real.sinOrderIso_applyₓ'. -/
 theorem sinOrderIso_apply (x : Icc (-(π / 2)) (π / 2)) : sinOrderIso x = ⟨sin x, sin_mem_Icc x⟩ :=
   rfl

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

@@ -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.basic
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
+! leanprover-community/mathlib commit 50251fd6309cca5ca2e747882ffecd2729f38c5d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.SpecialFunctions.Exp
 /-!
 # Trigonometric functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 This file contains the definition of `π`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/f8c79b0a623404854a2902b836eac32156fd7712

@@ -52,6 +52,12 @@ open Set Filter
 
 namespace Complex
 
+/- warning: complex.continuous_sin -> Complex.continuous_sin is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Complex.sin
+but is expected to have type
+  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.sin
+Case conversion may be inaccurate. Consider using '#align complex.continuous_sin Complex.continuous_sinₓ'. -/
 @[continuity]
 theorem continuous_sin : Continuous sin :=
   by
@@ -59,10 +65,22 @@ theorem continuous_sin : Continuous sin :=
   continuity
 #align complex.continuous_sin Complex.continuous_sin
 
+/- warning: complex.continuous_on_sin -> Complex.continuousOn_sin is a dubious translation:
+lean 3 declaration is
+  forall {s : Set.{0} Complex}, ContinuousOn.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Complex.sin s
+but is expected to have type
+  forall {s : Set.{0} Complex}, ContinuousOn.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.sin s
+Case conversion may be inaccurate. Consider using '#align complex.continuous_on_sin Complex.continuousOn_sinₓ'. -/
 theorem continuousOn_sin {s : Set ℂ} : ContinuousOn sin s :=
   continuous_sin.ContinuousOn
 #align complex.continuous_on_sin Complex.continuousOn_sin
 
+/- warning: complex.continuous_cos -> Complex.continuous_cos is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Complex.cos
+but is expected to have type
+  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.cos
+Case conversion may be inaccurate. Consider using '#align complex.continuous_cos Complex.continuous_cosₓ'. -/
 @[continuity]
 theorem continuous_cos : Continuous cos :=
   by
@@ -70,10 +88,22 @@ theorem continuous_cos : Continuous cos :=
   continuity
 #align complex.continuous_cos Complex.continuous_cos
 
+/- warning: complex.continuous_on_cos -> Complex.continuousOn_cos is a dubious translation:
+lean 3 declaration is
+  forall {s : Set.{0} Complex}, ContinuousOn.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Complex.cos s
+but is expected to have type
+  forall {s : Set.{0} Complex}, ContinuousOn.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.cos s
+Case conversion may be inaccurate. Consider using '#align complex.continuous_on_cos Complex.continuousOn_cosₓ'. -/
 theorem continuousOn_cos {s : Set ℂ} : ContinuousOn cos s :=
   continuous_cos.ContinuousOn
 #align complex.continuous_on_cos Complex.continuousOn_cos
 
+/- warning: complex.continuous_sinh -> Complex.continuous_sinh is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Complex.sinh
+but is expected to have type
+  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.sinh
+Case conversion may be inaccurate. Consider using '#align complex.continuous_sinh Complex.continuous_sinhₓ'. -/
 @[continuity]
 theorem continuous_sinh : Continuous sinh :=
   by
@@ -81,6 +111,12 @@ theorem continuous_sinh : Continuous sinh :=
   continuity
 #align complex.continuous_sinh Complex.continuous_sinh
 
+/- warning: complex.continuous_cosh -> Complex.continuous_cosh is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Complex.cosh
+but is expected to have type
+  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.cosh
+Case conversion may be inaccurate. Consider using '#align complex.continuous_cosh Complex.continuous_coshₓ'. -/
 @[continuity]
 theorem continuous_cosh : Continuous cosh :=
   by
@@ -94,73 +130,119 @@ namespace Real
 
 variable {x y z : ℝ}
 
+#print Real.continuous_sin /-
 @[continuity]
 theorem continuous_sin : Continuous sin :=
   Complex.continuous_re.comp (Complex.continuous_sin.comp Complex.continuous_ofReal)
 #align real.continuous_sin Real.continuous_sin
+-/
 
+#print Real.continuousOn_sin /-
 theorem continuousOn_sin {s} : ContinuousOn sin s :=
   continuous_sin.ContinuousOn
 #align real.continuous_on_sin Real.continuousOn_sin
+-/
 
+#print Real.continuous_cos /-
 @[continuity]
 theorem continuous_cos : Continuous cos :=
   Complex.continuous_re.comp (Complex.continuous_cos.comp Complex.continuous_ofReal)
 #align real.continuous_cos Real.continuous_cos
+-/
 
+#print Real.continuousOn_cos /-
 theorem continuousOn_cos {s} : ContinuousOn cos s :=
   continuous_cos.ContinuousOn
 #align real.continuous_on_cos Real.continuousOn_cos
+-/
 
+#print Real.continuous_sinh /-
 @[continuity]
 theorem continuous_sinh : Continuous sinh :=
   Complex.continuous_re.comp (Complex.continuous_sinh.comp Complex.continuous_ofReal)
 #align real.continuous_sinh Real.continuous_sinh
+-/
 
+#print Real.continuous_cosh /-
 @[continuity]
 theorem continuous_cosh : Continuous cosh :=
   Complex.continuous_re.comp (Complex.continuous_cosh.comp Complex.continuous_ofReal)
 #align real.continuous_cosh Real.continuous_cosh
+-/
 
 end Real
 
 namespace Real
 
+/- warning: real.exists_cos_eq_zero -> Real.exists_cos_eq_zero is a dubious translation:
+lean 3 declaration is
+  Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.image.{0, 0} Real Real Real.cos (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))
+but is expected to have type
+  Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.image.{0, 0} Real Real Real.cos (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+Case conversion may be inaccurate. Consider using '#align real.exists_cos_eq_zero Real.exists_cos_eq_zeroₓ'. -/
 theorem exists_cos_eq_zero : 0 ∈ cos '' Icc (1 : ℝ) 2 :=
   intermediate_value_Icc' (by norm_num) continuousOn_cos
     ⟨le_of_lt cos_two_neg, le_of_lt cos_one_pos⟩
 #align real.exists_cos_eq_zero Real.exists_cos_eq_zero
 
+#print Real.pi /-
 /-- The number π = 3.14159265... Defined here using choice as twice a zero of cos in [1,2], from
 which one can derive all its properties. For explicit bounds on π, see `data.real.pi.bounds`. -/
 protected noncomputable def pi : ℝ :=
   2 * Classical.choose exists_cos_eq_zero
 #align real.pi Real.pi
+-/
 
 -- mathport name: real.pi
 scoped notation "π" => Real.pi
 
+#print Real.cos_pi_div_two /-
 @[simp]
 theorem cos_pi_div_two : cos (π / 2) = 0 := by
   rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)] <;>
     exact (Classical.choose_spec exists_cos_eq_zero).2
 #align real.cos_pi_div_two Real.cos_pi_div_two
+-/
 
+/- warning: real.one_le_pi_div_two -> Real.one_le_pi_div_two is a dubious translation:
+lean 3 declaration is
+  LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))
+but is expected to have type
+  LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+Case conversion may be inaccurate. Consider using '#align real.one_le_pi_div_two Real.one_le_pi_div_twoₓ'. -/
 theorem one_le_pi_div_two : (1 : ℝ) ≤ π / 2 := by
   rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)] <;>
     exact (Classical.choose_spec exists_cos_eq_zero).1.1
 #align real.one_le_pi_div_two Real.one_le_pi_div_two
 
+/- warning: real.pi_div_two_le_two -> Real.pi_div_two_le_two is a dubious translation:
+lean 3 declaration is
+  LE.le.{0} Real Real.hasLe (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  LE.le.{0} Real Real.instLEReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+Case conversion may be inaccurate. Consider using '#align real.pi_div_two_le_two Real.pi_div_two_le_twoₓ'. -/
 theorem pi_div_two_le_two : π / 2 ≤ 2 := by
   rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)] <;>
     exact (Classical.choose_spec exists_cos_eq_zero).1.2
 #align real.pi_div_two_le_two Real.pi_div_two_le_two
 
+/- warning: real.two_le_pi -> Real.two_le_pi is a dubious translation:
+lean 3 declaration is
+  LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) Real.pi
+but is expected to have type
+  LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi
+Case conversion may be inaccurate. Consider using '#align real.two_le_pi Real.two_le_piₓ'. -/
 theorem two_le_pi : (2 : ℝ) ≤ π :=
   (div_le_div_right (show (0 : ℝ) < 2 by norm_num)).1
     (by rw [div_self (two_ne_zero' ℝ)] <;> exact one_le_pi_div_two)
 #align real.two_le_pi Real.two_le_pi
 
+/- warning: real.pi_le_four -> Real.pi_le_four is a dubious translation:
+lean 3 declaration is
+  LE.le.{0} Real Real.hasLe Real.pi (OfNat.ofNat.{0} Real 4 (OfNat.mk.{0} Real 4 (bit0.{0} Real Real.hasAdd (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))
+but is expected to have type
+  LE.le.{0} Real Real.instLEReal Real.pi (OfNat.ofNat.{0} Real 4 (instOfNat.{0} Real 4 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
+Case conversion may be inaccurate. Consider using '#align real.pi_le_four Real.pi_le_fourₓ'. -/
 theorem pi_le_four : π ≤ 4 :=
   (div_le_div_right (show (0 : ℝ) < 2 by norm_num)).1
     (calc
@@ -169,18 +251,42 @@ theorem pi_le_four : π ≤ 4 :=
       )
 #align real.pi_le_four Real.pi_le_four
 
+/- warning: real.pi_pos -> Real.pi_pos is a dubious translation:
+lean 3 declaration is
+  LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) Real.pi
+but is expected to have type
+  LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) Real.pi
+Case conversion may be inaccurate. Consider using '#align real.pi_pos Real.pi_posₓ'. -/
 theorem pi_pos : 0 < π :=
   lt_of_lt_of_le (by norm_num) two_le_pi
 #align real.pi_pos Real.pi_pos
 
+/- warning: real.pi_ne_zero -> Real.pi_ne_zero is a dubious translation:
+lean 3 declaration is
+  Ne.{1} Real Real.pi (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  Ne.{1} Real Real.pi (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align real.pi_ne_zero Real.pi_ne_zeroₓ'. -/
 theorem pi_ne_zero : π ≠ 0 :=
   ne_of_gt pi_pos
 #align real.pi_ne_zero Real.pi_ne_zero
 
+/- warning: real.pi_div_two_pos -> Real.pi_div_two_pos is a dubious translation:
+lean 3 declaration is
+  LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))
+but is expected to have type
+  LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+Case conversion may be inaccurate. Consider using '#align real.pi_div_two_pos Real.pi_div_two_posₓ'. -/
 theorem pi_div_two_pos : 0 < π / 2 :=
   half_pos pi_pos
 #align real.pi_div_two_pos Real.pi_div_two_pos
 
+/- warning: real.two_pi_pos -> Real.two_pi_pos is a dubious translation:
+lean 3 declaration is
+  LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) Real.pi)
+but is expected to have type
+  LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)
+Case conversion may be inaccurate. Consider using '#align real.two_pi_pos Real.two_pi_posₓ'. -/
 theorem two_pi_pos : 0 < 2 * π := by linarith [pi_pos]
 #align real.two_pi_pos Real.two_pi_pos
 
@@ -192,19 +298,39 @@ open Real
 
 open Real NNReal
 
+#print NNReal.pi /-
 /-- `π` considered as a nonnegative real. -/
 noncomputable def pi : ℝ≥0 :=
   ⟨π, Real.pi_pos.le⟩
 #align nnreal.pi NNReal.pi
+-/
 
+/- warning: nnreal.coe_real_pi -> NNReal.coe_real_pi is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) NNReal.pi) Real.pi
+but is expected to have type
+  Eq.{1} Real (NNReal.toReal NNReal.pi) Real.pi
+Case conversion may be inaccurate. Consider using '#align nnreal.coe_real_pi NNReal.coe_real_piₓ'. -/
 @[simp]
 theorem coe_real_pi : (pi : ℝ) = π :=
   rfl
 #align nnreal.coe_real_pi NNReal.coe_real_pi
 
+/- warning: nnreal.pi_pos -> NNReal.pi_pos is a dubious translation:
+lean 3 declaration is
+  LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) NNReal.pi
+but is expected to have type
+  LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) NNReal.pi
+Case conversion may be inaccurate. Consider using '#align nnreal.pi_pos NNReal.pi_posₓ'. -/
 theorem pi_pos : 0 < pi := by exact_mod_cast Real.pi_pos
 #align nnreal.pi_pos NNReal.pi_pos
 
+/- warning: nnreal.pi_ne_zero -> NNReal.pi_ne_zero is a dubious translation:
+lean 3 declaration is
+  Ne.{1} NNReal NNReal.pi (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
+but is expected to have type
+  Ne.{1} NNReal NNReal.pi (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
+Case conversion may be inaccurate. Consider using '#align nnreal.pi_ne_zero NNReal.pi_ne_zeroₓ'. -/
 theorem pi_ne_zero : pi ≠ 0 :=
   pi_pos.ne'
 #align nnreal.pi_ne_zero NNReal.pi_ne_zero
@@ -215,199 +341,293 @@ namespace Real
 
 open Real
 
+/- warning: real.sin_pi -> Real.sin_pi is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Real.sin Real.pi) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  Eq.{1} Real (Real.sin Real.pi) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align real.sin_pi Real.sin_piₓ'. -/
 @[simp]
 theorem sin_pi : sin π = 0 := by
   rw [← mul_div_cancel_left π (two_ne_zero' ℝ), two_mul, add_div, sin_add, cos_pi_div_two] <;> simp
 #align real.sin_pi Real.sin_pi
 
+/- warning: real.cos_pi -> Real.cos_pi is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Real.cos Real.pi) (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  Eq.{1} Real (Real.cos Real.pi) (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align real.cos_pi Real.cos_piₓ'. -/
 @[simp]
 theorem cos_pi : cos π = -1 := by
   rw [← mul_div_cancel_left π (two_ne_zero' ℝ), mul_div_assoc, cos_two_mul, cos_pi_div_two] <;>
     simp [bit0, pow_add]
 #align real.cos_pi Real.cos_pi
 
+#print Real.sin_two_pi /-
 @[simp]
 theorem sin_two_pi : sin (2 * π) = 0 := by simp [two_mul, sin_add]
 #align real.sin_two_pi Real.sin_two_pi
+-/
 
+#print Real.cos_two_pi /-
 @[simp]
 theorem cos_two_pi : cos (2 * π) = 1 := by simp [two_mul, cos_add]
 #align real.cos_two_pi Real.cos_two_pi
+-/
 
+#print Real.sin_antiperiodic /-
 theorem sin_antiperiodic : Function.Antiperiodic sin π := by simp [sin_add]
 #align real.sin_antiperiodic Real.sin_antiperiodic
+-/
 
+#print Real.sin_periodic /-
 theorem sin_periodic : Function.Periodic sin (2 * π) :=
   sin_antiperiodic.Periodic
 #align real.sin_periodic Real.sin_periodic
+-/
 
+#print Real.sin_add_pi /-
 @[simp]
 theorem sin_add_pi (x : ℝ) : sin (x + π) = -sin x :=
   sin_antiperiodic x
 #align real.sin_add_pi Real.sin_add_pi
+-/
 
+#print Real.sin_add_two_pi /-
 @[simp]
 theorem sin_add_two_pi (x : ℝ) : sin (x + 2 * π) = sin x :=
   sin_periodic x
 #align real.sin_add_two_pi Real.sin_add_two_pi
+-/
 
+#print Real.sin_sub_pi /-
 @[simp]
 theorem sin_sub_pi (x : ℝ) : sin (x - π) = -sin x :=
   sin_antiperiodic.sub_eq x
 #align real.sin_sub_pi Real.sin_sub_pi
+-/
 
+#print Real.sin_sub_two_pi /-
 @[simp]
 theorem sin_sub_two_pi (x : ℝ) : sin (x - 2 * π) = sin x :=
   sin_periodic.sub_eq x
 #align real.sin_sub_two_pi Real.sin_sub_two_pi
+-/
 
+#print Real.sin_pi_sub /-
 @[simp]
 theorem sin_pi_sub (x : ℝ) : sin (π - x) = sin x :=
   neg_neg (sin x) ▸ sin_neg x ▸ sin_antiperiodic.sub_eq'
 #align real.sin_pi_sub Real.sin_pi_sub
+-/
 
+#print Real.sin_two_pi_sub /-
 @[simp]
 theorem sin_two_pi_sub (x : ℝ) : sin (2 * π - x) = -sin x :=
   sin_neg x ▸ sin_periodic.sub_eq'
 #align real.sin_two_pi_sub Real.sin_two_pi_sub
+-/
 
+#print Real.sin_nat_mul_pi /-
 @[simp]
 theorem sin_nat_mul_pi (n : ℕ) : sin (n * π) = 0 :=
   sin_antiperiodic.nat_mul_eq_of_eq_zero sin_zero n
 #align real.sin_nat_mul_pi Real.sin_nat_mul_pi
+-/
 
+#print Real.sin_int_mul_pi /-
 @[simp]
 theorem sin_int_mul_pi (n : ℤ) : sin (n * π) = 0 :=
   sin_antiperiodic.int_mul_eq_of_eq_zero sin_zero n
 #align real.sin_int_mul_pi Real.sin_int_mul_pi
+-/
 
+#print Real.sin_add_nat_mul_two_pi /-
 @[simp]
 theorem sin_add_nat_mul_two_pi (x : ℝ) (n : ℕ) : sin (x + n * (2 * π)) = sin x :=
   sin_periodic.nat_mul n x
 #align real.sin_add_nat_mul_two_pi Real.sin_add_nat_mul_two_pi
+-/
 
+#print Real.sin_add_int_mul_two_pi /-
 @[simp]
 theorem sin_add_int_mul_two_pi (x : ℝ) (n : ℤ) : sin (x + n * (2 * π)) = sin x :=
   sin_periodic.int_mul n x
 #align real.sin_add_int_mul_two_pi Real.sin_add_int_mul_two_pi
+-/
 
+#print Real.sin_sub_nat_mul_two_pi /-
 @[simp]
 theorem sin_sub_nat_mul_two_pi (x : ℝ) (n : ℕ) : sin (x - n * (2 * π)) = sin x :=
   sin_periodic.sub_nat_mul_eq n
 #align real.sin_sub_nat_mul_two_pi Real.sin_sub_nat_mul_two_pi
+-/
 
+#print Real.sin_sub_int_mul_two_pi /-
 @[simp]
 theorem sin_sub_int_mul_two_pi (x : ℝ) (n : ℤ) : sin (x - n * (2 * π)) = sin x :=
   sin_periodic.sub_int_mul_eq n
 #align real.sin_sub_int_mul_two_pi Real.sin_sub_int_mul_two_pi
+-/
 
+#print Real.sin_nat_mul_two_pi_sub /-
 @[simp]
 theorem sin_nat_mul_two_pi_sub (x : ℝ) (n : ℕ) : sin (n * (2 * π) - x) = -sin x :=
   sin_neg x ▸ sin_periodic.nat_mul_sub_eq n
 #align real.sin_nat_mul_two_pi_sub Real.sin_nat_mul_two_pi_sub
+-/
 
+#print Real.sin_int_mul_two_pi_sub /-
 @[simp]
 theorem sin_int_mul_two_pi_sub (x : ℝ) (n : ℤ) : sin (n * (2 * π) - x) = -sin x :=
   sin_neg x ▸ sin_periodic.int_mul_sub_eq n
 #align real.sin_int_mul_two_pi_sub Real.sin_int_mul_two_pi_sub
+-/
 
+#print Real.cos_antiperiodic /-
 theorem cos_antiperiodic : Function.Antiperiodic cos π := by simp [cos_add]
 #align real.cos_antiperiodic Real.cos_antiperiodic
+-/
 
+#print Real.cos_periodic /-
 theorem cos_periodic : Function.Periodic cos (2 * π) :=
   cos_antiperiodic.Periodic
 #align real.cos_periodic Real.cos_periodic
+-/
 
+#print Real.cos_add_pi /-
 @[simp]
 theorem cos_add_pi (x : ℝ) : cos (x + π) = -cos x :=
   cos_antiperiodic x
 #align real.cos_add_pi Real.cos_add_pi
+-/
 
+#print Real.cos_add_two_pi /-
 @[simp]
 theorem cos_add_two_pi (x : ℝ) : cos (x + 2 * π) = cos x :=
   cos_periodic x
 #align real.cos_add_two_pi Real.cos_add_two_pi
+-/
 
+#print Real.cos_sub_pi /-
 @[simp]
 theorem cos_sub_pi (x : ℝ) : cos (x - π) = -cos x :=
   cos_antiperiodic.sub_eq x
 #align real.cos_sub_pi Real.cos_sub_pi
+-/
 
+#print Real.cos_sub_two_pi /-
 @[simp]
 theorem cos_sub_two_pi (x : ℝ) : cos (x - 2 * π) = cos x :=
   cos_periodic.sub_eq x
 #align real.cos_sub_two_pi Real.cos_sub_two_pi
+-/
 
+#print Real.cos_pi_sub /-
 @[simp]
 theorem cos_pi_sub (x : ℝ) : cos (π - x) = -cos x :=
   cos_neg x ▸ cos_antiperiodic.sub_eq'
 #align real.cos_pi_sub Real.cos_pi_sub
+-/
 
+#print Real.cos_two_pi_sub /-
 @[simp]
 theorem cos_two_pi_sub (x : ℝ) : cos (2 * π - x) = cos x :=
   cos_neg x ▸ cos_periodic.sub_eq'
 #align real.cos_two_pi_sub Real.cos_two_pi_sub
+-/
 
+#print Real.cos_nat_mul_two_pi /-
 @[simp]
 theorem cos_nat_mul_two_pi (n : ℕ) : cos (n * (2 * π)) = 1 :=
   (cos_periodic.nat_mul_eq n).trans cos_zero
 #align real.cos_nat_mul_two_pi Real.cos_nat_mul_two_pi
+-/
 
+#print Real.cos_int_mul_two_pi /-
 @[simp]
 theorem cos_int_mul_two_pi (n : ℤ) : cos (n * (2 * π)) = 1 :=
   (cos_periodic.int_mul_eq n).trans cos_zero
 #align real.cos_int_mul_two_pi Real.cos_int_mul_two_pi
+-/
 
+#print Real.cos_add_nat_mul_two_pi /-
 @[simp]
 theorem cos_add_nat_mul_two_pi (x : ℝ) (n : ℕ) : cos (x + n * (2 * π)) = cos x :=
   cos_periodic.nat_mul n x
 #align real.cos_add_nat_mul_two_pi Real.cos_add_nat_mul_two_pi
+-/
 
+#print Real.cos_add_int_mul_two_pi /-
 @[simp]
 theorem cos_add_int_mul_two_pi (x : ℝ) (n : ℤ) : cos (x + n * (2 * π)) = cos x :=
   cos_periodic.int_mul n x
 #align real.cos_add_int_mul_two_pi Real.cos_add_int_mul_two_pi
+-/
 
+#print Real.cos_sub_nat_mul_two_pi /-
 @[simp]
 theorem cos_sub_nat_mul_two_pi (x : ℝ) (n : ℕ) : cos (x - n * (2 * π)) = cos x :=
   cos_periodic.sub_nat_mul_eq n
 #align real.cos_sub_nat_mul_two_pi Real.cos_sub_nat_mul_two_pi
+-/
 
+#print Real.cos_sub_int_mul_two_pi /-
 @[simp]
 theorem cos_sub_int_mul_two_pi (x : ℝ) (n : ℤ) : cos (x - n * (2 * π)) = cos x :=
   cos_periodic.sub_int_mul_eq n
 #align real.cos_sub_int_mul_two_pi Real.cos_sub_int_mul_two_pi
+-/
 
+#print Real.cos_nat_mul_two_pi_sub /-
 @[simp]
 theorem cos_nat_mul_two_pi_sub (x : ℝ) (n : ℕ) : cos (n * (2 * π) - x) = cos x :=
   cos_neg x ▸ cos_periodic.nat_mul_sub_eq n
 #align real.cos_nat_mul_two_pi_sub Real.cos_nat_mul_two_pi_sub
+-/
 
+#print Real.cos_int_mul_two_pi_sub /-
 @[simp]
 theorem cos_int_mul_two_pi_sub (x : ℝ) (n : ℤ) : cos (n * (2 * π) - x) = cos x :=
   cos_neg x ▸ cos_periodic.int_mul_sub_eq n
 #align real.cos_int_mul_two_pi_sub Real.cos_int_mul_two_pi_sub
+-/
 
+#print Real.cos_nat_mul_two_pi_add_pi /-
 @[simp]
 theorem cos_nat_mul_two_pi_add_pi (n : ℕ) : cos (n * (2 * π) + π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.nat_mul n).add_antiperiod_eq cos_antiperiodic
 #align real.cos_nat_mul_two_pi_add_pi Real.cos_nat_mul_two_pi_add_pi
+-/
 
+#print Real.cos_int_mul_two_pi_add_pi /-
 @[simp]
 theorem cos_int_mul_two_pi_add_pi (n : ℤ) : cos (n * (2 * π) + π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.int_mul n).add_antiperiod_eq cos_antiperiodic
 #align real.cos_int_mul_two_pi_add_pi Real.cos_int_mul_two_pi_add_pi
+-/
 
+#print Real.cos_nat_mul_two_pi_sub_pi /-
 @[simp]
 theorem cos_nat_mul_two_pi_sub_pi (n : ℕ) : cos (n * (2 * π) - π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.nat_mul n).sub_antiperiod_eq cos_antiperiodic
 #align real.cos_nat_mul_two_pi_sub_pi Real.cos_nat_mul_two_pi_sub_pi
+-/
 
+#print Real.cos_int_mul_two_pi_sub_pi /-
 @[simp]
 theorem cos_int_mul_two_pi_sub_pi (n : ℤ) : cos (n * (2 * π) - π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.int_mul n).sub_antiperiod_eq cos_antiperiodic
 #align real.cos_int_mul_two_pi_sub_pi Real.cos_int_mul_two_pi_sub_pi
+-/
 
+/- warning: real.sin_pos_of_pos_of_lt_pi -> Real.sin_pos_of_pos_of_lt_pi is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LT.lt.{0} Real Real.hasLt x Real.pi) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.sin x))
+but is expected to have type
+  forall {x : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LT.lt.{0} Real Real.instLTReal x Real.pi) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.sin x))
+Case conversion may be inaccurate. Consider using '#align real.sin_pos_of_pos_of_lt_pi Real.sin_pos_of_pos_of_lt_piₓ'. -/
 theorem sin_pos_of_pos_of_lt_pi {x : ℝ} (h0x : 0 < x) (hxp : x < π) : 0 < sin x :=
   if hx2 : x ≤ 2 then sin_pos_of_pos_of_le_two h0x hx2
   else
@@ -417,10 +637,22 @@ theorem sin_pos_of_pos_of_lt_pi {x : ℝ} (h0x : 0 < x) (hxp : x < π) : 0 < sin
     sin_pi_sub x ▸ sin_pos_of_pos_of_le_two (sub_pos.2 hxp) this
 #align real.sin_pos_of_pos_of_lt_pi Real.sin_pos_of_pos_of_lt_pi
 
+/- warning: real.sin_pos_of_mem_Ioo -> Real.sin_pos_of_mem_Ioo is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Ioo.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) Real.pi)) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.sin x))
+but is expected to have type
+  forall {x : Real}, (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioo.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) Real.pi)) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.sin x))
+Case conversion may be inaccurate. Consider using '#align real.sin_pos_of_mem_Ioo Real.sin_pos_of_mem_Iooₓ'. -/
 theorem sin_pos_of_mem_Ioo {x : ℝ} (hx : x ∈ Ioo 0 π) : 0 < sin x :=
   sin_pos_of_pos_of_lt_pi hx.1 hx.2
 #align real.sin_pos_of_mem_Ioo Real.sin_pos_of_mem_Ioo
 
+/- warning: real.sin_nonneg_of_mem_Icc -> Real.sin_nonneg_of_mem_Icc is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) Real.pi)) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.sin x))
+but is expected to have type
+  forall {x : Real}, (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) Real.pi)) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.sin x))
+Case conversion may be inaccurate. Consider using '#align real.sin_nonneg_of_mem_Icc Real.sin_nonneg_of_mem_Iccₓ'. -/
 theorem sin_nonneg_of_mem_Icc {x : ℝ} (hx : x ∈ Icc 0 π) : 0 ≤ sin x :=
   by
   rw [← closure_Ioo pi_ne_zero.symm] at hx
@@ -429,18 +661,37 @@ theorem sin_nonneg_of_mem_Icc {x : ℝ} (hx : x ∈ Icc 0 π) : 0 ≤ sin x :=
       (closure_mono (fun y => sin_pos_of_mem_Ioo) hx)
 #align real.sin_nonneg_of_mem_Icc Real.sin_nonneg_of_mem_Icc
 
+/- warning: real.sin_nonneg_of_nonneg_of_le_pi -> Real.sin_nonneg_of_nonneg_of_le_pi is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LE.le.{0} Real Real.hasLe x Real.pi) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.sin x))
+but is expected to have type
+  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LE.le.{0} Real Real.instLEReal x Real.pi) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.sin x))
+Case conversion may be inaccurate. Consider using '#align real.sin_nonneg_of_nonneg_of_le_pi Real.sin_nonneg_of_nonneg_of_le_piₓ'. -/
 theorem sin_nonneg_of_nonneg_of_le_pi {x : ℝ} (h0x : 0 ≤ x) (hxp : x ≤ π) : 0 ≤ sin x :=
   sin_nonneg_of_mem_Icc ⟨h0x, hxp⟩
 #align real.sin_nonneg_of_nonneg_of_le_pi Real.sin_nonneg_of_nonneg_of_le_pi
 
+/- warning: real.sin_neg_of_neg_of_neg_pi_lt -> Real.sin_neg_of_neg_of_neg_pi_lt is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LT.lt.{0} Real Real.hasLt x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Real Real.hasLt (Neg.neg.{0} Real Real.hasNeg Real.pi) x) -> (LT.lt.{0} Real Real.hasLt (Real.sin x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {x : Real}, (LT.lt.{0} Real Real.instLTReal x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LT.lt.{0} Real Real.instLTReal (Neg.neg.{0} Real Real.instNegReal Real.pi) x) -> (LT.lt.{0} Real Real.instLTReal (Real.sin x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align real.sin_neg_of_neg_of_neg_pi_lt Real.sin_neg_of_neg_of_neg_pi_ltₓ'. -/
 theorem sin_neg_of_neg_of_neg_pi_lt {x : ℝ} (hx0 : x < 0) (hpx : -π < x) : sin x < 0 :=
   neg_pos.1 <| sin_neg x ▸ sin_pos_of_pos_of_lt_pi (neg_pos.2 hx0) (neg_lt.1 hpx)
 #align real.sin_neg_of_neg_of_neg_pi_lt Real.sin_neg_of_neg_of_neg_pi_lt
 
+/- warning: real.sin_nonpos_of_nonnpos_of_neg_pi_le -> Real.sin_nonpos_of_nonnpos_of_neg_pi_le is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LE.le.{0} Real Real.hasLe x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LE.le.{0} Real Real.hasLe (Neg.neg.{0} Real Real.hasNeg Real.pi) x) -> (LE.le.{0} Real Real.hasLe (Real.sin x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {x : Real}, (LE.le.{0} Real Real.instLEReal x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LE.le.{0} Real Real.instLEReal (Neg.neg.{0} Real Real.instNegReal Real.pi) x) -> (LE.le.{0} Real Real.instLEReal (Real.sin x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align real.sin_nonpos_of_nonnpos_of_neg_pi_le Real.sin_nonpos_of_nonnpos_of_neg_pi_leₓ'. -/
 theorem sin_nonpos_of_nonnpos_of_neg_pi_le {x : ℝ} (hx0 : x ≤ 0) (hpx : -π ≤ x) : sin x ≤ 0 :=
   neg_nonneg.1 <| sin_neg x ▸ sin_nonneg_of_nonneg_of_le_pi (neg_nonneg.2 hx0) (neg_le.1 hpx)
 #align real.sin_nonpos_of_nonnpos_of_neg_pi_le Real.sin_nonpos_of_nonnpos_of_neg_pi_le
 
+#print Real.sin_pi_div_two /-
 @[simp]
 theorem sin_pi_div_two : sin (π / 2) = 1 :=
   have : sin (π / 2) = 1 ∨ sin (π / 2) = -1 := by
@@ -449,59 +700,120 @@ theorem sin_pi_div_two : sin (π / 2) = 1 :=
     show ¬(0 : ℝ) < -1 by norm_num <|
       h ▸ sin_pos_of_pos_of_lt_pi pi_div_two_pos (half_lt_self pi_pos)
 #align real.sin_pi_div_two Real.sin_pi_div_two
+-/
 
+#print Real.sin_add_pi_div_two /-
 theorem sin_add_pi_div_two (x : ℝ) : sin (x + π / 2) = cos x := by simp [sin_add]
 #align real.sin_add_pi_div_two Real.sin_add_pi_div_two
+-/
 
+#print Real.sin_sub_pi_div_two /-
 theorem sin_sub_pi_div_two (x : ℝ) : sin (x - π / 2) = -cos x := by simp [sub_eq_add_neg, sin_add]
 #align real.sin_sub_pi_div_two Real.sin_sub_pi_div_two
+-/
 
+#print Real.sin_pi_div_two_sub /-
 theorem sin_pi_div_two_sub (x : ℝ) : sin (π / 2 - x) = cos x := by simp [sub_eq_add_neg, sin_add]
 #align real.sin_pi_div_two_sub Real.sin_pi_div_two_sub
+-/
 
+#print Real.cos_add_pi_div_two /-
 theorem cos_add_pi_div_two (x : ℝ) : cos (x + π / 2) = -sin x := by simp [cos_add]
 #align real.cos_add_pi_div_two Real.cos_add_pi_div_two
+-/
 
+#print Real.cos_sub_pi_div_two /-
 theorem cos_sub_pi_div_two (x : ℝ) : cos (x - π / 2) = sin x := by simp [sub_eq_add_neg, cos_add]
 #align real.cos_sub_pi_div_two Real.cos_sub_pi_div_two
+-/
 
+#print Real.cos_pi_div_two_sub /-
 theorem cos_pi_div_two_sub (x : ℝ) : cos (π / 2 - x) = sin x := by
   rw [← cos_neg, neg_sub, cos_sub_pi_div_two]
 #align real.cos_pi_div_two_sub Real.cos_pi_div_two_sub
+-/
 
+/- warning: real.cos_pos_of_mem_Ioo -> Real.cos_pos_of_mem_Ioo is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Ioo.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.cos x))
+but is expected to have type
+  forall {x : Real}, (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioo.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.cos x))
+Case conversion may be inaccurate. Consider using '#align real.cos_pos_of_mem_Ioo Real.cos_pos_of_mem_Iooₓ'. -/
 theorem cos_pos_of_mem_Ioo {x : ℝ} (hx : x ∈ Ioo (-(π / 2)) (π / 2)) : 0 < cos x :=
   sin_add_pi_div_two x ▸ sin_pos_of_mem_Ioo ⟨by linarith [hx.1], by linarith [hx.2]⟩
 #align real.cos_pos_of_mem_Ioo Real.cos_pos_of_mem_Ioo
 
+/- warning: real.cos_nonneg_of_mem_Icc -> Real.cos_nonneg_of_mem_Icc is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.cos x))
+but is expected to have type
+  forall {x : Real}, (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.cos x))
+Case conversion may be inaccurate. Consider using '#align real.cos_nonneg_of_mem_Icc Real.cos_nonneg_of_mem_Iccₓ'. -/
 theorem cos_nonneg_of_mem_Icc {x : ℝ} (hx : x ∈ Icc (-(π / 2)) (π / 2)) : 0 ≤ cos x :=
   sin_add_pi_div_two x ▸ sin_nonneg_of_mem_Icc ⟨by linarith [hx.1], by linarith [hx.2]⟩
 #align real.cos_nonneg_of_mem_Icc Real.cos_nonneg_of_mem_Icc
 
+/- warning: real.cos_nonneg_of_neg_pi_div_two_le_of_le -> Real.cos_nonneg_of_neg_pi_div_two_le_of_le is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LE.le.{0} Real Real.hasLe (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) x) -> (LE.le.{0} Real Real.hasLe x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.cos x))
+but is expected to have type
+  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) x) -> (LE.le.{0} Real Real.instLEReal x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.cos x))
+Case conversion may be inaccurate. Consider using '#align real.cos_nonneg_of_neg_pi_div_two_le_of_le Real.cos_nonneg_of_neg_pi_div_two_le_of_leₓ'. -/
 theorem cos_nonneg_of_neg_pi_div_two_le_of_le {x : ℝ} (hl : -(π / 2) ≤ x) (hu : x ≤ π / 2) :
     0 ≤ cos x :=
   cos_nonneg_of_mem_Icc ⟨hl, hu⟩
 #align real.cos_nonneg_of_neg_pi_div_two_le_of_le Real.cos_nonneg_of_neg_pi_div_two_le_of_le
 
+/- warning: real.cos_neg_of_pi_div_two_lt_of_lt -> Real.cos_neg_of_pi_div_two_lt_of_lt is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LT.lt.{0} Real Real.hasLt (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) x) -> (LT.lt.{0} Real Real.hasLt x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) Real.pi (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) -> (LT.lt.{0} Real Real.hasLt (Real.cos x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {x : Real}, (LT.lt.{0} Real Real.instLTReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) x) -> (LT.lt.{0} Real Real.instLTReal x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) Real.pi (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) -> (LT.lt.{0} Real Real.instLTReal (Real.cos x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align real.cos_neg_of_pi_div_two_lt_of_lt Real.cos_neg_of_pi_div_two_lt_of_ltₓ'. -/
 theorem cos_neg_of_pi_div_two_lt_of_lt {x : ℝ} (hx₁ : π / 2 < x) (hx₂ : x < π + π / 2) :
     cos x < 0 :=
   neg_pos.1 <| cos_pi_sub x ▸ cos_pos_of_mem_Ioo ⟨by linarith, by linarith⟩
 #align real.cos_neg_of_pi_div_two_lt_of_lt Real.cos_neg_of_pi_div_two_lt_of_lt
 
+/- warning: real.cos_nonpos_of_pi_div_two_le_of_le -> Real.cos_nonpos_of_pi_div_two_le_of_le is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LE.le.{0} Real Real.hasLe (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) x) -> (LE.le.{0} Real Real.hasLe x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) Real.pi (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) -> (LE.le.{0} Real Real.hasLe (Real.cos x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) x) -> (LE.le.{0} Real Real.instLEReal x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) Real.pi (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) -> (LE.le.{0} Real Real.instLEReal (Real.cos x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align real.cos_nonpos_of_pi_div_two_le_of_le Real.cos_nonpos_of_pi_div_two_le_of_leₓ'. -/
 theorem cos_nonpos_of_pi_div_two_le_of_le {x : ℝ} (hx₁ : π / 2 ≤ x) (hx₂ : x ≤ π + π / 2) :
     cos x ≤ 0 :=
   neg_nonneg.1 <| cos_pi_sub x ▸ cos_nonneg_of_mem_Icc ⟨by linarith, by linarith⟩
 #align real.cos_nonpos_of_pi_div_two_le_of_le Real.cos_nonpos_of_pi_div_two_le_of_le
 
+/- warning: real.sin_eq_sqrt_one_sub_cos_sq -> Real.sin_eq_sqrt_one_sub_cos_sq is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LE.le.{0} Real Real.hasLe x Real.pi) -> (Eq.{1} Real (Real.sin x) (Real.sqrt (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Real.cos 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
+  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LE.le.{0} Real Real.instLEReal x Real.pi) -> (Eq.{1} Real (Real.sin x) (Real.sqrt (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Real.cos x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
+Case conversion may be inaccurate. Consider using '#align real.sin_eq_sqrt_one_sub_cos_sq Real.sin_eq_sqrt_one_sub_cos_sqₓ'. -/
 theorem sin_eq_sqrt_one_sub_cos_sq {x : ℝ} (hl : 0 ≤ x) (hu : x ≤ π) :
     sin x = sqrt (1 - cos x ^ 2) := by
   rw [← abs_sin_eq_sqrt_one_sub_cos_sq, abs_of_nonneg (sin_nonneg_of_nonneg_of_le_pi hl hu)]
 #align real.sin_eq_sqrt_one_sub_cos_sq Real.sin_eq_sqrt_one_sub_cos_sq
 
+/- warning: real.cos_eq_sqrt_one_sub_sin_sq -> Real.cos_eq_sqrt_one_sub_sin_sq is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LE.le.{0} Real Real.hasLe (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) x) -> (LE.le.{0} Real Real.hasLe x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (Eq.{1} Real (Real.cos x) (Real.sqrt (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Real.sin 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
+  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) x) -> (LE.le.{0} Real Real.instLEReal x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (Eq.{1} Real (Real.cos x) (Real.sqrt (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Real.sin x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
+Case conversion may be inaccurate. Consider using '#align real.cos_eq_sqrt_one_sub_sin_sq Real.cos_eq_sqrt_one_sub_sin_sqₓ'. -/
 theorem cos_eq_sqrt_one_sub_sin_sq {x : ℝ} (hl : -(π / 2) ≤ x) (hu : x ≤ π / 2) :
     cos x = sqrt (1 - sin x ^ 2) := by
   rw [← abs_cos_eq_sqrt_one_sub_sin_sq, abs_of_nonneg (cos_nonneg_of_mem_Icc ⟨hl, hu⟩)]
 #align real.cos_eq_sqrt_one_sub_sin_sq Real.cos_eq_sqrt_one_sub_sin_sq
 
+/- warning: real.sin_eq_zero_iff_of_lt_of_lt -> Real.sin_eq_zero_iff_of_lt_of_lt is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LT.lt.{0} Real Real.hasLt (Neg.neg.{0} Real Real.hasNeg Real.pi) x) -> (LT.lt.{0} Real Real.hasLt x Real.pi) -> (Iff (Eq.{1} Real (Real.sin x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  forall {x : Real}, (LT.lt.{0} Real Real.instLTReal (Neg.neg.{0} Real Real.instNegReal Real.pi) x) -> (LT.lt.{0} Real Real.instLTReal x Real.pi) -> (Iff (Eq.{1} Real (Real.sin x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align real.sin_eq_zero_iff_of_lt_of_lt Real.sin_eq_zero_iff_of_lt_of_ltₓ'. -/
 theorem sin_eq_zero_iff_of_lt_of_lt {x : ℝ} (hx₁ : -π < x) (hx₂ : x < π) : sin x = 0 ↔ x = 0 :=
   ⟨fun h =>
     le_antisymm
@@ -520,6 +832,12 @@ theorem sin_eq_zero_iff_of_lt_of_lt {x : ℝ} (hx₁ : -π < x) (hx₂ : x < π)
     fun h => by simp [h]⟩
 #align real.sin_eq_zero_iff_of_lt_of_lt Real.sin_eq_zero_iff_of_lt_of_lt
 
+/- warning: real.sin_eq_zero_iff -> Real.sin_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Iff (Eq.{1} Real (Real.sin x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Exists.{1} Int (fun (n : Int) => Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n) Real.pi) x))
+but is expected to have type
+  forall {x : Real}, Iff (Eq.{1} Real (Real.sin x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Exists.{1} Int (fun (n : Int) => Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Int.cast.{0} Real Real.intCast n) Real.pi) x))
+Case conversion may be inaccurate. Consider using '#align real.sin_eq_zero_iff Real.sin_eq_zero_iffₓ'. -/
 theorem sin_eq_zero_iff {x : ℝ} : sin x = 0 ↔ ∃ n : ℤ, (n : ℝ) * π = x :=
   ⟨fun h =>
     ⟨⌊x / π⌋,
@@ -531,15 +849,33 @@ theorem sin_eq_zero_iff {x : ℝ} : sin x = 0 ↔ ∃ n : ℤ, (n : ℝ) * π =
     fun ⟨n, hn⟩ => hn ▸ sin_int_mul_pi _⟩
 #align real.sin_eq_zero_iff Real.sin_eq_zero_iff
 
+/- warning: real.sin_ne_zero_iff -> Real.sin_ne_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Iff (Ne.{1} Real (Real.sin x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (forall (n : Int), Ne.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n) Real.pi) x)
+but is expected to have type
+  forall {x : Real}, Iff (Ne.{1} Real (Real.sin x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (n : Int), Ne.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Int.cast.{0} Real Real.intCast n) Real.pi) x)
+Case conversion may be inaccurate. Consider using '#align real.sin_ne_zero_iff Real.sin_ne_zero_iffₓ'. -/
 theorem sin_ne_zero_iff {x : ℝ} : sin x ≠ 0 ↔ ∀ n : ℤ, (n : ℝ) * π ≠ x := by
   rw [← not_exists, not_iff_not, sin_eq_zero_iff]
 #align real.sin_ne_zero_iff Real.sin_ne_zero_iff
 
+/- warning: real.sin_eq_zero_iff_cos_eq -> Real.sin_eq_zero_iff_cos_eq is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Iff (Eq.{1} Real (Real.sin x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Or (Eq.{1} Real (Real.cos x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Eq.{1} Real (Real.cos x) (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))))
+but is expected to have type
+  forall {x : Real}, Iff (Eq.{1} Real (Real.sin x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Or (Eq.{1} Real (Real.cos x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Eq.{1} Real (Real.cos x) (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))))
+Case conversion may be inaccurate. Consider using '#align real.sin_eq_zero_iff_cos_eq Real.sin_eq_zero_iff_cos_eqₓ'. -/
 theorem sin_eq_zero_iff_cos_eq {x : ℝ} : sin x = 0 ↔ cos x = 1 ∨ cos x = -1 := by
   rw [← mul_self_eq_one_iff, ← sin_sq_add_cos_sq x, sq, sq, ← sub_eq_iff_eq_add, sub_self] <;>
     exact ⟨fun h => by rw [h, MulZeroClass.mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
 #align real.sin_eq_zero_iff_cos_eq Real.sin_eq_zero_iff_cos_eq
 
+/- warning: real.cos_eq_one_iff -> Real.cos_eq_one_iff is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), Iff (Eq.{1} Real (Real.cos x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Exists.{1} Int (fun (n : Int) => Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) Real.pi)) x))
+but is expected to have type
+  forall (x : Real), Iff (Eq.{1} Real (Real.cos x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Exists.{1} Int (fun (n : Int) => Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Int.cast.{0} Real Real.intCast n) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)) x))
+Case conversion may be inaccurate. Consider using '#align real.cos_eq_one_iff Real.cos_eq_one_iffₓ'. -/
 theorem cos_eq_one_iff (x : ℝ) : cos x = 1 ↔ ∃ n : ℤ, (n : ℝ) * (2 * π) = x :=
   ⟨fun h =>
     let ⟨n, hn⟩ := sin_eq_zero_iff.1 (sin_eq_zero_iff_cos_eq.2 (Or.inl h))
@@ -556,6 +892,12 @@ theorem cos_eq_one_iff (x : ℝ) : cos x = 1 ↔ ∃ n : ℤ, (n : ℝ) * (2 * 
     fun ⟨n, hn⟩ => hn ▸ cos_int_mul_two_pi _⟩
 #align real.cos_eq_one_iff Real.cos_eq_one_iff
 
+/- warning: real.cos_eq_one_iff_of_lt_of_lt -> Real.cos_eq_one_iff_of_lt_of_lt is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LT.lt.{0} Real Real.hasLt (Neg.neg.{0} Real Real.hasNeg (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) Real.pi)) x) -> (LT.lt.{0} Real Real.hasLt x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) Real.pi)) -> (Iff (Eq.{1} Real (Real.cos x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  forall {x : Real}, (LT.lt.{0} Real Real.instLTReal (Neg.neg.{0} Real Real.instNegReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)) x) -> (LT.lt.{0} Real Real.instLTReal x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)) -> (Iff (Eq.{1} Real (Real.cos x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align real.cos_eq_one_iff_of_lt_of_lt Real.cos_eq_one_iff_of_lt_of_ltₓ'. -/
 theorem cos_eq_one_iff_of_lt_of_lt {x : ℝ} (hx₁ : -(2 * π) < x) (hx₂ : x < 2 * π) :
     cos x = 1 ↔ x = 0 :=
   ⟨fun h => by
@@ -567,6 +909,12 @@ theorem cos_eq_one_iff_of_lt_of_lt {x : ℝ} (hx₁ : -(2 * π) < x) (hx₂ : x
     simp, fun h => by simp [h]⟩
 #align real.cos_eq_one_iff_of_lt_of_lt Real.cos_eq_one_iff_of_lt_of_lt
 
+/- warning: real.cos_lt_cos_of_nonneg_of_le_pi_div_two -> Real.cos_lt_cos_of_nonneg_of_le_pi_div_two is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LE.le.{0} Real Real.hasLe y (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (LT.lt.{0} Real Real.hasLt x y) -> (LT.lt.{0} Real Real.hasLt (Real.cos y) (Real.cos x))
+but is expected to have type
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LE.le.{0} Real Real.instLEReal y (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LT.lt.{0} Real Real.instLTReal x y) -> (LT.lt.{0} Real Real.instLTReal (Real.cos y) (Real.cos x))
+Case conversion may be inaccurate. Consider using '#align real.cos_lt_cos_of_nonneg_of_le_pi_div_two Real.cos_lt_cos_of_nonneg_of_le_pi_div_twoₓ'. -/
 theorem cos_lt_cos_of_nonneg_of_le_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y ≤ π / 2)
     (hxy : x < y) : cos y < cos x :=
   by
@@ -576,6 +924,12 @@ theorem cos_lt_cos_of_nonneg_of_le_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy
   nlinarith
 #align real.cos_lt_cos_of_nonneg_of_le_pi_div_two Real.cos_lt_cos_of_nonneg_of_le_pi_div_two
 
+/- warning: real.cos_lt_cos_of_nonneg_of_le_pi -> Real.cos_lt_cos_of_nonneg_of_le_pi is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LE.le.{0} Real Real.hasLe y Real.pi) -> (LT.lt.{0} Real Real.hasLt x y) -> (LT.lt.{0} Real Real.hasLt (Real.cos y) (Real.cos x))
+but is expected to have type
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LE.le.{0} Real Real.instLEReal y Real.pi) -> (LT.lt.{0} Real Real.instLTReal x y) -> (LT.lt.{0} Real Real.instLTReal (Real.cos y) (Real.cos x))
+Case conversion may be inaccurate. Consider using '#align real.cos_lt_cos_of_nonneg_of_le_pi Real.cos_lt_cos_of_nonneg_of_le_piₓ'. -/
 theorem cos_lt_cos_of_nonneg_of_le_pi {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y ≤ π) (hxy : x < y) :
     cos y < cos x :=
   match (le_total x (π / 2) : x ≤ π / 2 ∨ π / 2 ≤ x), le_total y (π / 2) with
@@ -600,15 +954,33 @@ theorem cos_lt_cos_of_nonneg_of_le_pi {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y 
           linarith)
 #align real.cos_lt_cos_of_nonneg_of_le_pi Real.cos_lt_cos_of_nonneg_of_le_pi
 
+/- warning: real.strict_anti_on_cos -> Real.strictAntiOn_cos is a dubious translation:
+lean 3 declaration is
+  StrictAntiOn.{0, 0} Real Real Real.preorder Real.preorder Real.cos (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) Real.pi)
+but is expected to have type
+  StrictAntiOn.{0, 0} Real Real Real.instPreorderReal Real.instPreorderReal Real.cos (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) Real.pi)
+Case conversion may be inaccurate. Consider using '#align real.strict_anti_on_cos Real.strictAntiOn_cosₓ'. -/
 theorem strictAntiOn_cos : StrictAntiOn cos (Icc 0 π) := fun x hx y hy hxy =>
   cos_lt_cos_of_nonneg_of_le_pi hx.1 hy.2 hxy
 #align real.strict_anti_on_cos Real.strictAntiOn_cos
 
+/- warning: real.cos_le_cos_of_nonneg_of_le_pi -> Real.cos_le_cos_of_nonneg_of_le_pi is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LE.le.{0} Real Real.hasLe y Real.pi) -> (LE.le.{0} Real Real.hasLe x y) -> (LE.le.{0} Real Real.hasLe (Real.cos y) (Real.cos x))
+but is expected to have type
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LE.le.{0} Real Real.instLEReal y Real.pi) -> (LE.le.{0} Real Real.instLEReal x y) -> (LE.le.{0} Real Real.instLEReal (Real.cos y) (Real.cos x))
+Case conversion may be inaccurate. Consider using '#align real.cos_le_cos_of_nonneg_of_le_pi Real.cos_le_cos_of_nonneg_of_le_piₓ'. -/
 theorem cos_le_cos_of_nonneg_of_le_pi {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y ≤ π) (hxy : x ≤ y) :
     cos y ≤ cos x :=
   (strictAntiOn_cos.le_iff_le ⟨hx₁.trans hxy, hy₂⟩ ⟨hx₁, hxy.trans hy₂⟩).2 hxy
 #align real.cos_le_cos_of_nonneg_of_le_pi Real.cos_le_cos_of_nonneg_of_le_pi
 
+/- warning: real.sin_lt_sin_of_lt_of_le_pi_div_two -> Real.sin_lt_sin_of_lt_of_le_pi_div_two is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.hasLe (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) x) -> (LE.le.{0} Real Real.hasLe y (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (LT.lt.{0} Real Real.hasLt x y) -> (LT.lt.{0} Real Real.hasLt (Real.sin x) (Real.sin y))
+but is expected to have type
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.instLEReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) x) -> (LE.le.{0} Real Real.instLEReal y (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LT.lt.{0} Real Real.instLTReal x y) -> (LT.lt.{0} Real Real.instLTReal (Real.sin x) (Real.sin y))
+Case conversion may be inaccurate. Consider using '#align real.sin_lt_sin_of_lt_of_le_pi_div_two Real.sin_lt_sin_of_lt_of_le_pi_div_twoₓ'. -/
 theorem sin_lt_sin_of_lt_of_le_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) ≤ x) (hy₂ : y ≤ π / 2)
     (hxy : x < y) : sin x < sin y := by
   rw [← cos_sub_pi_div_two, ← cos_sub_pi_div_two, ← cos_neg (x - _), ← cos_neg (y - _)] <;>
@@ -616,80 +988,169 @@ theorem sin_lt_sin_of_lt_of_le_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) ≤ x)
     linarith
 #align real.sin_lt_sin_of_lt_of_le_pi_div_two Real.sin_lt_sin_of_lt_of_le_pi_div_two
 
+/- warning: real.strict_mono_on_sin -> Real.strictMonoOn_sin is a dubious translation:
+lean 3 declaration is
+  StrictMonoOn.{0, 0} Real Real Real.preorder Real.preorder Real.sin (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))
+but is expected to have type
+  StrictMonoOn.{0, 0} Real Real Real.instPreorderReal Real.instPreorderReal Real.sin (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+Case conversion may be inaccurate. Consider using '#align real.strict_mono_on_sin Real.strictMonoOn_sinₓ'. -/
 theorem strictMonoOn_sin : StrictMonoOn sin (Icc (-(π / 2)) (π / 2)) := fun x hx y hy hxy =>
   sin_lt_sin_of_lt_of_le_pi_div_two hx.1 hy.2 hxy
 #align real.strict_mono_on_sin Real.strictMonoOn_sin
 
+/- warning: real.sin_le_sin_of_le_of_le_pi_div_two -> Real.sin_le_sin_of_le_of_le_pi_div_two is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.hasLe (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) x) -> (LE.le.{0} Real Real.hasLe y (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (LE.le.{0} Real Real.hasLe x y) -> (LE.le.{0} Real Real.hasLe (Real.sin x) (Real.sin y))
+but is expected to have type
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.instLEReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) x) -> (LE.le.{0} Real Real.instLEReal y (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LE.le.{0} Real Real.instLEReal x y) -> (LE.le.{0} Real Real.instLEReal (Real.sin x) (Real.sin y))
+Case conversion may be inaccurate. Consider using '#align real.sin_le_sin_of_le_of_le_pi_div_two Real.sin_le_sin_of_le_of_le_pi_div_twoₓ'. -/
 theorem sin_le_sin_of_le_of_le_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) ≤ x) (hy₂ : y ≤ π / 2)
     (hxy : x ≤ y) : sin x ≤ sin y :=
   (strictMonoOn_sin.le_iff_le ⟨hx₁, hxy.trans hy₂⟩ ⟨hx₁.trans hxy, hy₂⟩).2 hxy
 #align real.sin_le_sin_of_le_of_le_pi_div_two Real.sin_le_sin_of_le_of_le_pi_div_two
 
+/- warning: real.inj_on_sin -> Real.injOn_sin is a dubious translation:
+lean 3 declaration is
+  Set.InjOn.{0, 0} Real Real Real.sin (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))
+but is expected to have type
+  Set.InjOn.{0, 0} Real Real Real.sin (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+Case conversion may be inaccurate. Consider using '#align real.inj_on_sin Real.injOn_sinₓ'. -/
 theorem injOn_sin : InjOn sin (Icc (-(π / 2)) (π / 2)) :=
   strictMonoOn_sin.InjOn
 #align real.inj_on_sin Real.injOn_sin
 
+/- warning: real.inj_on_cos -> Real.injOn_cos is a dubious translation:
+lean 3 declaration is
+  Set.InjOn.{0, 0} Real Real Real.cos (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) Real.pi)
+but is expected to have type
+  Set.InjOn.{0, 0} Real Real Real.cos (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) Real.pi)
+Case conversion may be inaccurate. Consider using '#align real.inj_on_cos Real.injOn_cosₓ'. -/
 theorem injOn_cos : InjOn cos (Icc 0 π) :=
   strictAntiOn_cos.InjOn
 #align real.inj_on_cos Real.injOn_cos
 
+/- warning: real.surj_on_sin -> Real.surjOn_sin is a dubious translation:
+lean 3 declaration is
+  Set.SurjOn.{0, 0} Real Real Real.sin (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  Set.SurjOn.{0, 0} Real Real Real.sin (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align real.surj_on_sin Real.surjOn_sinₓ'. -/
 theorem surjOn_sin : SurjOn sin (Icc (-(π / 2)) (π / 2)) (Icc (-1) 1) := by
   simpa only [sin_neg, sin_pi_div_two] using
     intermediate_value_Icc (neg_le_self pi_div_two_pos.le) continuous_sin.continuous_on
 #align real.surj_on_sin Real.surjOn_sin
 
+/- warning: real.surj_on_cos -> Real.surjOn_cos is a dubious translation:
+lean 3 declaration is
+  Set.SurjOn.{0, 0} Real Real Real.cos (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) Real.pi) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  Set.SurjOn.{0, 0} Real Real Real.cos (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) Real.pi) (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align real.surj_on_cos Real.surjOn_cosₓ'. -/
 theorem surjOn_cos : SurjOn cos (Icc 0 π) (Icc (-1) 1) := by
   simpa only [cos_zero, cos_pi] using intermediate_value_Icc' pi_pos.le continuous_cos.continuous_on
 #align real.surj_on_cos Real.surjOn_cos
 
+/- warning: real.sin_mem_Icc -> Real.sin_mem_Icc is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (Real.sin x) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall (x : Real), Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (Real.sin x) (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align real.sin_mem_Icc Real.sin_mem_Iccₓ'. -/
 theorem sin_mem_Icc (x : ℝ) : sin x ∈ Icc (-1 : ℝ) 1 :=
   ⟨neg_one_le_sin x, sin_le_one x⟩
 #align real.sin_mem_Icc Real.sin_mem_Icc
 
+/- warning: real.cos_mem_Icc -> Real.cos_mem_Icc is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (Real.cos x) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall (x : Real), Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (Real.cos x) (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align real.cos_mem_Icc Real.cos_mem_Iccₓ'. -/
 theorem cos_mem_Icc (x : ℝ) : cos x ∈ Icc (-1 : ℝ) 1 :=
   ⟨neg_one_le_cos x, cos_le_one x⟩
 #align real.cos_mem_Icc Real.cos_mem_Icc
 
+/- warning: real.maps_to_sin -> Real.mapsTo_sin is a dubious translation:
+lean 3 declaration is
+  forall (s : Set.{0} Real), Set.MapsTo.{0, 0} Real Real Real.sin s (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall (s : Set.{0} Real), Set.MapsTo.{0, 0} Real Real Real.sin s (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align real.maps_to_sin Real.mapsTo_sinₓ'. -/
 theorem mapsTo_sin (s : Set ℝ) : MapsTo sin s (Icc (-1 : ℝ) 1) := fun x _ => sin_mem_Icc x
 #align real.maps_to_sin Real.mapsTo_sin
 
+/- warning: real.maps_to_cos -> Real.mapsTo_cos is a dubious translation:
+lean 3 declaration is
+  forall (s : Set.{0} Real), Set.MapsTo.{0, 0} Real Real Real.cos s (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall (s : Set.{0} Real), Set.MapsTo.{0, 0} Real Real Real.cos s (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align real.maps_to_cos Real.mapsTo_cosₓ'. -/
 theorem mapsTo_cos (s : Set ℝ) : MapsTo cos s (Icc (-1 : ℝ) 1) := fun x _ => cos_mem_Icc x
 #align real.maps_to_cos Real.mapsTo_cos
 
+/- warning: real.bij_on_sin -> Real.bijOn_sin is a dubious translation:
+lean 3 declaration is
+  Set.BijOn.{0, 0} Real Real Real.sin (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  Set.BijOn.{0, 0} Real Real Real.sin (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align real.bij_on_sin Real.bijOn_sinₓ'. -/
 theorem bijOn_sin : BijOn sin (Icc (-(π / 2)) (π / 2)) (Icc (-1) 1) :=
   ⟨mapsTo_sin _, injOn_sin, surjOn_sin⟩
 #align real.bij_on_sin Real.bijOn_sin
 
+/- warning: real.bij_on_cos -> Real.bijOn_cos is a dubious translation:
+lean 3 declaration is
+  Set.BijOn.{0, 0} Real Real Real.cos (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) Real.pi) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  Set.BijOn.{0, 0} Real Real Real.cos (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) Real.pi) (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align real.bij_on_cos Real.bijOn_cosₓ'. -/
 theorem bijOn_cos : BijOn cos (Icc 0 π) (Icc (-1) 1) :=
   ⟨mapsTo_cos _, injOn_cos, surjOn_cos⟩
 #align real.bij_on_cos Real.bijOn_cos
 
+/- warning: real.range_cos -> Real.range_cos is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Real Real.cos) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Real Real.cos) (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align real.range_cos Real.range_cosₓ'. -/
 @[simp]
 theorem range_cos : range cos = (Icc (-1) 1 : Set ℝ) :=
   Subset.antisymm (range_subset_iff.2 cos_mem_Icc) surjOn_cos.subset_range
 #align real.range_cos Real.range_cos
 
+/- warning: real.range_sin -> Real.range_sin is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Real Real.sin) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Real Real.sin) (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align real.range_sin Real.range_sinₓ'. -/
 @[simp]
 theorem range_sin : range sin = (Icc (-1) 1 : Set ℝ) :=
   Subset.antisymm (range_subset_iff.2 sin_mem_Icc) surjOn_sin.subset_range
 #align real.range_sin Real.range_sin
 
+#print Real.range_cos_infinite /-
 theorem range_cos_infinite : (range Real.cos).Infinite :=
   by
   rw [Real.range_cos]
   exact Icc_infinite (by norm_num)
 #align real.range_cos_infinite Real.range_cos_infinite
+-/
 
+#print Real.range_sin_infinite /-
 theorem range_sin_infinite : (range Real.sin).Infinite :=
   by
   rw [Real.range_sin]
   exact Icc_infinite (by norm_num)
 #align real.range_sin_infinite Real.range_sin_infinite
+-/
 
 section CosDivSq
 
 variable (x : ℝ)
 
+#print Real.sqrtTwoAddSeries /-
 /-- the series `sqrt_two_add_series x n` is `sqrt(2 + sqrt(2 + ... ))` with `n` square roots,
   starting with `x`. We define it here because `cos (pi / 2 ^ (n+1)) = sqrt_two_add_series 0 n / 2`
 -/
@@ -698,26 +1159,59 @@ noncomputable def sqrtTwoAddSeries (x : ℝ) : ℕ → ℝ
   | 0 => x
   | n + 1 => sqrt (2 + sqrt_two_add_series n)
 #align real.sqrt_two_add_series Real.sqrtTwoAddSeries
+-/
 
+#print Real.sqrtTwoAddSeries_zero /-
 theorem sqrtTwoAddSeries_zero : sqrtTwoAddSeries x 0 = x := by simp
 #align real.sqrt_two_add_series_zero Real.sqrtTwoAddSeries_zero
+-/
 
+/- warning: real.sqrt_two_add_series_one -> Real.sqrtTwoAddSeries_one is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Real.sqrtTwoAddSeries (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))
+but is expected to have type
+  Eq.{1} Real (Real.sqrtTwoAddSeries (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_one Real.sqrtTwoAddSeries_oneₓ'. -/
 theorem sqrtTwoAddSeries_one : sqrtTwoAddSeries 0 1 = sqrt 2 := by simp
 #align real.sqrt_two_add_series_one Real.sqrtTwoAddSeries_one
 
+/- warning: real.sqrt_two_add_series_two -> Real.sqrtTwoAddSeries_two is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Real.sqrtTwoAddSeries (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Real.sqrt (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))))
+but is expected to have type
+  Eq.{1} Real (Real.sqrtTwoAddSeries (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Real.sqrt (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))
+Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_two Real.sqrtTwoAddSeries_twoₓ'. -/
 theorem sqrtTwoAddSeries_two : sqrtTwoAddSeries 0 2 = sqrt (2 + sqrt 2) := by simp
 #align real.sqrt_two_add_series_two Real.sqrtTwoAddSeries_two
 
+/- warning: real.sqrt_two_add_series_zero_nonneg -> Real.sqrtTwoAddSeries_zero_nonneg is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.sqrtTwoAddSeries (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) n)
+but is expected to have type
+  forall (n : Nat), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.sqrtTwoAddSeries (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) n)
+Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_zero_nonneg Real.sqrtTwoAddSeries_zero_nonnegₓ'. -/
 theorem sqrtTwoAddSeries_zero_nonneg : ∀ n : ℕ, 0 ≤ sqrtTwoAddSeries 0 n
   | 0 => le_refl 0
   | n + 1 => sqrt_nonneg _
 #align real.sqrt_two_add_series_zero_nonneg Real.sqrtTwoAddSeries_zero_nonneg
 
+/- warning: real.sqrt_two_add_series_nonneg -> Real.sqrtTwoAddSeries_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (forall (n : Nat), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.sqrtTwoAddSeries x n))
+but is expected to have type
+  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (forall (n : Nat), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.sqrtTwoAddSeries x n))
+Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_nonneg Real.sqrtTwoAddSeries_nonnegₓ'. -/
 theorem sqrtTwoAddSeries_nonneg {x : ℝ} (h : 0 ≤ x) : ∀ n : ℕ, 0 ≤ sqrtTwoAddSeries x n
   | 0 => h
   | n + 1 => sqrt_nonneg _
 #align real.sqrt_two_add_series_nonneg Real.sqrtTwoAddSeries_nonneg
 
+/- warning: real.sqrt_two_add_series_lt_two -> Real.sqrtTwoAddSeries_lt_two is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), LT.lt.{0} Real Real.hasLt (Real.sqrtTwoAddSeries (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) n) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall (n : Nat), LT.lt.{0} Real Real.instLTReal (Real.sqrtTwoAddSeries (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) n) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_lt_two Real.sqrtTwoAddSeries_lt_twoₓ'. -/
 theorem sqrtTwoAddSeries_lt_two : ∀ n : ℕ, sqrtTwoAddSeries 0 n < 2
   | 0 => by norm_num
   | n + 1 => by
@@ -728,12 +1222,24 @@ theorem sqrtTwoAddSeries_lt_two : ∀ n : ℕ, sqrtTwoAddSeries 0 n < 2
     · exact add_nonneg zero_le_two (sqrt_two_add_series_zero_nonneg n)
 #align real.sqrt_two_add_series_lt_two Real.sqrtTwoAddSeries_lt_two
 
+/- warning: real.sqrt_two_add_series_succ -> Real.sqrtTwoAddSeries_succ is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (n : Nat), Eq.{1} Real (Real.sqrtTwoAddSeries x (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Real.sqrtTwoAddSeries (Real.sqrt (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) x)) n)
+but is expected to have type
+  forall (x : Real) (n : Nat), Eq.{1} Real (Real.sqrtTwoAddSeries x (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Real.sqrtTwoAddSeries (Real.sqrt (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x)) n)
+Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_succ Real.sqrtTwoAddSeries_succₓ'. -/
 theorem sqrtTwoAddSeries_succ (x : ℝ) :
     ∀ n : ℕ, sqrtTwoAddSeries x (n + 1) = sqrtTwoAddSeries (sqrt (2 + x)) n
   | 0 => rfl
   | n + 1 => by rw [sqrt_two_add_series, sqrt_two_add_series_succ, sqrt_two_add_series]
 #align real.sqrt_two_add_series_succ Real.sqrtTwoAddSeries_succ
 
+/- warning: real.sqrt_two_add_series_monotone_left -> Real.sqrtTwoAddSeries_monotone_left is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.hasLe x y) -> (forall (n : Nat), LE.le.{0} Real Real.hasLe (Real.sqrtTwoAddSeries x n) (Real.sqrtTwoAddSeries y n))
+but is expected to have type
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.instLEReal x y) -> (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Real.sqrtTwoAddSeries x n) (Real.sqrtTwoAddSeries y n))
+Case conversion may be inaccurate. Consider using '#align real.sqrt_two_add_series_monotone_left Real.sqrtTwoAddSeries_monotone_leftₓ'. -/
 theorem sqrtTwoAddSeries_monotone_left {x y : ℝ} (h : x ≤ y) :
     ∀ n : ℕ, sqrtTwoAddSeries x n ≤ sqrtTwoAddSeries y n
   | 0 => h
@@ -742,6 +1248,7 @@ theorem sqrtTwoAddSeries_monotone_left {x y : ℝ} (h : x ≤ y) :
     exact sqrt_le_sqrt (add_le_add_left (sqrt_two_add_series_monotone_left _) _)
 #align real.sqrt_two_add_series_monotone_left Real.sqrtTwoAddSeries_monotone_left
 
+#print Real.cos_pi_over_two_pow /-
 @[simp]
 theorem cos_pi_over_two_pow : ∀ n : ℕ, cos (π / 2 ^ (n + 1)) = sqrtTwoAddSeries 0 n / 2
   | 0 => by simp
@@ -766,12 +1273,25 @@ theorem cos_pi_over_two_pow : ∀ n : ℕ, cos (π / 2 ^ (n + 1)) = sqrtTwoAddSe
     refine' lt_of_le_of_lt (le_of_eq (pow_one _).symm) _
     apply pow_lt_pow; norm_num; apply Nat.succ_lt_succ; apply Nat.succ_pos; all_goals norm_num
 #align real.cos_pi_over_two_pow Real.cos_pi_over_two_pow
+-/
 
+/- warning: real.sin_sq_pi_over_two_pow -> Real.sin_sq_pi_over_two_pow is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Real.sin (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Real.sqrtTwoAddSeries (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) n) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (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 (n : Nat), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Real.sin (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Real.sqrtTwoAddSeries (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) n) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+Case conversion may be inaccurate. Consider using '#align real.sin_sq_pi_over_two_pow Real.sin_sq_pi_over_two_powₓ'. -/
 theorem sin_sq_pi_over_two_pow (n : ℕ) :
     sin (π / 2 ^ (n + 1)) ^ 2 = 1 - (sqrtTwoAddSeries 0 n / 2) ^ 2 := by
   rw [sin_sq, cos_pi_over_two_pow]
 #align real.sin_sq_pi_over_two_pow Real.sin_sq_pi_over_two_pow
 
+/- warning: real.sin_sq_pi_over_two_pow_succ -> Real.sin_sq_pi_over_two_pow_succ is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Real.sin (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) 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 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Real.sqrtTwoAddSeries (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) n) (OfNat.ofNat.{0} Real 4 (OfNat.mk.{0} Real 4 (bit0.{0} Real Real.hasAdd (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))))
+but is expected to have type
+  forall (n : Nat), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Real.sin (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Real.sqrtTwoAddSeries (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) n) (OfNat.ofNat.{0} Real 4 (instOfNat.{0} Real 4 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
+Case conversion may be inaccurate. Consider using '#align real.sin_sq_pi_over_two_pow_succ Real.sin_sq_pi_over_two_pow_succₓ'. -/
 theorem sin_sq_pi_over_two_pow_succ (n : ℕ) :
     sin (π / 2 ^ (n + 2)) ^ 2 = 1 / 2 - sqrtTwoAddSeries 0 n / 4 :=
   by
@@ -779,6 +1299,7 @@ theorem sin_sq_pi_over_two_pow_succ (n : ℕ) :
   congr ; norm_num; norm_num; apply add_nonneg; norm_num; apply sqrt_two_add_series_zero_nonneg
 #align real.sin_sq_pi_over_two_pow_succ Real.sin_sq_pi_over_two_pow_succ
 
+#print Real.sin_pi_over_two_pow_succ /-
 @[simp]
 theorem sin_pi_over_two_pow_succ (n : ℕ) :
     sin (π / 2 ^ (n + 2)) = sqrt (2 - sqrtTwoAddSeries 0 n) / 2 :=
@@ -803,7 +1324,9 @@ theorem sin_pi_over_two_pow_succ (n : ℕ) :
   apply pow_lt_pow; norm_num; apply Nat.succ_pos; apply pi_pos
   apply pow_pos; all_goals norm_num
 #align real.sin_pi_over_two_pow_succ Real.sin_pi_over_two_pow_succ
+-/
 
+#print Real.cos_pi_div_four /-
 @[simp]
 theorem cos_pi_div_four : cos (π / 4) = sqrt 2 / 2 :=
   by
@@ -812,7 +1335,9 @@ theorem cos_pi_div_four : cos (π / 4) = sqrt 2 / 2 :=
   norm_num
   simp
 #align real.cos_pi_div_four Real.cos_pi_div_four
+-/
 
+#print Real.sin_pi_div_four /-
 @[simp]
 theorem sin_pi_div_four : sin (π / 4) = sqrt 2 / 2 :=
   by
@@ -821,7 +1346,9 @@ theorem sin_pi_div_four : sin (π / 4) = sqrt 2 / 2 :=
   norm_num
   simp
 #align real.sin_pi_div_four Real.sin_pi_div_four
+-/
 
+#print Real.cos_pi_div_eight /-
 @[simp]
 theorem cos_pi_div_eight : cos (π / 8) = sqrt (2 + sqrt 2) / 2 :=
   by
@@ -830,7 +1357,9 @@ theorem cos_pi_div_eight : cos (π / 8) = sqrt (2 + sqrt 2) / 2 :=
   norm_num
   simp
 #align real.cos_pi_div_eight Real.cos_pi_div_eight
+-/
 
+#print Real.sin_pi_div_eight /-
 @[simp]
 theorem sin_pi_div_eight : sin (π / 8) = sqrt (2 - sqrt 2) / 2 :=
   by
@@ -839,7 +1368,9 @@ theorem sin_pi_div_eight : sin (π / 8) = sqrt (2 - sqrt 2) / 2 :=
   norm_num
   simp
 #align real.sin_pi_div_eight Real.sin_pi_div_eight
+-/
 
+#print Real.cos_pi_div_sixteen /-
 @[simp]
 theorem cos_pi_div_sixteen : cos (π / 16) = sqrt (2 + sqrt (2 + sqrt 2)) / 2 :=
   by
@@ -848,7 +1379,9 @@ theorem cos_pi_div_sixteen : cos (π / 16) = sqrt (2 + sqrt (2 + sqrt 2)) / 2 :=
   norm_num
   simp
 #align real.cos_pi_div_sixteen Real.cos_pi_div_sixteen
+-/
 
+#print Real.sin_pi_div_sixteen /-
 @[simp]
 theorem sin_pi_div_sixteen : sin (π / 16) = sqrt (2 - sqrt (2 + sqrt 2)) / 2 :=
   by
@@ -857,7 +1390,9 @@ theorem sin_pi_div_sixteen : sin (π / 16) = sqrt (2 - sqrt (2 + sqrt 2)) / 2 :=
   norm_num
   simp
 #align real.sin_pi_div_sixteen Real.sin_pi_div_sixteen
+-/
 
+#print Real.cos_pi_div_thirty_two /-
 @[simp]
 theorem cos_pi_div_thirty_two : cos (π / 32) = sqrt (2 + sqrt (2 + sqrt (2 + sqrt 2))) / 2 :=
   by
@@ -866,7 +1401,9 @@ theorem cos_pi_div_thirty_two : cos (π / 32) = sqrt (2 + sqrt (2 + sqrt (2 + sq
   norm_num
   simp
 #align real.cos_pi_div_thirty_two Real.cos_pi_div_thirty_two
+-/
 
+#print Real.sin_pi_div_thirty_two /-
 @[simp]
 theorem sin_pi_div_thirty_two : sin (π / 32) = sqrt (2 - sqrt (2 + sqrt (2 + sqrt 2))) / 2 :=
   by
@@ -875,7 +1412,9 @@ theorem sin_pi_div_thirty_two : sin (π / 32) = sqrt (2 - sqrt (2 + sqrt (2 + sq
   norm_num
   simp
 #align real.sin_pi_div_thirty_two Real.sin_pi_div_thirty_two
+-/
 
+#print Real.cos_pi_div_three /-
 -- This section is also a convenient location for other explicit values of `sin` and `cos`.
 /-- The cosine of `π / 3` is `1 / 2`. -/
 @[simp]
@@ -893,7 +1432,14 @@ theorem cos_pi_div_three : cos (π / 3) = 1 / 2 :=
       refine' cos_lt_cos_of_nonneg_of_le_pi _ rfl.ge _ <;> linarith [pi_pos]
     linarith [cos_pi]
 #align real.cos_pi_div_three Real.cos_pi_div_three
+-/
 
+/- warning: real.sq_cos_pi_div_six -> Real.sq_cos_pi_div_six is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Real.cos (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 6 (OfNat.mk.{0} Real 6 (bit0.{0} Real Real.hasAdd (bit1.{0} Real Real.hasOne Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 3 (OfNat.mk.{0} Real 3 (bit1.{0} Real Real.hasOne Real.hasAdd (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 4 (OfNat.mk.{0} Real 4 (bit0.{0} Real Real.hasAdd (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))
+but is expected to have type
+  Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Real.cos (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 6 (instOfNat.{0} Real 6 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 3 (instOfNat.{0} Real 3 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} Real 4 (instOfNat.{0} Real 4 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
+Case conversion may be inaccurate. Consider using '#align real.sq_cos_pi_div_six Real.sq_cos_pi_div_sixₓ'. -/
 /-- The square of the cosine of `π / 6` is `3 / 4` (this is sometimes more convenient than the
 result for cosine itself). -/
 theorem sq_cos_pi_div_six : cos (π / 6) ^ 2 = 3 / 4 :=
@@ -908,6 +1454,7 @@ theorem sq_cos_pi_div_six : cos (π / 6) ^ 2 = 3 / 4 :=
   ring
 #align real.sq_cos_pi_div_six Real.sq_cos_pi_div_six
 
+#print Real.cos_pi_div_six /-
 /-- The cosine of `π / 6` is `√3 / 2`. -/
 @[simp]
 theorem cos_pi_div_six : cos (π / 6) = sqrt 3 / 2 :=
@@ -925,7 +1472,9 @@ theorem cos_pi_div_six : cos (π / 6) = sqrt 3 / 2 :=
   · have : 0 < cos (π / 6) := by apply cos_pos_of_mem_Ioo <;> constructor <;> linarith [pi_pos]
     linarith
 #align real.cos_pi_div_six Real.cos_pi_div_six
+-/
 
+#print Real.sin_pi_div_six /-
 /-- The sine of `π / 6` is `1 / 2`. -/
 @[simp]
 theorem sin_pi_div_six : sin (π / 6) = 1 / 2 :=
@@ -934,7 +1483,14 @@ theorem sin_pi_div_six : sin (π / 6) = 1 / 2 :=
   congr
   ring
 #align real.sin_pi_div_six Real.sin_pi_div_six
+-/
 
+/- warning: real.sq_sin_pi_div_three -> Real.sq_sin_pi_div_three 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 real.sq_sin_pi_div_three Real.sq_sin_pi_div_threeₓ'. -/
 /-- The square of the sine of `π / 3` is `3 / 4` (this is sometimes more convenient than the
 result for cosine itself). -/
 theorem sq_sin_pi_div_three : sin (π / 3) ^ 2 = 3 / 4 :=
@@ -944,6 +1500,7 @@ theorem sq_sin_pi_div_three : sin (π / 3) ^ 2 = 3 / 4 :=
   ring
 #align real.sq_sin_pi_div_three Real.sq_sin_pi_div_three
 
+#print Real.sin_pi_div_three /-
 /-- The sine of `π / 3` is `√3 / 2`. -/
 @[simp]
 theorem sin_pi_div_three : sin (π / 3) = sqrt 3 / 2 :=
@@ -952,23 +1509,43 @@ theorem sin_pi_div_three : sin (π / 3) = sqrt 3 / 2 :=
   congr
   ring
 #align real.sin_pi_div_three Real.sin_pi_div_three
+-/
 
 end CosDivSq
 
+/- warning: real.sin_order_iso -> Real.sinOrderIso is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align real.sin_order_iso Real.sinOrderIsoₓ'. -/
 /-- `real.sin` as an `order_iso` between `[-(π / 2), π / 2]` and `[-1, 1]`. -/
 def sinOrderIso : Icc (-(π / 2)) (π / 2) ≃o Icc (-1 : ℝ) 1 :=
   (strictMonoOn_sin.OrderIso _ _).trans <| OrderIso.setCongr _ _ bijOn_sin.image_eq
 #align real.sin_order_iso Real.sinOrderIso
 
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(HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))))))) x))
+but is expected to have type
+  forall (x : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))), Eq.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (fun (_x : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real 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2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real 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+Case conversion may be inaccurate. Consider using '#align real.coe_sin_order_iso_apply Real.coe_sinOrderIso_applyₓ'. -/
 @[simp]
 theorem coe_sinOrderIso_apply (x : Icc (-(π / 2)) (π / 2)) : (sinOrderIso x : ℝ) = sin x :=
   rfl
 #align real.coe_sin_order_iso_apply Real.coe_sinOrderIso_apply
 
+/- warning: real.sin_order_iso_apply -> Real.sinOrderIso_apply is a dubious translation:
+lean 3 declaration is
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(DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg 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+but is expected to have type
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2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) Real.sinOrderIso x) (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Real.sin (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) x)) (Real.sin_mem_Icc (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) x)))
+Case conversion may be inaccurate. Consider using '#align real.sin_order_iso_apply Real.sinOrderIso_applyₓ'. -/
 theorem sinOrderIso_apply (x : Icc (-(π / 2)) (π / 2)) : sinOrderIso x = ⟨sin x, sin_mem_Icc x⟩ :=
   rfl
 #align real.sin_order_iso_apply Real.sinOrderIso_apply
 
+#print Real.tan_pi_div_four /-
 @[simp]
 theorem tan_pi_div_four : tan (π / 4) = 1 :=
   by
@@ -976,17 +1553,32 @@ theorem tan_pi_div_four : tan (π / 4) = 1 :=
   have h : sqrt 2 / 2 > 0 := by cancel_denoms
   exact div_self (ne_of_gt h)
 #align real.tan_pi_div_four Real.tan_pi_div_four
+-/
 
+#print Real.tan_pi_div_two /-
 @[simp]
 theorem tan_pi_div_two : tan (π / 2) = 0 := by simp [tan_eq_sin_div_cos]
 #align real.tan_pi_div_two Real.tan_pi_div_two
+-/
 
+/- warning: real.tan_pos_of_pos_of_lt_pi_div_two -> Real.tan_pos_of_pos_of_lt_pi_div_two is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LT.lt.{0} Real Real.hasLt x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.tan x))
+but is expected to have type
+  forall {x : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LT.lt.{0} Real Real.instLTReal x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.tan x))
+Case conversion may be inaccurate. Consider using '#align real.tan_pos_of_pos_of_lt_pi_div_two Real.tan_pos_of_pos_of_lt_pi_div_twoₓ'. -/
 theorem tan_pos_of_pos_of_lt_pi_div_two {x : ℝ} (h0x : 0 < x) (hxp : x < π / 2) : 0 < tan x := by
   rw [tan_eq_sin_div_cos] <;>
     exact
       div_pos (sin_pos_of_pos_of_lt_pi h0x (by linarith)) (cos_pos_of_mem_Ioo ⟨by linarith, hxp⟩)
 #align real.tan_pos_of_pos_of_lt_pi_div_two Real.tan_pos_of_pos_of_lt_pi_div_two
 
+/- warning: real.tan_nonneg_of_nonneg_of_le_pi_div_two -> Real.tan_nonneg_of_nonneg_of_le_pi_div_two is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LE.le.{0} Real Real.hasLe x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Real.tan x))
+but is expected to have type
+  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LE.le.{0} Real Real.instLEReal x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Real.tan x))
+Case conversion may be inaccurate. Consider using '#align real.tan_nonneg_of_nonneg_of_le_pi_div_two Real.tan_nonneg_of_nonneg_of_le_pi_div_twoₓ'. -/
 theorem tan_nonneg_of_nonneg_of_le_pi_div_two {x : ℝ} (h0x : 0 ≤ x) (hxp : x ≤ π / 2) : 0 ≤ tan x :=
   match lt_or_eq_of_le h0x, lt_or_eq_of_le hxp with
   | Or.inl hx0, Or.inl hxp => le_of_lt (tan_pos_of_pos_of_lt_pi_div_two hx0 hxp)
@@ -994,15 +1586,33 @@ theorem tan_nonneg_of_nonneg_of_le_pi_div_two {x : ℝ} (h0x : 0 ≤ x) (hxp : x
   | Or.inr hx0, _ => by simp [hx0.symm]
 #align real.tan_nonneg_of_nonneg_of_le_pi_div_two Real.tan_nonneg_of_nonneg_of_le_pi_div_two
 
+/- warning: real.tan_neg_of_neg_of_pi_div_two_lt -> Real.tan_neg_of_neg_of_pi_div_two_lt is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LT.lt.{0} Real Real.hasLt x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Real Real.hasLt (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) x) -> (LT.lt.{0} Real Real.hasLt (Real.tan x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {x : Real}, (LT.lt.{0} Real Real.instLTReal x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LT.lt.{0} Real Real.instLTReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) x) -> (LT.lt.{0} Real Real.instLTReal (Real.tan x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align real.tan_neg_of_neg_of_pi_div_two_lt Real.tan_neg_of_neg_of_pi_div_two_ltₓ'. -/
 theorem tan_neg_of_neg_of_pi_div_two_lt {x : ℝ} (hx0 : x < 0) (hpx : -(π / 2) < x) : tan x < 0 :=
   neg_pos.1 (tan_neg x ▸ tan_pos_of_pos_of_lt_pi_div_two (by linarith) (by linarith [pi_pos]))
 #align real.tan_neg_of_neg_of_pi_div_two_lt Real.tan_neg_of_neg_of_pi_div_two_lt
 
+/- warning: real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le -> Real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LE.le.{0} Real Real.hasLe x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LE.le.{0} Real Real.hasLe (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) x) -> (LE.le.{0} Real Real.hasLe (Real.tan x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {x : Real}, (LE.le.{0} Real Real.instLEReal x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LE.le.{0} Real Real.instLEReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) x) -> (LE.le.{0} Real Real.instLEReal (Real.tan x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le Real.tan_nonpos_of_nonpos_of_neg_pi_div_two_leₓ'. -/
 theorem tan_nonpos_of_nonpos_of_neg_pi_div_two_le {x : ℝ} (hx0 : x ≤ 0) (hpx : -(π / 2) ≤ x) :
     tan x ≤ 0 :=
   neg_nonneg.1 (tan_neg x ▸ tan_nonneg_of_nonneg_of_le_pi_div_two (by linarith) (by linarith))
 #align real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le Real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le
 
+/- warning: real.tan_lt_tan_of_nonneg_of_lt_pi_div_two -> Real.tan_lt_tan_of_nonneg_of_lt_pi_div_two is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LT.lt.{0} Real Real.hasLt y (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (LT.lt.{0} Real Real.hasLt x y) -> (LT.lt.{0} Real Real.hasLt (Real.tan x) (Real.tan y))
+but is expected to have type
+  forall {x : Real} {y : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LT.lt.{0} Real Real.instLTReal y (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LT.lt.{0} Real Real.instLTReal x y) -> (LT.lt.{0} Real Real.instLTReal (Real.tan x) (Real.tan y))
+Case conversion may be inaccurate. Consider using '#align real.tan_lt_tan_of_nonneg_of_lt_pi_div_two Real.tan_lt_tan_of_nonneg_of_lt_pi_div_twoₓ'. -/
 theorem tan_lt_tan_of_nonneg_of_lt_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y < π / 2)
     (hxy : x < y) : tan x < tan y :=
   by
@@ -1014,6 +1624,12 @@ theorem tan_lt_tan_of_nonneg_of_lt_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy
       (cos_pos_of_mem_Ioo ⟨by linarith, hy₂⟩)
 #align real.tan_lt_tan_of_nonneg_of_lt_pi_div_two Real.tan_lt_tan_of_nonneg_of_lt_pi_div_two
 
+/- warning: real.tan_lt_tan_of_lt_of_lt_pi_div_two -> Real.tan_lt_tan_of_lt_of_lt_pi_div_two is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, (LT.lt.{0} Real Real.hasLt (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) x) -> (LT.lt.{0} Real Real.hasLt y (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (LT.lt.{0} Real Real.hasLt x y) -> (LT.lt.{0} Real Real.hasLt (Real.tan x) (Real.tan y))
+but is expected to have type
+  forall {x : Real} {y : Real}, (LT.lt.{0} Real Real.instLTReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) x) -> (LT.lt.{0} Real Real.instLTReal y (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LT.lt.{0} Real Real.instLTReal x y) -> (LT.lt.{0} Real Real.instLTReal (Real.tan x) (Real.tan y))
+Case conversion may be inaccurate. Consider using '#align real.tan_lt_tan_of_lt_of_lt_pi_div_two Real.tan_lt_tan_of_lt_of_lt_pi_div_twoₓ'. -/
 theorem tan_lt_tan_of_lt_of_lt_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) < x) (hy₂ : y < π / 2)
     (hxy : x < y) : tan x < tan y :=
   match le_total x 0, le_total y 0 with
@@ -1035,77 +1651,133 @@ theorem tan_lt_tan_of_lt_of_lt_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) < x) (h
   | Or.inr hx0, Or.inr hy0 => tan_lt_tan_of_nonneg_of_lt_pi_div_two hx0 hy₂ hxy
 #align real.tan_lt_tan_of_lt_of_lt_pi_div_two Real.tan_lt_tan_of_lt_of_lt_pi_div_two
 
+/- warning: real.strict_mono_on_tan -> Real.strictMonoOn_tan is a dubious translation:
+lean 3 declaration is
+  StrictMonoOn.{0, 0} Real Real Real.preorder Real.preorder Real.tan (Set.Ioo.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))
+but is expected to have type
+  StrictMonoOn.{0, 0} Real Real Real.instPreorderReal Real.instPreorderReal Real.tan (Set.Ioo.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+Case conversion may be inaccurate. Consider using '#align real.strict_mono_on_tan Real.strictMonoOn_tanₓ'. -/
 theorem strictMonoOn_tan : StrictMonoOn tan (Ioo (-(π / 2)) (π / 2)) := fun x hx y hy =>
   tan_lt_tan_of_lt_of_lt_pi_div_two hx.1 hy.2
 #align real.strict_mono_on_tan Real.strictMonoOn_tan
 
+/- warning: real.inj_on_tan -> Real.injOn_tan is a dubious translation:
+lean 3 declaration is
+  Set.InjOn.{0, 0} Real Real Real.tan (Set.Ioo.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))
+but is expected to have type
+  Set.InjOn.{0, 0} Real Real Real.tan (Set.Ioo.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+Case conversion may be inaccurate. Consider using '#align real.inj_on_tan Real.injOn_tanₓ'. -/
 theorem injOn_tan : InjOn tan (Ioo (-(π / 2)) (π / 2)) :=
   strictMonoOn_tan.InjOn
 #align real.inj_on_tan Real.injOn_tan
 
+/- warning: real.tan_inj_of_lt_of_lt_pi_div_two -> Real.tan_inj_of_lt_of_lt_pi_div_two is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, (LT.lt.{0} Real Real.hasLt (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) x) -> (LT.lt.{0} Real Real.hasLt x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (LT.lt.{0} Real Real.hasLt (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) y) -> (LT.lt.{0} Real Real.hasLt y (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (Eq.{1} Real (Real.tan x) (Real.tan y)) -> (Eq.{1} Real x y)
+but is expected to have type
+  forall {x : Real} {y : Real}, (LT.lt.{0} Real Real.instLTReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) x) -> (LT.lt.{0} Real Real.instLTReal x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LT.lt.{0} Real Real.instLTReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) y) -> (LT.lt.{0} Real Real.instLTReal y (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (Eq.{1} Real (Real.tan x) (Real.tan y)) -> (Eq.{1} Real x y)
+Case conversion may be inaccurate. Consider using '#align real.tan_inj_of_lt_of_lt_pi_div_two Real.tan_inj_of_lt_of_lt_pi_div_twoₓ'. -/
 theorem tan_inj_of_lt_of_lt_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) < x) (hx₂ : x < π / 2)
     (hy₁ : -(π / 2) < y) (hy₂ : y < π / 2) (hxy : tan x = tan y) : x = y :=
   injOn_tan ⟨hx₁, hx₂⟩ ⟨hy₁, hy₂⟩ hxy
 #align real.tan_inj_of_lt_of_lt_pi_div_two Real.tan_inj_of_lt_of_lt_pi_div_two
 
+#print Real.tan_periodic /-
 theorem tan_periodic : Function.Periodic tan π := by
   simpa only [Function.Periodic, tan_eq_sin_div_cos] using sin_antiperiodic.div cos_antiperiodic
 #align real.tan_periodic Real.tan_periodic
+-/
 
+#print Real.tan_add_pi /-
 theorem tan_add_pi (x : ℝ) : tan (x + π) = tan x :=
   tan_periodic x
 #align real.tan_add_pi Real.tan_add_pi
+-/
 
+#print Real.tan_sub_pi /-
 theorem tan_sub_pi (x : ℝ) : tan (x - π) = tan x :=
   tan_periodic.sub_eq x
 #align real.tan_sub_pi Real.tan_sub_pi
+-/
 
+#print Real.tan_pi_sub /-
 theorem tan_pi_sub (x : ℝ) : tan (π - x) = -tan x :=
   tan_neg x ▸ tan_periodic.sub_eq'
 #align real.tan_pi_sub Real.tan_pi_sub
+-/
 
+#print Real.tan_pi_div_two_sub /-
 theorem tan_pi_div_two_sub (x : ℝ) : tan (π / 2 - x) = (tan x)⁻¹ := by
   rw [tan_eq_sin_div_cos, tan_eq_sin_div_cos, inv_div, sin_pi_div_two_sub, cos_pi_div_two_sub]
 #align real.tan_pi_div_two_sub Real.tan_pi_div_two_sub
+-/
 
+#print Real.tan_nat_mul_pi /-
 theorem tan_nat_mul_pi (n : ℕ) : tan (n * π) = 0 :=
   tan_zero ▸ tan_periodic.nat_mul_eq n
 #align real.tan_nat_mul_pi Real.tan_nat_mul_pi
+-/
 
+#print Real.tan_int_mul_pi /-
 theorem tan_int_mul_pi (n : ℤ) : tan (n * π) = 0 :=
   tan_zero ▸ tan_periodic.int_mul_eq n
 #align real.tan_int_mul_pi Real.tan_int_mul_pi
+-/
 
+#print Real.tan_add_nat_mul_pi /-
 theorem tan_add_nat_mul_pi (x : ℝ) (n : ℕ) : tan (x + n * π) = tan x :=
   tan_periodic.nat_mul n x
 #align real.tan_add_nat_mul_pi Real.tan_add_nat_mul_pi
+-/
 
+#print Real.tan_add_int_mul_pi /-
 theorem tan_add_int_mul_pi (x : ℝ) (n : ℤ) : tan (x + n * π) = tan x :=
   tan_periodic.int_mul n x
 #align real.tan_add_int_mul_pi Real.tan_add_int_mul_pi
+-/
 
+#print Real.tan_sub_nat_mul_pi /-
 theorem tan_sub_nat_mul_pi (x : ℝ) (n : ℕ) : tan (x - n * π) = tan x :=
   tan_periodic.sub_nat_mul_eq n
 #align real.tan_sub_nat_mul_pi Real.tan_sub_nat_mul_pi
+-/
 
+#print Real.tan_sub_int_mul_pi /-
 theorem tan_sub_int_mul_pi (x : ℝ) (n : ℤ) : tan (x - n * π) = tan x :=
   tan_periodic.sub_int_mul_eq n
 #align real.tan_sub_int_mul_pi Real.tan_sub_int_mul_pi
+-/
 
+#print Real.tan_nat_mul_pi_sub /-
 theorem tan_nat_mul_pi_sub (x : ℝ) (n : ℕ) : tan (n * π - x) = -tan x :=
   tan_neg x ▸ tan_periodic.nat_mul_sub_eq n
 #align real.tan_nat_mul_pi_sub Real.tan_nat_mul_pi_sub
+-/
 
+#print Real.tan_int_mul_pi_sub /-
 theorem tan_int_mul_pi_sub (x : ℝ) (n : ℤ) : tan (n * π - x) = -tan x :=
   tan_neg x ▸ tan_periodic.int_mul_sub_eq n
 #align real.tan_int_mul_pi_sub Real.tan_int_mul_pi_sub
+-/
 
+/- warning: real.tendsto_sin_pi_div_two -> Real.tendsto_sin_pi_div_two is a dubious translation:
+lean 3 declaration is
+  Filter.Tendsto.{0, 0} Real Real Real.sin (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (Set.Iio.{0} Real Real.preorder (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  Filter.Tendsto.{0, 0} Real Real Real.sin (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Set.Iio.{0} Real Real.instPreorderReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align real.tendsto_sin_pi_div_two Real.tendsto_sin_pi_div_twoₓ'. -/
 theorem tendsto_sin_pi_div_two : Tendsto sin (𝓝[<] (π / 2)) (𝓝 1) :=
   by
   convert continuous_sin.continuous_within_at
   simp
 #align real.tendsto_sin_pi_div_two Real.tendsto_sin_pi_div_two
 
+/- warning: real.tendsto_cos_pi_div_two -> Real.tendsto_cos_pi_div_two is a dubious translation:
+lean 3 declaration is
+  Filter.Tendsto.{0, 0} Real Real Real.cos (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (Set.Iio.{0} Real Real.preorder (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  Filter.Tendsto.{0, 0} Real Real Real.cos (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Set.Iio.{0} Real Real.instPreorderReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align real.tendsto_cos_pi_div_two Real.tendsto_cos_pi_div_twoₓ'. -/
 theorem tendsto_cos_pi_div_two : Tendsto cos (𝓝[<] (π / 2)) (𝓝[>] 0) :=
   by
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
@@ -1116,18 +1788,36 @@ theorem tendsto_cos_pi_div_two : Tendsto cos (𝓝[<] (π / 2)) (𝓝[>] 0) :=
         (right_mem_Ioc.mpr (neg_lt_self pi_div_two_pos))]with x hx using cos_pos_of_mem_Ioo hx
 #align real.tendsto_cos_pi_div_two Real.tendsto_cos_pi_div_two
 
+/- warning: real.tendsto_tan_pi_div_two -> Real.tendsto_tan_pi_div_two is a dubious translation:
+lean 3 declaration is
+  Filter.Tendsto.{0, 0} Real Real Real.tan (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (Set.Iio.{0} Real Real.preorder (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (Filter.atTop.{0} Real Real.preorder)
+but is expected to have type
+  Filter.Tendsto.{0, 0} Real Real Real.tan (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Set.Iio.{0} Real Real.instPreorderReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Filter.atTop.{0} Real Real.instPreorderReal)
+Case conversion may be inaccurate. Consider using '#align real.tendsto_tan_pi_div_two Real.tendsto_tan_pi_div_twoₓ'. -/
 theorem tendsto_tan_pi_div_two : Tendsto tan (𝓝[<] (π / 2)) atTop :=
   by
   convert tendsto_cos_pi_div_two.inv_tendsto_zero.at_top_mul zero_lt_one tendsto_sin_pi_div_two
   simp only [Pi.inv_apply, ← div_eq_inv_mul, ← tan_eq_sin_div_cos]
 #align real.tendsto_tan_pi_div_two Real.tendsto_tan_pi_div_two
 
+/- warning: real.tendsto_sin_neg_pi_div_two -> Real.tendsto_sin_neg_pi_div_two is a dubious translation:
+lean 3 declaration is
+  Filter.Tendsto.{0, 0} Real Real Real.sin (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Set.Ioi.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
+but is expected to have type
+  Filter.Tendsto.{0, 0} Real Real Real.sin (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Set.Ioi.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+Case conversion may be inaccurate. Consider using '#align real.tendsto_sin_neg_pi_div_two Real.tendsto_sin_neg_pi_div_twoₓ'. -/
 theorem tendsto_sin_neg_pi_div_two : Tendsto sin (𝓝[>] (-(π / 2))) (𝓝 (-1)) :=
   by
   convert continuous_sin.continuous_within_at
   simp
 #align real.tendsto_sin_neg_pi_div_two Real.tendsto_sin_neg_pi_div_two
 
+/- warning: real.tendsto_cos_neg_pi_div_two -> Real.tendsto_cos_neg_pi_div_two is a dubious translation:
+lean 3 declaration is
+  Filter.Tendsto.{0, 0} Real Real Real.cos (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Set.Ioi.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))))) (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  Filter.Tendsto.{0, 0} Real Real Real.cos (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Set.Ioi.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align real.tendsto_cos_neg_pi_div_two Real.tendsto_cos_neg_pi_div_twoₓ'. -/
 theorem tendsto_cos_neg_pi_div_two : Tendsto cos (𝓝[>] (-(π / 2))) (𝓝[>] 0) :=
   by
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
@@ -1138,6 +1828,12 @@ theorem tendsto_cos_neg_pi_div_two : Tendsto cos (𝓝[>] (-(π / 2))) (𝓝[>]
         (left_mem_Ico.mpr (neg_lt_self pi_div_two_pos))]with x hx using cos_pos_of_mem_Ioo hx
 #align real.tendsto_cos_neg_pi_div_two Real.tendsto_cos_neg_pi_div_two
 
+/- warning: real.tendsto_tan_neg_pi_div_two -> Real.tendsto_tan_neg_pi_div_two is a dubious translation:
+lean 3 declaration is
+  Filter.Tendsto.{0, 0} Real Real Real.tan (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Set.Ioi.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))))) (Filter.atBot.{0} Real Real.preorder)
+but is expected to have type
+  Filter.Tendsto.{0, 0} Real Real Real.tan (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Set.Ioi.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))) (Filter.atBot.{0} Real Real.instPreorderReal)
+Case conversion may be inaccurate. Consider using '#align real.tendsto_tan_neg_pi_div_two Real.tendsto_tan_neg_pi_div_twoₓ'. -/
 theorem tendsto_tan_neg_pi_div_two : Tendsto tan (𝓝[>] (-(π / 2))) atBot :=
   by
   convert tendsto_cos_neg_pi_div_two.inv_tendsto_zero.at_top_mul_neg (by norm_num)
@@ -1151,11 +1847,18 @@ namespace Complex
 
 open Real
 
+/- warning: complex.sin_eq_zero_iff_cos_eq -> Complex.sin_eq_zero_iff_cos_eq is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, Iff (Eq.{1} Complex (Complex.sin z) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (Or (Eq.{1} Complex (Complex.cos z) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (Eq.{1} Complex (Complex.cos z) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))))
+but is expected to have type
+  forall {z : Complex}, Iff (Eq.{1} Complex (Complex.sin z) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (Or (Eq.{1} Complex (Complex.cos z) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (Eq.{1} Complex (Complex.cos z) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))))
+Case conversion may be inaccurate. Consider using '#align complex.sin_eq_zero_iff_cos_eq Complex.sin_eq_zero_iff_cos_eqₓ'. -/
 theorem sin_eq_zero_iff_cos_eq {z : ℂ} : sin z = 0 ↔ cos z = 1 ∨ cos z = -1 := by
   rw [← mul_self_eq_one_iff, ← sin_sq_add_cos_sq, sq, sq, ← sub_eq_iff_eq_add, sub_self] <;>
     exact ⟨fun h => by rw [h, MulZeroClass.mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
 #align complex.sin_eq_zero_iff_cos_eq Complex.sin_eq_zero_iff_cos_eq
 
+#print Complex.cos_pi_div_two /-
 @[simp]
 theorem cos_pi_div_two : cos (π / 2) = 0 :=
   calc
@@ -1163,7 +1866,9 @@ theorem cos_pi_div_two : cos (π / 2) = 0 :=
     _ = 0 := by simp
     
 #align complex.cos_pi_div_two Complex.cos_pi_div_two
+-/
 
+#print Complex.sin_pi_div_two /-
 @[simp]
 theorem sin_pi_div_two : sin (π / 2) = 1 :=
   calc
@@ -1171,281 +1876,466 @@ theorem sin_pi_div_two : sin (π / 2) = 1 :=
     _ = 1 := by simp
     
 #align complex.sin_pi_div_two Complex.sin_pi_div_two
+-/
 
+#print Complex.sin_pi /-
 @[simp]
 theorem sin_pi : sin π = 0 := by rw [← of_real_sin, Real.sin_pi] <;> simp
 #align complex.sin_pi Complex.sin_pi
+-/
 
+#print Complex.cos_pi /-
 @[simp]
 theorem cos_pi : cos π = -1 := by rw [← of_real_cos, Real.cos_pi] <;> simp
 #align complex.cos_pi Complex.cos_pi
+-/
 
+#print Complex.sin_two_pi /-
 @[simp]
 theorem sin_two_pi : sin (2 * π) = 0 := by simp [two_mul, sin_add]
 #align complex.sin_two_pi Complex.sin_two_pi
+-/
 
+#print Complex.cos_two_pi /-
 @[simp]
 theorem cos_two_pi : cos (2 * π) = 1 := by simp [two_mul, cos_add]
 #align complex.cos_two_pi Complex.cos_two_pi
+-/
 
+#print Complex.sin_antiperiodic /-
 theorem sin_antiperiodic : Function.Antiperiodic sin π := by simp [sin_add]
 #align complex.sin_antiperiodic Complex.sin_antiperiodic
+-/
 
+#print Complex.sin_periodic /-
 theorem sin_periodic : Function.Periodic sin (2 * π) :=
   sin_antiperiodic.Periodic
 #align complex.sin_periodic Complex.sin_periodic
+-/
 
+#print Complex.sin_add_pi /-
 theorem sin_add_pi (x : ℂ) : sin (x + π) = -sin x :=
   sin_antiperiodic x
 #align complex.sin_add_pi Complex.sin_add_pi
+-/
 
+#print Complex.sin_add_two_pi /-
 theorem sin_add_two_pi (x : ℂ) : sin (x + 2 * π) = sin x :=
   sin_periodic x
 #align complex.sin_add_two_pi Complex.sin_add_two_pi
+-/
 
+#print Complex.sin_sub_pi /-
 theorem sin_sub_pi (x : ℂ) : sin (x - π) = -sin x :=
   sin_antiperiodic.sub_eq x
 #align complex.sin_sub_pi Complex.sin_sub_pi
+-/
 
+#print Complex.sin_sub_two_pi /-
 theorem sin_sub_two_pi (x : ℂ) : sin (x - 2 * π) = sin x :=
   sin_periodic.sub_eq x
 #align complex.sin_sub_two_pi Complex.sin_sub_two_pi
+-/
 
+#print Complex.sin_pi_sub /-
 theorem sin_pi_sub (x : ℂ) : sin (π - x) = sin x :=
   neg_neg (sin x) ▸ sin_neg x ▸ sin_antiperiodic.sub_eq'
 #align complex.sin_pi_sub Complex.sin_pi_sub
+-/
 
+#print Complex.sin_two_pi_sub /-
 theorem sin_two_pi_sub (x : ℂ) : sin (2 * π - x) = -sin x :=
   sin_neg x ▸ sin_periodic.sub_eq'
 #align complex.sin_two_pi_sub Complex.sin_two_pi_sub
+-/
 
+#print Complex.sin_nat_mul_pi /-
 theorem sin_nat_mul_pi (n : ℕ) : sin (n * π) = 0 :=
   sin_antiperiodic.nat_mul_eq_of_eq_zero sin_zero n
 #align complex.sin_nat_mul_pi Complex.sin_nat_mul_pi
+-/
 
+#print Complex.sin_int_mul_pi /-
 theorem sin_int_mul_pi (n : ℤ) : sin (n * π) = 0 :=
   sin_antiperiodic.int_mul_eq_of_eq_zero sin_zero n
 #align complex.sin_int_mul_pi Complex.sin_int_mul_pi
+-/
 
+#print Complex.sin_add_nat_mul_two_pi /-
 theorem sin_add_nat_mul_two_pi (x : ℂ) (n : ℕ) : sin (x + n * (2 * π)) = sin x :=
   sin_periodic.nat_mul n x
 #align complex.sin_add_nat_mul_two_pi Complex.sin_add_nat_mul_two_pi
+-/
 
+#print Complex.sin_add_int_mul_two_pi /-
 theorem sin_add_int_mul_two_pi (x : ℂ) (n : ℤ) : sin (x + n * (2 * π)) = sin x :=
   sin_periodic.int_mul n x
 #align complex.sin_add_int_mul_two_pi Complex.sin_add_int_mul_two_pi
+-/
 
+#print Complex.sin_sub_nat_mul_two_pi /-
 theorem sin_sub_nat_mul_two_pi (x : ℂ) (n : ℕ) : sin (x - n * (2 * π)) = sin x :=
   sin_periodic.sub_nat_mul_eq n
 #align complex.sin_sub_nat_mul_two_pi Complex.sin_sub_nat_mul_two_pi
+-/
 
+#print Complex.sin_sub_int_mul_two_pi /-
 theorem sin_sub_int_mul_two_pi (x : ℂ) (n : ℤ) : sin (x - n * (2 * π)) = sin x :=
   sin_periodic.sub_int_mul_eq n
 #align complex.sin_sub_int_mul_two_pi Complex.sin_sub_int_mul_two_pi
+-/
 
+#print Complex.sin_nat_mul_two_pi_sub /-
 theorem sin_nat_mul_two_pi_sub (x : ℂ) (n : ℕ) : sin (n * (2 * π) - x) = -sin x :=
   sin_neg x ▸ sin_periodic.nat_mul_sub_eq n
 #align complex.sin_nat_mul_two_pi_sub Complex.sin_nat_mul_two_pi_sub
+-/
 
+#print Complex.sin_int_mul_two_pi_sub /-
 theorem sin_int_mul_two_pi_sub (x : ℂ) (n : ℤ) : sin (n * (2 * π) - x) = -sin x :=
   sin_neg x ▸ sin_periodic.int_mul_sub_eq n
 #align complex.sin_int_mul_two_pi_sub Complex.sin_int_mul_two_pi_sub
+-/
 
+#print Complex.cos_antiperiodic /-
 theorem cos_antiperiodic : Function.Antiperiodic cos π := by simp [cos_add]
 #align complex.cos_antiperiodic Complex.cos_antiperiodic
+-/
 
+#print Complex.cos_periodic /-
 theorem cos_periodic : Function.Periodic cos (2 * π) :=
   cos_antiperiodic.Periodic
 #align complex.cos_periodic Complex.cos_periodic
+-/
 
+#print Complex.cos_add_pi /-
 theorem cos_add_pi (x : ℂ) : cos (x + π) = -cos x :=
   cos_antiperiodic x
 #align complex.cos_add_pi Complex.cos_add_pi
+-/
 
+#print Complex.cos_add_two_pi /-
 theorem cos_add_two_pi (x : ℂ) : cos (x + 2 * π) = cos x :=
   cos_periodic x
 #align complex.cos_add_two_pi Complex.cos_add_two_pi
+-/
 
+#print Complex.cos_sub_pi /-
 theorem cos_sub_pi (x : ℂ) : cos (x - π) = -cos x :=
   cos_antiperiodic.sub_eq x
 #align complex.cos_sub_pi Complex.cos_sub_pi
+-/
 
+#print Complex.cos_sub_two_pi /-
 theorem cos_sub_two_pi (x : ℂ) : cos (x - 2 * π) = cos x :=
   cos_periodic.sub_eq x
 #align complex.cos_sub_two_pi Complex.cos_sub_two_pi
+-/
 
+#print Complex.cos_pi_sub /-
 theorem cos_pi_sub (x : ℂ) : cos (π - x) = -cos x :=
   cos_neg x ▸ cos_antiperiodic.sub_eq'
 #align complex.cos_pi_sub Complex.cos_pi_sub
+-/
 
+#print Complex.cos_two_pi_sub /-
 theorem cos_two_pi_sub (x : ℂ) : cos (2 * π - x) = cos x :=
   cos_neg x ▸ cos_periodic.sub_eq'
 #align complex.cos_two_pi_sub Complex.cos_two_pi_sub
+-/
 
+#print Complex.cos_nat_mul_two_pi /-
 theorem cos_nat_mul_two_pi (n : ℕ) : cos (n * (2 * π)) = 1 :=
   (cos_periodic.nat_mul_eq n).trans cos_zero
 #align complex.cos_nat_mul_two_pi Complex.cos_nat_mul_two_pi
+-/
 
+#print Complex.cos_int_mul_two_pi /-
 theorem cos_int_mul_two_pi (n : ℤ) : cos (n * (2 * π)) = 1 :=
   (cos_periodic.int_mul_eq n).trans cos_zero
 #align complex.cos_int_mul_two_pi Complex.cos_int_mul_two_pi
+-/
 
+#print Complex.cos_add_nat_mul_two_pi /-
 theorem cos_add_nat_mul_two_pi (x : ℂ) (n : ℕ) : cos (x + n * (2 * π)) = cos x :=
   cos_periodic.nat_mul n x
 #align complex.cos_add_nat_mul_two_pi Complex.cos_add_nat_mul_two_pi
+-/
 
+#print Complex.cos_add_int_mul_two_pi /-
 theorem cos_add_int_mul_two_pi (x : ℂ) (n : ℤ) : cos (x + n * (2 * π)) = cos x :=
   cos_periodic.int_mul n x
 #align complex.cos_add_int_mul_two_pi Complex.cos_add_int_mul_two_pi
+-/
 
+#print Complex.cos_sub_nat_mul_two_pi /-
 theorem cos_sub_nat_mul_two_pi (x : ℂ) (n : ℕ) : cos (x - n * (2 * π)) = cos x :=
   cos_periodic.sub_nat_mul_eq n
 #align complex.cos_sub_nat_mul_two_pi Complex.cos_sub_nat_mul_two_pi
+-/
 
+#print Complex.cos_sub_int_mul_two_pi /-
 theorem cos_sub_int_mul_two_pi (x : ℂ) (n : ℤ) : cos (x - n * (2 * π)) = cos x :=
   cos_periodic.sub_int_mul_eq n
 #align complex.cos_sub_int_mul_two_pi Complex.cos_sub_int_mul_two_pi
+-/
 
+#print Complex.cos_nat_mul_two_pi_sub /-
 theorem cos_nat_mul_two_pi_sub (x : ℂ) (n : ℕ) : cos (n * (2 * π) - x) = cos x :=
   cos_neg x ▸ cos_periodic.nat_mul_sub_eq n
 #align complex.cos_nat_mul_two_pi_sub Complex.cos_nat_mul_two_pi_sub
+-/
 
+#print Complex.cos_int_mul_two_pi_sub /-
 theorem cos_int_mul_two_pi_sub (x : ℂ) (n : ℤ) : cos (n * (2 * π) - x) = cos x :=
   cos_neg x ▸ cos_periodic.int_mul_sub_eq n
 #align complex.cos_int_mul_two_pi_sub Complex.cos_int_mul_two_pi_sub
+-/
 
+#print Complex.cos_nat_mul_two_pi_add_pi /-
 theorem cos_nat_mul_two_pi_add_pi (n : ℕ) : cos (n * (2 * π) + π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.nat_mul n).add_antiperiod_eq cos_antiperiodic
 #align complex.cos_nat_mul_two_pi_add_pi Complex.cos_nat_mul_two_pi_add_pi
+-/
 
+#print Complex.cos_int_mul_two_pi_add_pi /-
 theorem cos_int_mul_two_pi_add_pi (n : ℤ) : cos (n * (2 * π) + π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.int_mul n).add_antiperiod_eq cos_antiperiodic
 #align complex.cos_int_mul_two_pi_add_pi Complex.cos_int_mul_two_pi_add_pi
+-/
 
+#print Complex.cos_nat_mul_two_pi_sub_pi /-
 theorem cos_nat_mul_two_pi_sub_pi (n : ℕ) : cos (n * (2 * π) - π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.nat_mul n).sub_antiperiod_eq cos_antiperiodic
 #align complex.cos_nat_mul_two_pi_sub_pi Complex.cos_nat_mul_two_pi_sub_pi
+-/
 
+#print Complex.cos_int_mul_two_pi_sub_pi /-
 theorem cos_int_mul_two_pi_sub_pi (n : ℤ) : cos (n * (2 * π) - π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.int_mul n).sub_antiperiod_eq cos_antiperiodic
 #align complex.cos_int_mul_two_pi_sub_pi Complex.cos_int_mul_two_pi_sub_pi
+-/
 
+#print Complex.sin_add_pi_div_two /-
 theorem sin_add_pi_div_two (x : ℂ) : sin (x + π / 2) = cos x := by simp [sin_add]
 #align complex.sin_add_pi_div_two Complex.sin_add_pi_div_two
+-/
 
+#print Complex.sin_sub_pi_div_two /-
 theorem sin_sub_pi_div_two (x : ℂ) : sin (x - π / 2) = -cos x := by simp [sub_eq_add_neg, sin_add]
 #align complex.sin_sub_pi_div_two Complex.sin_sub_pi_div_two
+-/
 
+#print Complex.sin_pi_div_two_sub /-
 theorem sin_pi_div_two_sub (x : ℂ) : sin (π / 2 - x) = cos x := by simp [sub_eq_add_neg, sin_add]
 #align complex.sin_pi_div_two_sub Complex.sin_pi_div_two_sub
+-/
 
+#print Complex.cos_add_pi_div_two /-
 theorem cos_add_pi_div_two (x : ℂ) : cos (x + π / 2) = -sin x := by simp [cos_add]
 #align complex.cos_add_pi_div_two Complex.cos_add_pi_div_two
+-/
 
+#print Complex.cos_sub_pi_div_two /-
 theorem cos_sub_pi_div_two (x : ℂ) : cos (x - π / 2) = sin x := by simp [sub_eq_add_neg, cos_add]
 #align complex.cos_sub_pi_div_two Complex.cos_sub_pi_div_two
+-/
 
+#print Complex.cos_pi_div_two_sub /-
 theorem cos_pi_div_two_sub (x : ℂ) : cos (π / 2 - x) = sin x := by
   rw [← cos_neg, neg_sub, cos_sub_pi_div_two]
 #align complex.cos_pi_div_two_sub Complex.cos_pi_div_two_sub
+-/
 
+#print Complex.tan_periodic /-
 theorem tan_periodic : Function.Periodic tan π := by
   simpa only [tan_eq_sin_div_cos] using sin_antiperiodic.div cos_antiperiodic
 #align complex.tan_periodic Complex.tan_periodic
+-/
 
+#print Complex.tan_add_pi /-
 theorem tan_add_pi (x : ℂ) : tan (x + π) = tan x :=
   tan_periodic x
 #align complex.tan_add_pi Complex.tan_add_pi
+-/
 
+#print Complex.tan_sub_pi /-
 theorem tan_sub_pi (x : ℂ) : tan (x - π) = tan x :=
   tan_periodic.sub_eq x
 #align complex.tan_sub_pi Complex.tan_sub_pi
+-/
 
+#print Complex.tan_pi_sub /-
 theorem tan_pi_sub (x : ℂ) : tan (π - x) = -tan x :=
   tan_neg x ▸ tan_periodic.sub_eq'
 #align complex.tan_pi_sub Complex.tan_pi_sub
+-/
 
+#print Complex.tan_pi_div_two_sub /-
 theorem tan_pi_div_two_sub (x : ℂ) : tan (π / 2 - x) = (tan x)⁻¹ := by
   rw [tan_eq_sin_div_cos, tan_eq_sin_div_cos, inv_div, sin_pi_div_two_sub, cos_pi_div_two_sub]
 #align complex.tan_pi_div_two_sub Complex.tan_pi_div_two_sub
+-/
 
+#print Complex.tan_nat_mul_pi /-
 theorem tan_nat_mul_pi (n : ℕ) : tan (n * π) = 0 :=
   tan_zero ▸ tan_periodic.nat_mul_eq n
 #align complex.tan_nat_mul_pi Complex.tan_nat_mul_pi
+-/
 
+#print Complex.tan_int_mul_pi /-
 theorem tan_int_mul_pi (n : ℤ) : tan (n * π) = 0 :=
   tan_zero ▸ tan_periodic.int_mul_eq n
 #align complex.tan_int_mul_pi Complex.tan_int_mul_pi
+-/
 
+#print Complex.tan_add_nat_mul_pi /-
 theorem tan_add_nat_mul_pi (x : ℂ) (n : ℕ) : tan (x + n * π) = tan x :=
   tan_periodic.nat_mul n x
 #align complex.tan_add_nat_mul_pi Complex.tan_add_nat_mul_pi
+-/
 
+#print Complex.tan_add_int_mul_pi /-
 theorem tan_add_int_mul_pi (x : ℂ) (n : ℤ) : tan (x + n * π) = tan x :=
   tan_periodic.int_mul n x
 #align complex.tan_add_int_mul_pi Complex.tan_add_int_mul_pi
+-/
 
+#print Complex.tan_sub_nat_mul_pi /-
 theorem tan_sub_nat_mul_pi (x : ℂ) (n : ℕ) : tan (x - n * π) = tan x :=
   tan_periodic.sub_nat_mul_eq n
 #align complex.tan_sub_nat_mul_pi Complex.tan_sub_nat_mul_pi
+-/
 
+#print Complex.tan_sub_int_mul_pi /-
 theorem tan_sub_int_mul_pi (x : ℂ) (n : ℤ) : tan (x - n * π) = tan x :=
   tan_periodic.sub_int_mul_eq n
 #align complex.tan_sub_int_mul_pi Complex.tan_sub_int_mul_pi
+-/
 
+#print Complex.tan_nat_mul_pi_sub /-
 theorem tan_nat_mul_pi_sub (x : ℂ) (n : ℕ) : tan (n * π - x) = -tan x :=
   tan_neg x ▸ tan_periodic.nat_mul_sub_eq n
 #align complex.tan_nat_mul_pi_sub Complex.tan_nat_mul_pi_sub
+-/
 
+#print Complex.tan_int_mul_pi_sub /-
 theorem tan_int_mul_pi_sub (x : ℂ) (n : ℤ) : tan (n * π - x) = -tan x :=
   tan_neg x ▸ tan_periodic.int_mul_sub_eq n
 #align complex.tan_int_mul_pi_sub Complex.tan_int_mul_pi_sub
+-/
 
+/- warning: complex.exp_antiperiodic -> Complex.exp_antiperiodic is a dubious translation:
+lean 3 declaration is
+  Function.Antiperiodic.{0, 0} Complex Complex Complex.hasAdd Complex.hasNeg Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi) Complex.I)
+but is expected to have type
+  Function.Antiperiodic.{0, 0} Complex Complex Complex.instAddComplex Complex.instNegComplex Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' Real.pi) Complex.I)
+Case conversion may be inaccurate. Consider using '#align complex.exp_antiperiodic Complex.exp_antiperiodicₓ'. -/
 theorem exp_antiperiodic : Function.Antiperiodic exp (π * I) := by simp [exp_add, exp_mul_I]
 #align complex.exp_antiperiodic Complex.exp_antiperiodic
 
+/- warning: complex.exp_periodic -> Complex.exp_periodic is a dubious translation:
+lean 3 declaration is
+  Function.Periodic.{0, 0} Complex Complex Complex.hasAdd Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi)) Complex.I)
+but is expected to have type
+  Function.Periodic.{0, 0} Complex Complex Complex.instAddComplex Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.ofReal' Real.pi)) Complex.I)
+Case conversion may be inaccurate. Consider using '#align complex.exp_periodic Complex.exp_periodicₓ'. -/
 theorem exp_periodic : Function.Periodic exp (2 * π * I) :=
   (mul_assoc (2 : ℂ) π I).symm ▸ exp_antiperiodic.Periodic
 #align complex.exp_periodic Complex.exp_periodic
 
-theorem exp_mul_i_antiperiodic : Function.Antiperiodic (fun x => exp (x * I)) π := by
+/- warning: complex.exp_mul_I_antiperiodic -> Complex.exp_mul_I_antiperiodic is a dubious translation:
+lean 3 declaration is
+  Function.Antiperiodic.{0, 0} Complex Complex Complex.hasAdd Complex.hasNeg (fun (x : Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) x Complex.I)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi)
+but is expected to have type
+  Function.Antiperiodic.{0, 0} Complex Complex Complex.instAddComplex Complex.instNegComplex (fun (x : Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) x Complex.I)) (Complex.ofReal' Real.pi)
+Case conversion may be inaccurate. Consider using '#align complex.exp_mul_I_antiperiodic Complex.exp_mul_I_antiperiodicₓ'. -/
+theorem exp_mul_I_antiperiodic : Function.Antiperiodic (fun x => exp (x * I)) π := by
   simpa only [mul_inv_cancel_right₀ I_ne_zero] using exp_antiperiodic.mul_const I_ne_zero
-#align complex.exp_mul_I_antiperiodic Complex.exp_mul_i_antiperiodic
-
-theorem exp_mul_i_periodic : Function.Periodic (fun x => exp (x * I)) (2 * π) :=
-  exp_mul_i_antiperiodic.Periodic
-#align complex.exp_mul_I_periodic Complex.exp_mul_i_periodic
-
-@[simp]
-theorem exp_pi_mul_i : exp (π * I) = -1 :=
+#align complex.exp_mul_I_antiperiodic Complex.exp_mul_I_antiperiodic
+
+/- warning: complex.exp_mul_I_periodic -> Complex.exp_mul_I_periodic is a dubious translation:
+lean 3 declaration is
+  Function.Periodic.{0, 0} Complex Complex Complex.hasAdd (fun (x : Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) x Complex.I)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi))
+but is expected to have type
+  Function.Periodic.{0, 0} Complex Complex Complex.instAddComplex (fun (x : Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) x Complex.I)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.ofReal' Real.pi))
+Case conversion may be inaccurate. Consider using '#align complex.exp_mul_I_periodic Complex.exp_mul_I_periodicₓ'. -/
+theorem exp_mul_I_periodic : Function.Periodic (fun x => exp (x * I)) (2 * π) :=
+  exp_mul_I_antiperiodic.Periodic
+#align complex.exp_mul_I_periodic Complex.exp_mul_I_periodic
+
+/- warning: complex.exp_pi_mul_I -> Complex.exp_pi_mul_I is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi) Complex.I)) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))
+but is expected to have type
+  Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' Real.pi) Complex.I)) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
+Case conversion may be inaccurate. Consider using '#align complex.exp_pi_mul_I Complex.exp_pi_mul_Iₓ'. -/
+@[simp]
+theorem exp_pi_mul_I : exp (π * I) = -1 :=
   exp_zero ▸ exp_antiperiodic.Eq
-#align complex.exp_pi_mul_I Complex.exp_pi_mul_i
+#align complex.exp_pi_mul_I Complex.exp_pi_mul_I
 
+/- warning: complex.exp_two_pi_mul_I -> Complex.exp_two_pi_mul_I is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi)) Complex.I)) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))
+but is expected to have type
+  Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.ofReal' Real.pi)) Complex.I)) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))
+Case conversion may be inaccurate. Consider using '#align complex.exp_two_pi_mul_I Complex.exp_two_pi_mul_Iₓ'. -/
 @[simp]
-theorem exp_two_pi_mul_i : exp (2 * π * I) = 1 :=
+theorem exp_two_pi_mul_I : exp (2 * π * I) = 1 :=
   exp_periodic.Eq.trans exp_zero
-#align complex.exp_two_pi_mul_I Complex.exp_two_pi_mul_i
+#align complex.exp_two_pi_mul_I Complex.exp_two_pi_mul_I
 
+/- warning: complex.exp_nat_mul_two_pi_mul_I -> Complex.exp_nat_mul_two_pi_mul_I is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi)) Complex.I))) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))
+but is expected to have type
+  forall (n : Nat), Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.ofReal' Real.pi)) Complex.I))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))
+Case conversion may be inaccurate. Consider using '#align complex.exp_nat_mul_two_pi_mul_I Complex.exp_nat_mul_two_pi_mul_Iₓ'. -/
 @[simp]
-theorem exp_nat_mul_two_pi_mul_i (n : ℕ) : exp (n * (2 * π * I)) = 1 :=
+theorem exp_nat_mul_two_pi_mul_I (n : ℕ) : exp (n * (2 * π * I)) = 1 :=
   (exp_periodic.nat_mul_eq n).trans exp_zero
-#align complex.exp_nat_mul_two_pi_mul_I Complex.exp_nat_mul_two_pi_mul_i
+#align complex.exp_nat_mul_two_pi_mul_I Complex.exp_nat_mul_two_pi_mul_I
 
+/- warning: complex.exp_int_mul_two_pi_mul_I -> Complex.exp_int_mul_two_pi_mul_I is a dubious translation:
+lean 3 declaration is
+  forall (n : Int), Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi)) Complex.I))) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))
+but is expected to have type
+  forall (n : Int), Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.ofReal' Real.pi)) Complex.I))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))
+Case conversion may be inaccurate. Consider using '#align complex.exp_int_mul_two_pi_mul_I Complex.exp_int_mul_two_pi_mul_Iₓ'. -/
 @[simp]
-theorem exp_int_mul_two_pi_mul_i (n : ℤ) : exp (n * (2 * π * I)) = 1 :=
+theorem exp_int_mul_two_pi_mul_I (n : ℤ) : exp (n * (2 * π * I)) = 1 :=
   (exp_periodic.int_mul_eq n).trans exp_zero
-#align complex.exp_int_mul_two_pi_mul_I Complex.exp_int_mul_two_pi_mul_i
+#align complex.exp_int_mul_two_pi_mul_I Complex.exp_int_mul_two_pi_mul_I
 
+/- warning: complex.exp_add_pi_mul_I -> Complex.exp_add_pi_mul_I is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Complex (Complex.exp (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi) Complex.I))) (Neg.neg.{0} Complex Complex.hasNeg (Complex.exp z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Complex (Complex.exp (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' Real.pi) Complex.I))) (Neg.neg.{0} Complex Complex.instNegComplex (Complex.exp z))
+Case conversion may be inaccurate. Consider using '#align complex.exp_add_pi_mul_I Complex.exp_add_pi_mul_Iₓ'. -/
 @[simp]
-theorem exp_add_pi_mul_i (z : ℂ) : exp (z + π * I) = -exp z :=
+theorem exp_add_pi_mul_I (z : ℂ) : exp (z + π * I) = -exp z :=
   exp_antiperiodic z
-#align complex.exp_add_pi_mul_I Complex.exp_add_pi_mul_i
+#align complex.exp_add_pi_mul_I Complex.exp_add_pi_mul_I
 
+/- warning: complex.exp_sub_pi_mul_I -> Complex.exp_sub_pi_mul_I is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Complex (Complex.exp (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) Real.pi) Complex.I))) (Neg.neg.{0} Complex Complex.hasNeg (Complex.exp z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Complex (Complex.exp (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' Real.pi) Complex.I))) (Neg.neg.{0} Complex Complex.instNegComplex (Complex.exp z))
+Case conversion may be inaccurate. Consider using '#align complex.exp_sub_pi_mul_I Complex.exp_sub_pi_mul_Iₓ'. -/
 @[simp]
-theorem exp_sub_pi_mul_i (z : ℂ) : exp (z - π * I) = -exp z :=
+theorem exp_sub_pi_mul_I (z : ℂ) : exp (z - π * I) = -exp z :=
   exp_antiperiodic.sub_eq z
-#align complex.exp_sub_pi_mul_I Complex.exp_sub_pi_mul_i
-
+#align complex.exp_sub_pi_mul_I Complex.exp_sub_pi_mul_I
+
+/- warning: complex.abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le -> Complex.abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le is a dubious translation:
+lean 3 declaration is
+  forall {a : Real} {b : Real}, (LE.le.{0} Real Real.hasLe a (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall {z : Complex}, (LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)) b) -> (LE.le.{0} Real Real.hasLe b (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) Real.pi (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (LE.le.{0} Real Real.hasLe (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) a) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) (Complex.exp z) (Complex.exp (Neg.neg.{0} Complex Complex.hasNeg z)))))) (Real.exp (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) a (Real.cos b)) (Real.exp (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)))))))
+but is expected to have type
+  forall {a : Real} {b : Real}, (LE.le.{0} Real Real.instLEReal a (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall {z : Complex}, (LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) b) -> (LE.le.{0} Real Real.instLEReal b (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' a) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.exp z) (Complex.exp (Neg.neg.{0} Complex Complex.instNegComplex z)))))) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' a) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.exp z) (Complex.exp (Neg.neg.{0} Complex Complex.instNegComplex z)))))) (Real.exp (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) a (Real.cos b)) (Real.exp (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)))))))
+Case conversion may be inaccurate. Consider using '#align complex.abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le Complex.abs_exp_mul_exp_add_exp_neg_le_of_abs_im_leₓ'. -/
 /-- A supporting lemma for the **Phragmen-Lindelöf principle** in a horizontal strip. If `z : ℂ`
 belongs to a horizontal strip `|complex.im z| ≤ b`, `b ≤ π / 2`, and `a ≤ 0`, then
 $$\left|exp^{a\left(e^{z}+e^{-z}\right)}\right| \le e^{a\cos b \exp^{|re z|}}.$$

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ad820c4997738e2f542f8a20f32911f52020e26

@@ -96,7 +96,7 @@ variable {x y z : ℝ}
 
 @[continuity]
 theorem continuous_sin : Continuous sin :=
-  Complex.continuous_re.comp (Complex.continuous_sin.comp Complex.continuous_of_real)
+  Complex.continuous_re.comp (Complex.continuous_sin.comp Complex.continuous_ofReal)
 #align real.continuous_sin Real.continuous_sin
 
 theorem continuousOn_sin {s} : ContinuousOn sin s :=
@@ -105,7 +105,7 @@ theorem continuousOn_sin {s} : ContinuousOn sin s :=
 
 @[continuity]
 theorem continuous_cos : Continuous cos :=
-  Complex.continuous_re.comp (Complex.continuous_cos.comp Complex.continuous_of_real)
+  Complex.continuous_re.comp (Complex.continuous_cos.comp Complex.continuous_ofReal)
 #align real.continuous_cos Real.continuous_cos
 
 theorem continuousOn_cos {s} : ContinuousOn cos s :=
@@ -114,12 +114,12 @@ theorem continuousOn_cos {s} : ContinuousOn cos s :=
 
 @[continuity]
 theorem continuous_sinh : Continuous sinh :=
-  Complex.continuous_re.comp (Complex.continuous_sinh.comp Complex.continuous_of_real)
+  Complex.continuous_re.comp (Complex.continuous_sinh.comp Complex.continuous_ofReal)
 #align real.continuous_sinh Real.continuous_sinh
 
 @[continuity]
 theorem continuous_cosh : Continuous cosh :=
-  Complex.continuous_re.comp (Complex.continuous_cosh.comp Complex.continuous_of_real)
+  Complex.continuous_re.comp (Complex.continuous_cosh.comp Complex.continuous_ofReal)
 #align real.continuous_cosh Real.continuous_cosh
 
 end Real

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.basic
-! 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.Analysis.SpecialFunctions.Exp
-import Mathbin.Data.Set.Intervals.Infinite
 
 /-!
 # Trigonometric functions

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

@@ -1141,8 +1141,7 @@ theorem tendsto_cos_neg_pi_div_two : Tendsto cos (𝓝[>] (-(π / 2))) (𝓝[>]
 
 theorem tendsto_tan_neg_pi_div_two : Tendsto tan (𝓝[>] (-(π / 2))) atBot :=
   by
-  convert
-    tendsto_cos_neg_pi_div_two.inv_tendsto_zero.at_top_mul_neg (by norm_num)
+  convert tendsto_cos_neg_pi_div_two.inv_tendsto_zero.at_top_mul_neg (by norm_num)
       tendsto_sin_neg_pi_div_two
   simp only [Pi.inv_apply, ← div_eq_inv_mul, ← tan_eq_sin_div_cos]
 #align real.tendsto_tan_neg_pi_div_two Real.tendsto_tan_neg_pi_div_two

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

@@ -1454,8 +1454,7 @@ $$\left|exp^{a\left(e^{z}+e^{-z}\right)}\right| \le e^{a\cos b \exp^{|re z|}}.$$
 -/
 theorem abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le {a b : ℝ} (ha : a ≤ 0) {z : ℂ} (hz : |z.im| ≤ b)
     (hb : b ≤ π / 2) :
-    Complex.AbsTheory.Complex.abs (exp (a * (exp z + exp (-z)))) ≤
-      Real.exp (a * Real.cos b * Real.exp (|z.re|)) :=
+    abs (exp (a * (exp z + exp (-z)))) ≤ Real.exp (a * Real.cos b * Real.exp (|z.re|)) :=
   by
   simp only [abs_exp, Real.exp_le_exp, of_real_mul_re, add_re, exp_re, neg_im, Real.cos_neg, ←
     add_mul, mul_assoc, mul_comm (Real.cos b), neg_re, ← Real.cos_abs z.im]

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

@@ -538,7 +538,7 @@ theorem sin_ne_zero_iff {x : ℝ} : sin x ≠ 0 ↔ ∀ n : ℤ, (n : ℝ) * π
 
 theorem sin_eq_zero_iff_cos_eq {x : ℝ} : sin x = 0 ↔ cos x = 1 ∨ cos x = -1 := by
   rw [← mul_self_eq_one_iff, ← sin_sq_add_cos_sq x, sq, sq, ← sub_eq_iff_eq_add, sub_self] <;>
-    exact ⟨fun h => by rw [h, mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
+    exact ⟨fun h => by rw [h, MulZeroClass.mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
 #align real.sin_eq_zero_iff_cos_eq Real.sin_eq_zero_iff_cos_eq
 
 theorem cos_eq_one_iff (x : ℝ) : cos x = 1 ↔ ∃ n : ℤ, (n : ℝ) * (2 * π) = x :=
@@ -1155,7 +1155,7 @@ open Real
 
 theorem sin_eq_zero_iff_cos_eq {z : ℂ} : sin z = 0 ↔ cos z = 1 ∨ cos z = -1 := by
   rw [← mul_self_eq_one_iff, ← sin_sq_add_cos_sq, sq, sq, ← sub_eq_iff_eq_add, sub_self] <;>
-    exact ⟨fun h => by rw [h, mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
+    exact ⟨fun h => by rw [h, MulZeroClass.mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
 #align complex.sin_eq_zero_iff_cos_eq Complex.sin_eq_zero_iff_cos_eq
 
 @[simp]

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

@@ -1403,48 +1403,48 @@ theorem tan_int_mul_pi_sub (x : ℂ) (n : ℤ) : tan (n * π - x) = -tan x :=
   tan_neg x ▸ tan_periodic.int_mul_sub_eq n
 #align complex.tan_int_mul_pi_sub Complex.tan_int_mul_pi_sub
 
-theorem exp_antiperiodic : Function.Antiperiodic exp (π * i) := by simp [exp_add, exp_mul_I]
+theorem exp_antiperiodic : Function.Antiperiodic exp (π * I) := by simp [exp_add, exp_mul_I]
 #align complex.exp_antiperiodic Complex.exp_antiperiodic
 
-theorem exp_periodic : Function.Periodic exp (2 * π * i) :=
-  (mul_assoc (2 : ℂ) π i).symm ▸ exp_antiperiodic.Periodic
+theorem exp_periodic : Function.Periodic exp (2 * π * I) :=
+  (mul_assoc (2 : ℂ) π I).symm ▸ exp_antiperiodic.Periodic
 #align complex.exp_periodic Complex.exp_periodic
 
-theorem exp_mul_i_antiperiodic : Function.Antiperiodic (fun x => exp (x * i)) π := by
+theorem exp_mul_i_antiperiodic : Function.Antiperiodic (fun x => exp (x * I)) π := by
   simpa only [mul_inv_cancel_right₀ I_ne_zero] using exp_antiperiodic.mul_const I_ne_zero
 #align complex.exp_mul_I_antiperiodic Complex.exp_mul_i_antiperiodic
 
-theorem exp_mul_i_periodic : Function.Periodic (fun x => exp (x * i)) (2 * π) :=
+theorem exp_mul_i_periodic : Function.Periodic (fun x => exp (x * I)) (2 * π) :=
   exp_mul_i_antiperiodic.Periodic
 #align complex.exp_mul_I_periodic Complex.exp_mul_i_periodic
 
 @[simp]
-theorem exp_pi_mul_i : exp (π * i) = -1 :=
+theorem exp_pi_mul_i : exp (π * I) = -1 :=
   exp_zero ▸ exp_antiperiodic.Eq
 #align complex.exp_pi_mul_I Complex.exp_pi_mul_i
 
 @[simp]
-theorem exp_two_pi_mul_i : exp (2 * π * i) = 1 :=
+theorem exp_two_pi_mul_i : exp (2 * π * I) = 1 :=
   exp_periodic.Eq.trans exp_zero
 #align complex.exp_two_pi_mul_I Complex.exp_two_pi_mul_i
 
 @[simp]
-theorem exp_nat_mul_two_pi_mul_i (n : ℕ) : exp (n * (2 * π * i)) = 1 :=
+theorem exp_nat_mul_two_pi_mul_i (n : ℕ) : exp (n * (2 * π * I)) = 1 :=
   (exp_periodic.nat_mul_eq n).trans exp_zero
 #align complex.exp_nat_mul_two_pi_mul_I Complex.exp_nat_mul_two_pi_mul_i
 
 @[simp]
-theorem exp_int_mul_two_pi_mul_i (n : ℤ) : exp (n * (2 * π * i)) = 1 :=
+theorem exp_int_mul_two_pi_mul_i (n : ℤ) : exp (n * (2 * π * I)) = 1 :=
   (exp_periodic.int_mul_eq n).trans exp_zero
 #align complex.exp_int_mul_two_pi_mul_I Complex.exp_int_mul_two_pi_mul_i
 
 @[simp]
-theorem exp_add_pi_mul_i (z : ℂ) : exp (z + π * i) = -exp z :=
+theorem exp_add_pi_mul_i (z : ℂ) : exp (z + π * I) = -exp z :=
   exp_antiperiodic z
 #align complex.exp_add_pi_mul_I Complex.exp_add_pi_mul_i
 
 @[simp]
-theorem exp_sub_pi_mul_i (z : ℂ) : exp (z - π * i) = -exp z :=
+theorem exp_sub_pi_mul_i (z : ℂ) : exp (z - π * I) = -exp z :=
   exp_antiperiodic.sub_eq z
 #align complex.exp_sub_pi_mul_I Complex.exp_sub_pi_mul_i
 
@@ -1454,7 +1454,8 @@ $$\left|exp^{a\left(e^{z}+e^{-z}\right)}\right| \le e^{a\cos b \exp^{|re z|}}.$$
 -/
 theorem abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le {a b : ℝ} (ha : a ≤ 0) {z : ℂ} (hz : |z.im| ≤ b)
     (hb : b ≤ π / 2) :
-    abs (exp (a * (exp z + exp (-z)))) ≤ Real.exp (a * Real.cos b * Real.exp (|z.re|)) :=
+    Complex.AbsTheory.Complex.abs (exp (a * (exp z + exp (-z)))) ≤
+      Real.exp (a * Real.cos b * Real.exp (|z.re|)) :=
   by
   simp only [abs_exp, Real.exp_le_exp, of_real_mul_re, add_re, exp_re, neg_im, Real.cos_neg, ←
     add_mul, mul_assoc, mul_comm (Real.cos b), neg_re, ← Real.cos_abs z.im]

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

A PR accompanying #12339.

Zulip discussion

@@ -792,9 +792,9 @@ theorem sin_sq_pi_over_two_pow (n : ℕ) :
 theorem sin_sq_pi_over_two_pow_succ (n : ℕ) :
     sin (π / 2 ^ (n + 2)) ^ 2 = 1 / 2 - sqrtTwoAddSeries 0 n / 4 := by
   rw [sin_sq_pi_over_two_pow, sqrtTwoAddSeries, div_pow, sq_sqrt, add_div, ← sub_sub]
-  congr
-  · norm_num
-  · norm_num
+  · congr
+    · norm_num
+    · norm_num
   · exact add_nonneg two_pos.le (sqrtTwoAddSeries_zero_nonneg _)
 #align real.sin_sq_pi_over_two_pow_succ Real.sin_sq_pi_over_two_pow_succ
 

This adds the notation √r for Real.sqrt r. The precedence is such that √x⁻¹ is parsed as √(x⁻¹); not because this is particularly desirable, but because it's the default and the choice doesn't really matter.

This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing x.sqrt as that PR does.

While perhaps claiming √ for Real.sqrt is greedy; it:

• Is far more common thatn NNReal.sqrt and Nat.sqrt
• Is far more interesting to mathlib than sqrt on Float
• Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types.
• Will be replaced by a more general typeclass in a future PR.

Zulip

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -538,12 +538,12 @@ theorem cos_nonpos_of_pi_div_two_le_of_le {x : ℝ} (hx₁ : π / 2 ≤ x) (hx
 #align real.cos_nonpos_of_pi_div_two_le_of_le Real.cos_nonpos_of_pi_div_two_le_of_le
 
 theorem sin_eq_sqrt_one_sub_cos_sq {x : ℝ} (hl : 0 ≤ x) (hu : x ≤ π) :
-    sin x = sqrt (1 - cos x ^ 2) := by
+    sin x = √(1 - cos x ^ 2) := by
   rw [← abs_sin_eq_sqrt_one_sub_cos_sq, abs_of_nonneg (sin_nonneg_of_nonneg_of_le_pi hl hu)]
 #align real.sin_eq_sqrt_one_sub_cos_sq Real.sin_eq_sqrt_one_sub_cos_sq
 
 theorem cos_eq_sqrt_one_sub_sin_sq {x : ℝ} (hl : -(π / 2) ≤ x) (hu : x ≤ π / 2) :
-    cos x = sqrt (1 - sin x ^ 2) := by
+    cos x = √(1 - sin x ^ 2) := by
   rw [← abs_cos_eq_sqrt_one_sub_sin_sq, abs_of_nonneg (cos_nonneg_of_mem_Icc ⟨hl, hu⟩)]
 #align real.cos_eq_sqrt_one_sub_sin_sq Real.cos_eq_sqrt_one_sub_sin_sq
 
@@ -726,16 +726,16 @@ variable (x : ℝ)
 @[simp]
 noncomputable def sqrtTwoAddSeries (x : ℝ) : ℕ → ℝ
   | 0 => x
-  | n + 1 => sqrt (2 + sqrtTwoAddSeries x n)
+  | n + 1 => √(2 + sqrtTwoAddSeries x n)
 #align real.sqrt_two_add_series Real.sqrtTwoAddSeries
 
 theorem sqrtTwoAddSeries_zero : sqrtTwoAddSeries x 0 = x := by simp
 #align real.sqrt_two_add_series_zero Real.sqrtTwoAddSeries_zero
 
-theorem sqrtTwoAddSeries_one : sqrtTwoAddSeries 0 1 = sqrt 2 := by simp
+theorem sqrtTwoAddSeries_one : sqrtTwoAddSeries 0 1 = √2 := by simp
 #align real.sqrt_two_add_series_one Real.sqrtTwoAddSeries_one
 
-theorem sqrtTwoAddSeries_two : sqrtTwoAddSeries 0 2 = sqrt (2 + sqrt 2) := by simp
+theorem sqrtTwoAddSeries_two : sqrtTwoAddSeries 0 2 = √(2 + √2) := by simp
 #align real.sqrt_two_add_series_two Real.sqrtTwoAddSeries_two
 
 theorem sqrtTwoAddSeries_zero_nonneg : ∀ n : ℕ, 0 ≤ sqrtTwoAddSeries 0 n
@@ -759,7 +759,7 @@ theorem sqrtTwoAddSeries_lt_two : ∀ n : ℕ, sqrtTwoAddSeries 0 n < 2
 #align real.sqrt_two_add_series_lt_two Real.sqrtTwoAddSeries_lt_two
 
 theorem sqrtTwoAddSeries_succ (x : ℝ) :
-    ∀ n : ℕ, sqrtTwoAddSeries x (n + 1) = sqrtTwoAddSeries (sqrt (2 + x)) n
+    ∀ n : ℕ, sqrtTwoAddSeries x (n + 1) = sqrtTwoAddSeries (√(2 + x)) n
   | 0 => rfl
   | n + 1 => by rw [sqrtTwoAddSeries, sqrtTwoAddSeries_succ _ _, sqrtTwoAddSeries]
 #align real.sqrt_two_add_series_succ Real.sqrtTwoAddSeries_succ
@@ -800,7 +800,7 @@ theorem sin_sq_pi_over_two_pow_succ (n : ℕ) :
 
 @[simp]
 theorem sin_pi_over_two_pow_succ (n : ℕ) :
-    sin (π / 2 ^ (n + 2)) = sqrt (2 - sqrtTwoAddSeries 0 n) / 2 := by
+    sin (π / 2 ^ (n + 2)) = √(2 - sqrtTwoAddSeries 0 n) / 2 := by
   rw [eq_div_iff_mul_eq two_ne_zero, eq_comm, sqrt_eq_iff_sq_eq, mul_pow,
     sin_sq_pi_over_two_pow_succ, sub_mul]
   · congr <;> norm_num
@@ -812,7 +812,7 @@ theorem sin_pi_over_two_pow_succ (n : ℕ) :
 #align real.sin_pi_over_two_pow_succ Real.sin_pi_over_two_pow_succ
 
 @[simp]
-theorem cos_pi_div_four : cos (π / 4) = sqrt 2 / 2 := by
+theorem cos_pi_div_four : cos (π / 4) = √2 / 2 := by
   trans cos (π / 2 ^ 2)
   · congr
     norm_num
@@ -820,7 +820,7 @@ theorem cos_pi_div_four : cos (π / 4) = sqrt 2 / 2 := by
 #align real.cos_pi_div_four Real.cos_pi_div_four
 
 @[simp]
-theorem sin_pi_div_four : sin (π / 4) = sqrt 2 / 2 := by
+theorem sin_pi_div_four : sin (π / 4) = √2 / 2 := by
   trans sin (π / 2 ^ 2)
   · congr
     norm_num
@@ -828,7 +828,7 @@ theorem sin_pi_div_four : sin (π / 4) = sqrt 2 / 2 := by
 #align real.sin_pi_div_four Real.sin_pi_div_four
 
 @[simp]
-theorem cos_pi_div_eight : cos (π / 8) = sqrt (2 + sqrt 2) / 2 := by
+theorem cos_pi_div_eight : cos (π / 8) = √(2 + √2) / 2 := by
   trans cos (π / 2 ^ 3)
   · congr
     norm_num
@@ -836,7 +836,7 @@ theorem cos_pi_div_eight : cos (π / 8) = sqrt (2 + sqrt 2) / 2 := by
 #align real.cos_pi_div_eight Real.cos_pi_div_eight
 
 @[simp]
-theorem sin_pi_div_eight : sin (π / 8) = sqrt (2 - sqrt 2) / 2 := by
+theorem sin_pi_div_eight : sin (π / 8) = √(2 - √2) / 2 := by
   trans sin (π / 2 ^ 3)
   · congr
     norm_num
@@ -844,7 +844,7 @@ theorem sin_pi_div_eight : sin (π / 8) = sqrt (2 - sqrt 2) / 2 := by
 #align real.sin_pi_div_eight Real.sin_pi_div_eight
 
 @[simp]
-theorem cos_pi_div_sixteen : cos (π / 16) = sqrt (2 + sqrt (2 + sqrt 2)) / 2 := by
+theorem cos_pi_div_sixteen : cos (π / 16) = √(2 + √(2 + √2)) / 2 := by
   trans cos (π / 2 ^ 4)
   · congr
     norm_num
@@ -852,7 +852,7 @@ theorem cos_pi_div_sixteen : cos (π / 16) = sqrt (2 + sqrt (2 + sqrt 2)) / 2 :=
 #align real.cos_pi_div_sixteen Real.cos_pi_div_sixteen
 
 @[simp]
-theorem sin_pi_div_sixteen : sin (π / 16) = sqrt (2 - sqrt (2 + sqrt 2)) / 2 := by
+theorem sin_pi_div_sixteen : sin (π / 16) = √(2 - √(2 + √2)) / 2 := by
   trans sin (π / 2 ^ 4)
   · congr
     norm_num
@@ -860,7 +860,7 @@ theorem sin_pi_div_sixteen : sin (π / 16) = sqrt (2 - sqrt (2 + sqrt 2)) / 2 :=
 #align real.sin_pi_div_sixteen Real.sin_pi_div_sixteen
 
 @[simp]
-theorem cos_pi_div_thirty_two : cos (π / 32) = sqrt (2 + sqrt (2 + sqrt (2 + sqrt 2))) / 2 := by
+theorem cos_pi_div_thirty_two : cos (π / 32) = √(2 + √(2 + √(2 + √2))) / 2 := by
   trans cos (π / 2 ^ 5)
   · congr
     norm_num
@@ -868,7 +868,7 @@ theorem cos_pi_div_thirty_two : cos (π / 32) = sqrt (2 + sqrt (2 + sqrt (2 + sq
 #align real.cos_pi_div_thirty_two Real.cos_pi_div_thirty_two
 
 @[simp]
-theorem sin_pi_div_thirty_two : sin (π / 32) = sqrt (2 - sqrt (2 + sqrt (2 + sqrt 2))) / 2 := by
+theorem sin_pi_div_thirty_two : sin (π / 32) = √(2 - √(2 + √(2 + √2))) / 2 := by
   trans sin (π / 2 ^ 5)
   · congr
     norm_num
@@ -893,7 +893,7 @@ theorem cos_pi_div_three : cos (π / 3) = 1 / 2 := by
 
 /-- The cosine of `π / 6` is `√3 / 2`. -/
 @[simp]
-theorem cos_pi_div_six : cos (π / 6) = sqrt 3 / 2 := by
+theorem cos_pi_div_six : cos (π / 6) = √3 / 2 := by
   rw [show (6 : ℝ) = 3 * 2 by norm_num, div_mul_eq_div_div, cos_half, cos_pi_div_three, one_add_div,
     ← div_mul_eq_div_div, two_add_one_eq_three, sqrt_div, sqrt_mul_self] <;> linarith [pi_pos]
 #align real.cos_pi_div_six Real.cos_pi_div_six
@@ -922,7 +922,7 @@ theorem sq_sin_pi_div_three : sin (π / 3) ^ 2 = 3 / 4 := by
 
 /-- The sine of `π / 3` is `√3 / 2`. -/
 @[simp]
-theorem sin_pi_div_three : sin (π / 3) = sqrt 3 / 2 := by
+theorem sin_pi_div_three : sin (π / 3) = √3 / 2 := by
   rw [← cos_pi_div_two_sub, ← cos_pi_div_six]
   congr
   ring
@@ -947,7 +947,7 @@ theorem sinOrderIso_apply (x : Icc (-(π / 2)) (π / 2)) : sinOrderIso x = ⟨si
 @[simp]
 theorem tan_pi_div_four : tan (π / 4) = 1 := by
   rw [tan_eq_sin_div_cos, cos_pi_div_four, sin_pi_div_four]
-  have h : sqrt 2 / 2 > 0 := by cancel_denoms
+  have h : √2 / 2 > 0 := by positivity
   exact div_self (ne_of_gt h)
 #align real.tan_pi_div_four Real.tan_pi_div_four
 

Add @[simp] theorem negOnePow_two_mul_add_one to Algebra.GroupPower.NegOnePow, which states that (2 * n + 1).negOnePow = -1.

Add theorems to Algebra.Periodic about the value of f (x + n • c), f (x - n • c), and f (n • c - x), where we have Antiperiodic f c. All these theorems have variants for either n : ℕ or n : ℤ, and they also have variants using * instead of • if the domain and codomain of f are rings.

For all real numbers x and all integers n. deduce the following. All these theorems are in Analysis.SpecialFunctions.Trigonometric.Basic, they are not @[simp], and they have a variation (using the notation (-1) ^ n instead of n.negOnePow) for natural number n.

• sin (x + n * π) = n.negOnePow * sin x
• sin (x - n * π) = n.negOnePow * sin x
• sin (n * π - x) = -(n.negOnePow * sin x)
• cos (x + n * π) = n.negOnePow * cos x
• cos (x - n * π) = n.negOnePow * cos x
• cos (n * π - x) = n.negOnePow * cos x

@@ -5,6 +5,7 @@ Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin
 -/
 import Mathlib.Analysis.SpecialFunctions.Exp
 import Mathlib.Tactic.Positivity.Core
+import Mathlib.Algebra.GroupPower.NegOnePow
 
 #align_import analysis.special_functions.trigonometric.basic from "leanprover-community/mathlib"@"2c1d8ca2812b64f88992a5294ea3dba144755cd1"
 
@@ -247,7 +248,7 @@ theorem sin_antiperiodic : Function.Antiperiodic sin π := by simp [sin_add]
 #align real.sin_antiperiodic Real.sin_antiperiodic
 
 theorem sin_periodic : Function.Periodic sin (2 * π) :=
-  sin_antiperiodic.periodic
+  sin_antiperiodic.periodic_two_mul
 #align real.sin_periodic Real.sin_periodic
 
 @[simp]
@@ -320,11 +321,29 @@ theorem sin_int_mul_two_pi_sub (x : ℝ) (n : ℤ) : sin (n * (2 * π) - x) = -s
   sin_neg x ▸ sin_periodic.int_mul_sub_eq n
 #align real.sin_int_mul_two_pi_sub Real.sin_int_mul_two_pi_sub
 
+theorem sin_add_int_mul_pi (x : ℝ) (n : ℤ) : sin (x + n * π) = (-1) ^ n * sin x :=
+  n.coe_negOnePow ℝ ▸ sin_antiperiodic.add_int_mul_eq n
+
+theorem sin_add_nat_mul_pi (x : ℝ) (n : ℕ) : sin (x + n * π) = (-1) ^ n * sin x :=
+  sin_antiperiodic.add_nat_mul_eq n
+
+theorem sin_sub_int_mul_pi (x : ℝ) (n : ℤ) : sin (x - n * π) = (-1) ^ n * sin x :=
+  n.coe_negOnePow ℝ ▸ sin_antiperiodic.sub_int_mul_eq n
+
+theorem sin_sub_nat_mul_pi (x : ℝ) (n : ℕ) : sin (x - n * π) = (-1) ^ n * sin x :=
+  sin_antiperiodic.sub_nat_mul_eq n
+
+theorem sin_int_mul_pi_sub (x : ℝ) (n : ℤ) : sin (n * π - x) = -((-1) ^ n * sin x) := by
+  simpa only [sin_neg, mul_neg, Int.coe_negOnePow] using sin_antiperiodic.int_mul_sub_eq n
+
+theorem sin_nat_mul_pi_sub (x : ℝ) (n : ℕ) : sin (n * π - x) = -((-1) ^ n * sin x) := by
+  simpa only [sin_neg, mul_neg] using sin_antiperiodic.nat_mul_sub_eq n
+
 theorem cos_antiperiodic : Function.Antiperiodic cos π := by simp [cos_add]
 #align real.cos_antiperiodic Real.cos_antiperiodic
 
 theorem cos_periodic : Function.Periodic cos (2 * π) :=
-  cos_antiperiodic.periodic
+  cos_antiperiodic.periodic_two_mul
 #align real.cos_periodic Real.cos_periodic
 
 @[simp]
@@ -397,6 +416,24 @@ theorem cos_int_mul_two_pi_sub (x : ℝ) (n : ℤ) : cos (n * (2 * π) - x) = co
   cos_neg x ▸ cos_periodic.int_mul_sub_eq n
 #align real.cos_int_mul_two_pi_sub Real.cos_int_mul_two_pi_sub
 
+theorem cos_add_int_mul_pi (x : ℝ) (n : ℤ) : cos (x + n * π) = (-1) ^ n * cos x :=
+  n.coe_negOnePow ℝ ▸ cos_antiperiodic.add_int_mul_eq n
+
+theorem cos_add_nat_mul_pi (x : ℝ) (n : ℕ) : cos (x + n * π) = (-1) ^ n * cos x :=
+  cos_antiperiodic.add_nat_mul_eq n
+
+theorem cos_sub_int_mul_pi (x : ℝ) (n : ℤ) : cos (x - n * π) = (-1) ^ n * cos x :=
+  n.coe_negOnePow ℝ ▸ cos_antiperiodic.sub_int_mul_eq n
+
+theorem cos_sub_nat_mul_pi (x : ℝ) (n : ℕ) : cos (x - n * π) = (-1) ^ n * cos x :=
+  cos_antiperiodic.sub_nat_mul_eq n
+
+theorem cos_int_mul_pi_sub (x : ℝ) (n : ℤ) : cos (n * π - x) = (-1) ^ n * cos x :=
+  n.coe_negOnePow ℝ ▸ cos_neg x ▸ cos_antiperiodic.int_mul_sub_eq n
+
+theorem cos_nat_mul_pi_sub (x : ℝ) (n : ℕ) : cos (n * π - x) = (-1) ^ n * cos x :=
+  cos_neg x ▸ cos_antiperiodic.nat_mul_sub_eq n
+
 -- Porting note (#10618): was @[simp], but simp can prove it
 theorem cos_nat_mul_two_pi_add_pi (n : ℕ) : cos (n * (2 * π) + π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.nat_mul n).add_antiperiod_eq cos_antiperiodic
@@ -1114,7 +1151,7 @@ theorem sin_antiperiodic : Function.Antiperiodic sin π := by simp [sin_add]
 #align complex.sin_antiperiodic Complex.sin_antiperiodic
 
 theorem sin_periodic : Function.Periodic sin (2 * π) :=
-  sin_antiperiodic.periodic
+  sin_antiperiodic.periodic_two_mul
 #align complex.sin_periodic Complex.sin_periodic
 
 theorem sin_add_pi (x : ℂ) : sin (x + π) = -sin x :=
@@ -1177,7 +1214,7 @@ theorem cos_antiperiodic : Function.Antiperiodic cos π := by simp [cos_add]
 #align complex.cos_antiperiodic Complex.cos_antiperiodic
 
 theorem cos_periodic : Function.Periodic cos (2 * π) :=
-  cos_antiperiodic.periodic
+  cos_antiperiodic.periodic_two_mul
 #align complex.cos_periodic Complex.cos_periodic
 
 theorem cos_add_pi (x : ℂ) : cos (x + π) = -cos x :=
@@ -1327,7 +1364,7 @@ theorem exp_antiperiodic : Function.Antiperiodic exp (π * I) := by simp [exp_ad
 #align complex.exp_antiperiodic Complex.exp_antiperiodic
 
 theorem exp_periodic : Function.Periodic exp (2 * π * I) :=
-  (mul_assoc (2 : ℂ) π I).symm ▸ exp_antiperiodic.periodic
+  (mul_assoc (2 : ℂ) π I).symm ▸ exp_antiperiodic.periodic_two_mul
 #align complex.exp_periodic Complex.exp_periodic
 
 theorem exp_mul_I_antiperiodic : Function.Antiperiodic (fun x => exp (x * I)) π := by
@@ -1336,7 +1373,7 @@ set_option linter.uppercaseLean3 false in
 #align complex.exp_mul_I_antiperiodic Complex.exp_mul_I_antiperiodic
 
 theorem exp_mul_I_periodic : Function.Periodic (fun x => exp (x * I)) (2 * π) :=
-  exp_mul_I_antiperiodic.periodic
+  exp_mul_I_antiperiodic.periodic_two_mul
 set_option linter.uppercaseLean3 false in
 #align complex.exp_mul_I_periodic Complex.exp_mul_I_periodic
 

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

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

where the latter is more natural

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

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

but it seems to no longer apply.

Remarks on the PR :

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

@@ -742,7 +742,7 @@ theorem cos_pi_over_two_pow : ∀ n : ℕ, cos (π / 2 ^ (n + 1)) = sqrtTwoAddSe
     have A : (1 : ℝ) < 2 ^ (n + 1) := one_lt_pow one_lt_two n.succ_ne_zero
     have B : π / 2 ^ (n + 1) < π := div_lt_self pi_pos A
     have C : 0 < π / 2 ^ (n + 1) := by positivity
-    rw [pow_succ', div_mul_eq_div_div, cos_half, cos_pi_over_two_pow n, sqrtTwoAddSeries,
+    rw [pow_succ, div_mul_eq_div_div, cos_half, cos_pi_over_two_pow n, sqrtTwoAddSeries,
       add_div_eq_mul_add_div, one_mul, ← div_mul_eq_div_div, sqrt_div, sqrt_mul_self] <;>
       linarith [sqrtTwoAddSeries_nonneg le_rfl n]
 #align real.cos_pi_over_two_pow Real.cos_pi_over_two_pow

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 | |

@@ -135,17 +135,17 @@ scoped notation "π" => Real.pi
 
 @[simp]
 theorem cos_pi_div_two : cos (π / 2) = 0 := by
-  rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)]
+  rw [Real.pi, mul_div_cancel_left₀ _ (two_ne_zero' ℝ)]
   exact (Classical.choose_spec exists_cos_eq_zero).2
 #align real.cos_pi_div_two Real.cos_pi_div_two
 
 theorem one_le_pi_div_two : (1 : ℝ) ≤ π / 2 := by
-  rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)]
+  rw [Real.pi, mul_div_cancel_left₀ _ (two_ne_zero' ℝ)]
   exact (Classical.choose_spec exists_cos_eq_zero).1.1
 #align real.one_le_pi_div_two Real.one_le_pi_div_two
 
 theorem pi_div_two_le_two : π / 2 ≤ 2 := by
-  rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)]
+  rw [Real.pi, mul_div_cancel_left₀ _ (two_ne_zero' ℝ)]
   exact (Classical.choose_spec exists_cos_eq_zero).1.2
 #align real.pi_div_two_le_two Real.pi_div_two_le_two
 
@@ -226,12 +226,12 @@ open Real
 
 @[simp]
 theorem sin_pi : sin π = 0 := by
-  rw [← mul_div_cancel_left π (two_ne_zero' ℝ), two_mul, add_div, sin_add, cos_pi_div_two]; simp
+  rw [← mul_div_cancel_left₀ π (two_ne_zero' ℝ), two_mul, add_div, sin_add, cos_pi_div_two]; simp
 #align real.sin_pi Real.sin_pi
 
 @[simp]
 theorem cos_pi : cos π = -1 := by
-  rw [← mul_div_cancel_left π (two_ne_zero' ℝ), mul_div_assoc, cos_two_mul, cos_pi_div_two]
+  rw [← mul_div_cancel_left₀ π (two_ne_zero' ℝ), mul_div_assoc, cos_two_mul, cos_pi_div_two]
   norm_num
 #align real.cos_pi Real.cos_pi
 

Classifies by adding issue number #11432 to porting notes claiming "added theorem" or "added lemma".

@@ -979,7 +979,7 @@ theorem tan_periodic : Function.Periodic tan π := by
   simpa only [Function.Periodic, tan_eq_sin_div_cos] using sin_antiperiodic.div cos_antiperiodic
 #align real.tan_periodic Real.tan_periodic
 
--- Porting note: added
+-- Porting note (#10756): added theorem
 @[simp]
 theorem tan_pi : tan π = 0 := by rw [tan_periodic.eq, tan_zero]
 

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.

@@ -44,7 +44,8 @@ sin, cos, tan, angle
 
 noncomputable section
 
-open Classical Topology Filter Set
+open scoped Classical
+open Topology Filter Set
 
 namespace Complex
 

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

@@ -578,7 +578,7 @@ theorem cos_eq_one_iff_of_lt_of_lt {x : ℝ} (hx₁ : -(2 * π) < x) (hx₂ : x
     rw [mul_lt_iff_lt_one_left two_pi_pos] at hx₂
     rw [neg_lt, neg_mul_eq_neg_mul, mul_lt_iff_lt_one_left two_pi_pos] at hx₁
     norm_cast at hx₁ hx₂
-    obtain rfl : n = 0 := le_antisymm (by linarith) (by linarith)
+    obtain rfl : n = 0 := le_antisymm (by omega) (by omega)
     simp, fun h => by simp [h]⟩
 #align real.cos_eq_one_iff_of_lt_of_lt Real.cos_eq_one_iff_of_lt_of_lt
 

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to

• "simp can prove this"
• "simp can simplify this`"
• "was @[simp], now can be proved by simp"
• "was @[simp], but simp can prove it"
• "removed simp attribute as the equality can already be obtained by simp"
• "simp can already prove this"
• "simp already proves this"
• "simp can prove these"

@@ -396,22 +396,22 @@ theorem cos_int_mul_two_pi_sub (x : ℝ) (n : ℤ) : cos (n * (2 * π) - x) = co
   cos_neg x ▸ cos_periodic.int_mul_sub_eq n
 #align real.cos_int_mul_two_pi_sub Real.cos_int_mul_two_pi_sub
 
--- Porting note: was @[simp] but simp can prove it
+-- Porting note (#10618): was @[simp], but simp can prove it
 theorem cos_nat_mul_two_pi_add_pi (n : ℕ) : cos (n * (2 * π) + π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.nat_mul n).add_antiperiod_eq cos_antiperiodic
 #align real.cos_nat_mul_two_pi_add_pi Real.cos_nat_mul_two_pi_add_pi
 
--- Porting note: was @[simp] but simp can prove it
+-- Porting note (#10618): was @[simp], but simp can prove it
 theorem cos_int_mul_two_pi_add_pi (n : ℤ) : cos (n * (2 * π) + π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.int_mul n).add_antiperiod_eq cos_antiperiodic
 #align real.cos_int_mul_two_pi_add_pi Real.cos_int_mul_two_pi_add_pi
 
--- Porting note: was @[simp] but simp can prove it
+-- Porting note (#10618): was @[simp], but simp can prove it
 theorem cos_nat_mul_two_pi_sub_pi (n : ℕ) : cos (n * (2 * π) - π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.nat_mul n).sub_antiperiod_eq cos_antiperiodic
 #align real.cos_nat_mul_two_pi_sub_pi Real.cos_nat_mul_two_pi_sub_pi
 
--- Porting note: was @[simp] but simp can prove it
+-- Porting note (#10618): was @[simp], but simp can prove it
 theorem cos_int_mul_two_pi_sub_pi (n : ℤ) : cos (n * (2 * π) - π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.int_mul n).sub_antiperiod_eq cos_antiperiodic
 #align real.cos_int_mul_two_pi_sub_pi Real.cos_int_mul_two_pi_sub_pi

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

@@ -396,22 +396,22 @@ theorem cos_int_mul_two_pi_sub (x : ℝ) (n : ℤ) : cos (n * (2 * π) - x) = co
   cos_neg x ▸ cos_periodic.int_mul_sub_eq n
 #align real.cos_int_mul_two_pi_sub Real.cos_int_mul_two_pi_sub
 
--- porting note : was @[simp] but simp can prove it
+-- Porting note: was @[simp] but simp can prove it
 theorem cos_nat_mul_two_pi_add_pi (n : ℕ) : cos (n * (2 * π) + π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.nat_mul n).add_antiperiod_eq cos_antiperiodic
 #align real.cos_nat_mul_two_pi_add_pi Real.cos_nat_mul_two_pi_add_pi
 
--- porting note : was @[simp] but simp can prove it
+-- Porting note: was @[simp] but simp can prove it
 theorem cos_int_mul_two_pi_add_pi (n : ℤ) : cos (n * (2 * π) + π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.int_mul n).add_antiperiod_eq cos_antiperiodic
 #align real.cos_int_mul_two_pi_add_pi Real.cos_int_mul_two_pi_add_pi
 
--- porting note : was @[simp] but simp can prove it
+-- Porting note: was @[simp] but simp can prove it
 theorem cos_nat_mul_two_pi_sub_pi (n : ℕ) : cos (n * (2 * π) - π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.nat_mul n).sub_antiperiod_eq cos_antiperiodic
 #align real.cos_nat_mul_two_pi_sub_pi Real.cos_nat_mul_two_pi_sub_pi
 
--- porting note : was @[simp] but simp can prove it
+-- Porting note: was @[simp] but simp can prove it
 theorem cos_int_mul_two_pi_sub_pi (n : ℤ) : cos (n * (2 * π) - π) = -1 := by
   simpa only [cos_zero] using (cos_periodic.int_mul n).sub_antiperiod_eq cos_antiperiodic
 #align real.cos_int_mul_two_pi_sub_pi Real.cos_int_mul_two_pi_sub_pi

I think if Real.exp_nonneg exists as a separate lemma, Real.pi_nonneg is reasonable. And it's useful as a separate lemma for Aesop purposes too.

@@ -164,8 +164,11 @@ theorem pi_pos : 0 < π :=
   lt_of_lt_of_le (by norm_num) two_le_pi
 #align real.pi_pos Real.pi_pos
 
+theorem pi_nonneg : 0 ≤ π :=
+  pi_pos.le
+
 theorem pi_ne_zero : π ≠ 0 :=
-  ne_of_gt pi_pos
+  pi_pos.ne'
 #align real.pi_ne_zero Real.pi_ne_zero
 
 theorem pi_div_two_pos : 0 < π / 2 :=

four_mul_arctan_inv_5_sub_arctan_inv_239 is theorem 1 in my own #6091.

@@ -914,6 +914,16 @@ theorem tan_pi_div_four : tan (π / 4) = 1 := by
 theorem tan_pi_div_two : tan (π / 2) = 0 := by simp [tan_eq_sin_div_cos]
 #align real.tan_pi_div_two Real.tan_pi_div_two
 
+@[simp]
+theorem tan_pi_div_six : tan (π / 6) = 1 / sqrt 3 := by
+  rw [tan_eq_sin_div_cos, sin_pi_div_six, cos_pi_div_six]
+  ring
+
+@[simp]
+theorem tan_pi_div_three : tan (π / 3) = sqrt 3 := by
+  rw [tan_eq_sin_div_cos, sin_pi_div_three, cos_pi_div_three]
+  ring
+
 theorem tan_pos_of_pos_of_lt_pi_div_two {x : ℝ} (h0x : 0 < x) (hxp : x < π / 2) : 0 < tan x := by
   rw [tan_eq_sin_div_cos]
   exact div_pos (sin_pos_of_pos_of_lt_pi h0x (by linarith)) (cos_pos_of_mem_Ioo ⟨by linarith, hxp⟩)

The previous code often discarded the safety features of Qq by casting quoted terms to Expr and back. This is far from an exhaustive replacement.

This makes use of a bug fix in Lean 4.6.0rc1 that allows us to write things like

match u, α, e with
| 0, ~q(ℤ), ~q([@Int](https://github.com/Int).floor $α' $i $j $a) =>

Previously these matches did not generalize u correctly.

To make Qq happy, we introduce a few more assertInstancesCommute that were not previously here. Without them, there is a higher risk that positivity produces an ill-typed proof in weird situations. Like every assertInstancesCommute, this comes at a small performance cost that could be eliminated by using the unsafe assumeInstancesCommute instead.

Another very small performance hit here is from the (possibly unnecessary) defeq check of the types before checking defeq of the values. On the other hand, this might actually increase performance when the match fails due to a type mismatch.

There is probably some boilerplate that can be extracted from the repetition here; but I am declaring that out of scope for this PR: the goal is to establish a canonical spelling for this sort of matching, so that future extensions copy-pasted from these extensions inherit the spelling automatically.

@@ -182,8 +182,12 @@ open Lean.Meta Qq
 
 /-- Extension for the `positivity` tactic: `π` is always positive. -/
 @[positivity Real.pi]
-def evalRealPi : PositivityExt where eval {_ _} _ _ _ := do
-  pure (.positive (q(Real.pi_pos) : Lean.Expr))
+def evalRealPi : PositivityExt where eval {u α} _zα _pα e := do
+  match u, α, e with
+  | 0, ~q(ℝ), ~q(Real.pi) =>
+    assertInstancesCommute
+    pure (.positive q(Real.pi_pos))
+  | _, _, _ => throwError "not Real.pi"
 
 end Mathlib.Meta.Positivity
 

@@ -182,7 +182,7 @@ open Lean.Meta Qq
 
 /-- Extension for the `positivity` tactic: `π` is always positive. -/
 @[positivity Real.pi]
-def evalRealPi : Mathlib.Meta.Positivity.PositivityExt where eval {_ _} _ _ _ := do
+def evalRealPi : PositivityExt where eval {_ _} _ _ _ := do
   pure (.positive (q(Real.pi_pos) : Lean.Expr))
 
 end Mathlib.Meta.Positivity

@@ -575,36 +575,29 @@ theorem cos_eq_one_iff_of_lt_of_lt {x : ℝ} (hx₁ : -(2 * π) < x) (hx₂ : x
     simp, fun h => by simp [h]⟩
 #align real.cos_eq_one_iff_of_lt_of_lt Real.cos_eq_one_iff_of_lt_of_lt
 
-theorem cos_lt_cos_of_nonneg_of_le_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y ≤ π / 2)
-    (hxy : x < y) : cos y < cos x := by
-  rw [← sub_lt_zero, cos_sub_cos]
-  have : 0 < sin ((y + x) / 2) := by refine' sin_pos_of_pos_of_lt_pi _ _ <;> linarith
-  have : 0 < sin ((y - x) / 2) := by refine' sin_pos_of_pos_of_lt_pi _ _ <;> linarith
-  nlinarith
-#align real.cos_lt_cos_of_nonneg_of_le_pi_div_two Real.cos_lt_cos_of_nonneg_of_le_pi_div_two
+theorem sin_lt_sin_of_lt_of_le_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) ≤ x) (hy₂ : y ≤ π / 2)
+    (hxy : x < y) : sin x < sin y := by
+  rw [← sub_pos, sin_sub_sin]
+  have : 0 < sin ((y - x) / 2) := by apply sin_pos_of_pos_of_lt_pi <;> linarith
+  have : 0 < cos ((y + x) / 2) := by refine cos_pos_of_mem_Ioo ⟨?_, ?_⟩ <;> linarith
+  positivity
+#align real.sin_lt_sin_of_lt_of_le_pi_div_two Real.sin_lt_sin_of_lt_of_le_pi_div_two
+
+theorem strictMonoOn_sin : StrictMonoOn sin (Icc (-(π / 2)) (π / 2)) := fun _ hx _ hy hxy =>
+  sin_lt_sin_of_lt_of_le_pi_div_two hx.1 hy.2 hxy
+#align real.strict_mono_on_sin Real.strictMonoOn_sin
 
 theorem cos_lt_cos_of_nonneg_of_le_pi {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y ≤ π) (hxy : x < y) :
-    cos y < cos x :=
-  match (le_total x (π / 2) : x ≤ π / 2 ∨ π / 2 ≤ x), le_total y (π / 2) with
-  | Or.inl _, Or.inl hy => cos_lt_cos_of_nonneg_of_le_pi_div_two hx₁ hy hxy
-  | Or.inl hx, Or.inr hy =>
-    (lt_or_eq_of_le hx).elim
-      (fun hx =>
-        calc
-          cos y ≤ 0 := cos_nonpos_of_pi_div_two_le_of_le hy (by linarith [pi_pos])
-          _ < cos x := cos_pos_of_mem_Ioo ⟨by linarith, hx⟩)
-      fun hx =>
-      calc
-        cos y < 0 := cos_neg_of_pi_div_two_lt_of_lt (by linarith) (by linarith [pi_pos])
-        _ = cos x := by rw [hx, cos_pi_div_two]
-  | Or.inr hx, Or.inl hy => by linarith
-  | Or.inr hx, Or.inr hy =>
-    neg_lt_neg_iff.1
-      (by
-        rw [← cos_pi_sub, ← cos_pi_sub]; apply cos_lt_cos_of_nonneg_of_le_pi_div_two <;>
-          linarith)
+    cos y < cos x := by
+  rw [← sin_pi_div_two_sub, ← sin_pi_div_two_sub]
+  apply sin_lt_sin_of_lt_of_le_pi_div_two <;> linarith
 #align real.cos_lt_cos_of_nonneg_of_le_pi Real.cos_lt_cos_of_nonneg_of_le_pi
 
+theorem cos_lt_cos_of_nonneg_of_le_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y ≤ π / 2)
+    (hxy : x < y) : cos y < cos x :=
+  cos_lt_cos_of_nonneg_of_le_pi hx₁ (hy₂.trans (by linarith)) hxy
+#align real.cos_lt_cos_of_nonneg_of_le_pi_div_two Real.cos_lt_cos_of_nonneg_of_le_pi_div_two
+
 theorem strictAntiOn_cos : StrictAntiOn cos (Icc 0 π) := fun _ hx _ hy hxy =>
   cos_lt_cos_of_nonneg_of_le_pi hx.1 hy.2 hxy
 #align real.strict_anti_on_cos Real.strictAntiOn_cos
@@ -614,16 +607,6 @@ theorem cos_le_cos_of_nonneg_of_le_pi {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y 
   (strictAntiOn_cos.le_iff_le ⟨hx₁.trans hxy, hy₂⟩ ⟨hx₁, hxy.trans hy₂⟩).2 hxy
 #align real.cos_le_cos_of_nonneg_of_le_pi Real.cos_le_cos_of_nonneg_of_le_pi
 
-theorem sin_lt_sin_of_lt_of_le_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) ≤ x) (hy₂ : y ≤ π / 2)
-    (hxy : x < y) : sin x < sin y := by
-  rw [← cos_sub_pi_div_two, ← cos_sub_pi_div_two, ← cos_neg (x - _), ← cos_neg (y - _)]
-  apply cos_lt_cos_of_nonneg_of_le_pi <;> linarith
-#align real.sin_lt_sin_of_lt_of_le_pi_div_two Real.sin_lt_sin_of_lt_of_le_pi_div_two
-
-theorem strictMonoOn_sin : StrictMonoOn sin (Icc (-(π / 2)) (π / 2)) := fun _ hx _ hy hxy =>
-  sin_lt_sin_of_lt_of_le_pi_div_two hx.1 hy.2 hxy
-#align real.strict_mono_on_sin Real.strictMonoOn_sin
-
 theorem sin_le_sin_of_le_of_le_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) ≤ x) (hy₂ : y ≤ π / 2)
     (hxy : x ≤ y) : sin x ≤ sin y :=
   (strictMonoOn_sin.le_iff_le ⟨hx₁, hxy.trans hy₂⟩ ⟨hx₁.trans hxy, hy₂⟩).2 hxy
@@ -948,38 +931,22 @@ theorem tan_nonpos_of_nonpos_of_neg_pi_div_two_le {x : ℝ} (hx0 : x ≤ 0) (hpx
   neg_nonneg.1 (tan_neg x ▸ tan_nonneg_of_nonneg_of_le_pi_div_two (by linarith) (by linarith))
 #align real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le Real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le
 
-theorem tan_lt_tan_of_nonneg_of_lt_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y < π / 2)
-    (hxy : x < y) : tan x < tan y := by
-  rw [tan_eq_sin_div_cos, tan_eq_sin_div_cos]
-  exact
-    div_lt_div (sin_lt_sin_of_lt_of_le_pi_div_two (by linarith) (le_of_lt hy₂) hxy)
-      (cos_le_cos_of_nonneg_of_le_pi hx₁ (by linarith) (le_of_lt hxy))
-      (sin_nonneg_of_nonneg_of_le_pi (by linarith) (by linarith))
-      (cos_pos_of_mem_Ioo ⟨by linarith, hy₂⟩)
-#align real.tan_lt_tan_of_nonneg_of_lt_pi_div_two Real.tan_lt_tan_of_nonneg_of_lt_pi_div_two
+theorem strictMonoOn_tan : StrictMonoOn tan (Ioo (-(π / 2)) (π / 2)) := by
+  rintro x hx y hy hlt
+  rw [tan_eq_sin_div_cos, tan_eq_sin_div_cos,
+    div_lt_div_iff (cos_pos_of_mem_Ioo hx) (cos_pos_of_mem_Ioo hy), mul_comm, ← sub_pos, ← sin_sub]
+  exact sin_pos_of_pos_of_lt_pi (sub_pos.2 hlt) <| by linarith [hx.1, hy.2]
+#align real.strict_mono_on_tan Real.strictMonoOn_tan
 
 theorem tan_lt_tan_of_lt_of_lt_pi_div_two {x y : ℝ} (hx₁ : -(π / 2) < x) (hy₂ : y < π / 2)
     (hxy : x < y) : tan x < tan y :=
-  match le_total x 0, le_total y 0 with
-  | Or.inl hx0, Or.inl hy0 =>
-    neg_lt_neg_iff.1 <| by
-      rw [← tan_neg, ← tan_neg]
-      exact tan_lt_tan_of_nonneg_of_lt_pi_div_two (neg_nonneg.2 hy0) (neg_lt.2 hx₁) (neg_lt_neg hxy)
-  | Or.inl hx0, Or.inr hy0 =>
-    (lt_or_eq_of_le hy0).elim
-      (fun hy0 =>
-        calc
-          tan x ≤ 0 := tan_nonpos_of_nonpos_of_neg_pi_div_two_le hx0 (le_of_lt hx₁)
-          _ < tan y := tan_pos_of_pos_of_lt_pi_div_two hy0 hy₂)
-      fun hy0 => by
-      rw [← hy0, tan_zero]; exact tan_neg_of_neg_of_pi_div_two_lt (hy0.symm ▸ hxy) hx₁
-  | Or.inr hx0, Or.inl hy0 => by linarith
-  | Or.inr hx0, Or.inr _ => tan_lt_tan_of_nonneg_of_lt_pi_div_two hx0 hy₂ hxy
+  strictMonoOn_tan ⟨hx₁, hxy.trans hy₂⟩ ⟨hx₁.trans hxy, hy₂⟩ hxy
 #align real.tan_lt_tan_of_lt_of_lt_pi_div_two Real.tan_lt_tan_of_lt_of_lt_pi_div_two
 
-theorem strictMonoOn_tan : StrictMonoOn tan (Ioo (-(π / 2)) (π / 2)) := fun _ hx _ hy =>
-  tan_lt_tan_of_lt_of_lt_pi_div_two hx.1 hy.2
-#align real.strict_mono_on_tan Real.strictMonoOn_tan
+theorem tan_lt_tan_of_nonneg_of_lt_pi_div_two {x y : ℝ} (hx₁ : 0 ≤ x) (hy₂ : y < π / 2)
+    (hxy : x < y) : tan x < tan y :=
+  tan_lt_tan_of_lt_of_lt_pi_div_two (by linarith) hy₂ hxy
+#align real.tan_lt_tan_of_nonneg_of_lt_pi_div_two Real.tan_lt_tan_of_nonneg_of_lt_pi_div_two
 
 theorem injOn_tan : InjOn tan (Ioo (-(π / 2)) (π / 2)) :=
   strictMonoOn_tan.injOn

and rename ofReal_mul_re → re_mul_ofReal, ofReal_mul_im → im_mul_ofReal.

From LeanAPAP

@@ -1398,7 +1398,7 @@ $$\left|exp^{a\left(e^{z}+e^{-z}\right)}\right| \le e^{a\cos b \exp^{|re z|}}.$$
 theorem abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le {a b : ℝ} (ha : a ≤ 0) {z : ℂ} (hz : |z.im| ≤ b)
     (hb : b ≤ π / 2) :
     abs (exp (a * (exp z + exp (-z)))) ≤ Real.exp (a * Real.cos b * Real.exp |z.re|) := by
-  simp only [abs_exp, Real.exp_le_exp, ofReal_mul_re, add_re, exp_re, neg_im, Real.cos_neg, ←
+  simp only [abs_exp, Real.exp_le_exp, re_ofReal_mul, add_re, exp_re, neg_im, Real.cos_neg, ←
     add_mul, mul_assoc, mul_comm (Real.cos b), neg_re, ← Real.cos_abs z.im]
   have : Real.exp |z.re| ≤ Real.exp z.re + Real.exp (-z.re) :=
     apply_abs_le_add_of_nonneg (fun x => (Real.exp_pos x).le) z.re

Also fix the name of Real.Mathlib.Meta.Positivity.evalExp to Mathlib.Meta.Positivity.evalRealPi.

@@ -164,17 +164,6 @@ theorem pi_pos : 0 < π :=
   lt_of_lt_of_le (by norm_num) two_le_pi
 #align real.pi_pos Real.pi_pos
 
-namespace Mathlib.Meta.Positivity
-open Lean.Meta Qq
-
-/-- Extension for the `positivity` tactic: `π` is always positive. -/
-@[positivity π]
-def evalExp : Mathlib.Meta.Positivity.PositivityExt where eval {_ _} _ _ _ := do
-  pure (.positive (q(Real.pi_pos) : Lean.Expr))
-
-end Mathlib.Meta.Positivity
-
-
 theorem pi_ne_zero : π ≠ 0 :=
   ne_of_gt pi_pos
 #align real.pi_ne_zero Real.pi_ne_zero
@@ -188,6 +177,16 @@ theorem two_pi_pos : 0 < 2 * π := by linarith [pi_pos]
 
 end Real
 
+namespace Mathlib.Meta.Positivity
+open Lean.Meta Qq
+
+/-- Extension for the `positivity` tactic: `π` is always positive. -/
+@[positivity Real.pi]
+def evalRealPi : Mathlib.Meta.Positivity.PositivityExt where eval {_ _} _ _ _ := do
+  pure (.positive (q(Real.pi_pos) : Lean.Expr))
+
+end Mathlib.Meta.Positivity
+
 namespace NNReal
 
 open Real

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>

@@ -204,7 +204,7 @@ theorem coe_real_pi : (pi : ℝ) = π :=
   rfl
 #align nnreal.coe_real_pi NNReal.coe_real_pi
 
-theorem pi_pos : 0 < pi := by exact_mod_cast Real.pi_pos
+theorem pi_pos : 0 < pi := mod_cast Real.pi_pos
 #align nnreal.pi_pos NNReal.pi_pos
 
 theorem pi_ne_zero : pi ≠ 0 :=

Also add formula for cos (x / 2), sin (x / 2) and golf some proofs.

@@ -503,6 +503,23 @@ theorem cos_eq_sqrt_one_sub_sin_sq {x : ℝ} (hl : -(π / 2) ≤ x) (hu : x ≤
   rw [← abs_cos_eq_sqrt_one_sub_sin_sq, abs_of_nonneg (cos_nonneg_of_mem_Icc ⟨hl, hu⟩)]
 #align real.cos_eq_sqrt_one_sub_sin_sq Real.cos_eq_sqrt_one_sub_sin_sq
 
+lemma cos_half {x : ℝ} (hl : -π ≤ x) (hr : x ≤ π) : cos (x / 2) = sqrt ((1 + cos x) / 2) := by
+  have : 0 ≤ cos (x / 2) := cos_nonneg_of_mem_Icc <| by constructor <;> linarith
+  rw [← sqrt_sq this, cos_sq, add_div, two_mul, add_halves]
+
+lemma abs_sin_half (x : ℝ) : |sin (x / 2)| = sqrt ((1 - cos x) / 2) := by
+  rw [← sqrt_sq_eq_abs, sin_sq_eq_half_sub, two_mul, add_halves, sub_div]
+
+lemma sin_half_eq_sqrt {x : ℝ} (hl : 0 ≤ x) (hr : x ≤ 2 * π) :
+    sin (x / 2) = sqrt ((1 - cos x) / 2) := by
+  rw [← abs_sin_half, abs_of_nonneg]
+  apply sin_nonneg_of_nonneg_of_le_pi <;> linarith
+
+lemma sin_half_eq_neg_sqrt {x : ℝ} (hl : -(2 * π) ≤ x) (hr : x ≤ 0) :
+    sin (x / 2) = -sqrt ((1 - cos x) / 2) := by
+  rw [← abs_sin_half, abs_of_nonpos, neg_neg]
+  apply sin_nonpos_of_nonnpos_of_neg_pi_le <;> linarith
+
 theorem sin_eq_zero_iff_of_lt_of_lt {x : ℝ} (hx₁ : -π < x) (hx₂ : x < π) : sin x = 0 ↔ x = 0 :=
   ⟨fun h => by
     contrapose! h
@@ -732,24 +749,12 @@ theorem sqrtTwoAddSeries_monotone_left {x y : ℝ} (h : x ≤ y) :
 theorem cos_pi_over_two_pow : ∀ n : ℕ, cos (π / 2 ^ (n + 1)) = sqrtTwoAddSeries 0 n / 2
   | 0 => by simp
   | n + 1 => by
-    have : (2 : ℝ) ≠ 0 := two_ne_zero
-    rw [eq_div_iff_mul_eq this, eq_comm, sqrtTwoAddSeries, sqrt_eq_iff_sq_eq, mul_pow, cos_sq,
-      ← mul_div_assoc, pow_succ, mul_div_mul_left _ _ this, cos_pi_over_two_pow _, add_mul]
-    · congr
-      · norm_num
-      · rw [mul_comm, sq, mul_assoc, ← mul_div_assoc, mul_div_cancel_left _ this, ← mul_div_assoc,
-          mul_div_cancel_left _ this]
-    · exact add_nonneg two_pos.le (sqrtTwoAddSeries_zero_nonneg _)
-    refine le_of_lt <| mul_pos (cos_pos_of_mem_Ioo ⟨?_, ?_⟩) two_pos
-    · trans (0 : ℝ)
-      · rw [neg_lt_zero]
-        exact pi_div_two_pos
-      · exact div_pos pi_pos <| pow_pos two_pos _
-    apply div_lt_div' (le_refl π) _ pi_pos two_pos
-    refine' lt_of_le_of_lt (le_of_eq (pow_one _).symm) _
-    apply pow_lt_pow
-    · norm_num
-    · exact Nat.succ_lt_succ n.succ_pos
+    have A : (1 : ℝ) < 2 ^ (n + 1) := one_lt_pow one_lt_two n.succ_ne_zero
+    have B : π / 2 ^ (n + 1) < π := div_lt_self pi_pos A
+    have C : 0 < π / 2 ^ (n + 1) := by positivity
+    rw [pow_succ', div_mul_eq_div_div, cos_half, cos_pi_over_two_pow n, sqrtTwoAddSeries,
+      add_div_eq_mul_add_div, one_mul, ← div_mul_eq_div_div, sqrt_div, sqrt_mul_self] <;>
+      linarith [sqrtTwoAddSeries_nonneg le_rfl n]
 #align real.cos_pi_over_two_pow Real.cos_pi_over_two_pow
 
 theorem sin_sq_pi_over_two_pow (n : ℕ) :
@@ -774,14 +779,9 @@ theorem sin_pi_over_two_pow_succ (n : ℕ) :
   · congr <;> norm_num
   · rw [sub_nonneg]
     exact (sqrtTwoAddSeries_lt_two _).le
-  refine le_of_lt <| mul_pos (sin_pos_of_pos_of_lt_pi ?_ ?_) two_pos
-  · exact div_pos pi_pos <| pow_pos two_pos _
-  refine' lt_of_lt_of_le _ (le_of_eq (div_one _))
-  rw [div_lt_div_left pi_pos (pow_pos two_pos _) one_pos]
-  refine' lt_of_le_of_lt (le_of_eq (pow_zero 2).symm) _
-  apply pow_lt_pow
-  · norm_num
-  · apply Nat.succ_pos
+  refine mul_nonneg (sin_nonneg_of_nonneg_of_le_pi ?_ ?_) zero_le_two
+  · positivity
+  · exact div_le_self pi_pos.le <| one_le_pow_of_one_le one_le_two _
 #align real.sin_pi_over_two_pow_succ Real.sin_pi_over_two_pow_succ
 
 @[simp]
@@ -864,33 +864,19 @@ theorem cos_pi_div_three : cos (π / 3) = 1 / 2 := by
     linarith [cos_pi]
 #align real.cos_pi_div_three Real.cos_pi_div_three
 
-/-- The square of the cosine of `π / 6` is `3 / 4` (this is sometimes more convenient than the
-result for cosine itself). -/
-theorem sq_cos_pi_div_six : cos (π / 6) ^ 2 = 3 / 4 := by
-  have h1 : cos (π / 6) ^ 2 = 1 / 2 + 1 / 2 / 2 := by
-    convert cos_sq (π / 6) using 3
-    have h2 : 2 * (π / 6) = π / 3 := by linarith
-    rw [h2, cos_pi_div_three]
-  rw [← sub_eq_zero] at h1 ⊢
-  convert h1 using 1
-  ring
-#align real.sq_cos_pi_div_six Real.sq_cos_pi_div_six
-
 /-- The cosine of `π / 6` is `√3 / 2`. -/
 @[simp]
 theorem cos_pi_div_six : cos (π / 6) = sqrt 3 / 2 := by
-  suffices sqrt 3 = cos (π / 6) * 2 by
-    field_simp [(by norm_num : 0 ≠ 2), ← this]
-  rw [sqrt_eq_iff_sq_eq]
-  · have h1 := (mul_right_inj' (by norm_num : (4 : ℝ) ≠ 0)).mpr sq_cos_pi_div_six
-    rw [← sub_eq_zero] at h1 ⊢
-    convert h1 using 1
-    ring
-  · norm_num
-  · have : 0 < cos (π / 6) := by apply cos_pos_of_mem_Ioo; constructor <;> linarith [pi_pos]
-    linarith
+  rw [show (6 : ℝ) = 3 * 2 by norm_num, div_mul_eq_div_div, cos_half, cos_pi_div_three, one_add_div,
+    ← div_mul_eq_div_div, two_add_one_eq_three, sqrt_div, sqrt_mul_self] <;> linarith [pi_pos]
 #align real.cos_pi_div_six Real.cos_pi_div_six
 
+/-- The square of the cosine of `π / 6` is `3 / 4` (this is sometimes more convenient than the
+result for cosine itself). -/
+theorem sq_cos_pi_div_six : cos (π / 6) ^ 2 = 3 / 4 := by
+  rw [cos_pi_div_six, div_pow, sq_sqrt] <;> norm_num
+#align real.sq_cos_pi_div_six Real.sq_cos_pi_div_six
+
 /-- The sine of `π / 6` is `1 / 2`. -/
 @[simp]
 theorem sin_pi_div_six : sin (π / 6) = 1 / 2 := by

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -551,7 +551,7 @@ theorem cos_eq_one_iff (x : ℝ) : cos x = 1 ↔ ∃ n : ℤ, (n : ℝ) * (2 * 
 theorem cos_eq_one_iff_of_lt_of_lt {x : ℝ} (hx₁ : -(2 * π) < x) (hx₂ : x < 2 * π) :
     cos x = 1 ↔ x = 0 :=
   ⟨fun h => by
-    rcases(cos_eq_one_iff _).1 h with ⟨n, rfl⟩
+    rcases (cos_eq_one_iff _).1 h with ⟨n, rfl⟩
     rw [mul_lt_iff_lt_one_left two_pi_pos] at hx₂
     rw [neg_lt, neg_mul_eq_neg_mul, mul_lt_iff_lt_one_left two_pi_pos] at hx₁
     norm_cast at hx₁ hx₂

mathport was forgetting a space in filter_upwards [...]with instead of filter_upwards [...] with.

@@ -1071,7 +1071,7 @@ theorem tendsto_cos_pi_div_two : Tendsto cos (𝓝[<] (π / 2)) (𝓝[>] 0) := b
   · convert continuous_cos.continuousWithinAt.tendsto
     simp
   · filter_upwards [Ioo_mem_nhdsWithin_Iio
-        (right_mem_Ioc.mpr (neg_lt_self pi_div_two_pos))]with x hx using cos_pos_of_mem_Ioo hx
+        (right_mem_Ioc.mpr (neg_lt_self pi_div_two_pos))] with x hx using cos_pos_of_mem_Ioo hx
 #align real.tendsto_cos_pi_div_two Real.tendsto_cos_pi_div_two
 
 theorem tendsto_tan_pi_div_two : Tendsto tan (𝓝[<] (π / 2)) atTop := by
@@ -1090,7 +1090,7 @@ theorem tendsto_cos_neg_pi_div_two : Tendsto cos (𝓝[>] (-(π / 2))) (𝓝[>]
   · convert continuous_cos.continuousWithinAt.tendsto
     simp
   · filter_upwards [Ioo_mem_nhdsWithin_Ioi
-        (left_mem_Ico.mpr (neg_lt_self pi_div_two_pos))]with x hx using cos_pos_of_mem_Ioo hx
+        (left_mem_Ico.mpr (neg_lt_self pi_div_two_pos))] with x hx using cos_pos_of_mem_Ioo hx
 #align real.tendsto_cos_neg_pi_div_two Real.tendsto_cos_neg_pi_div_two
 
 theorem tendsto_tan_neg_pi_div_two : Tendsto tan (𝓝[>] (-(π / 2))) atBot := by

@@ -504,15 +504,12 @@ theorem cos_eq_sqrt_one_sub_sin_sq {x : ℝ} (hl : -(π / 2) ≤ x) (hu : x ≤
 #align real.cos_eq_sqrt_one_sub_sin_sq Real.cos_eq_sqrt_one_sub_sin_sq
 
 theorem sin_eq_zero_iff_of_lt_of_lt {x : ℝ} (hx₁ : -π < x) (hx₂ : x < π) : sin x = 0 ↔ x = 0 :=
-  ⟨fun h => le_antisymm (le_of_not_gt fun h0 => lt_irrefl (0 : ℝ) <|
-    calc
-      0 < sin x := sin_pos_of_pos_of_lt_pi h0 hx₂
-      _ = 0 := h)
-    (le_of_not_gt fun h0 => lt_irrefl (0 : ℝ) <|
-      calc
-        0 = sin x := h.symm
-        _ < 0 := sin_neg_of_neg_of_neg_pi_lt h0 hx₁),
-    fun h => by simp [h]⟩
+  ⟨fun h => by
+    contrapose! h
+    cases h.lt_or_lt with
+    | inl h0 => exact (sin_neg_of_neg_of_neg_pi_lt h0 hx₁).ne
+    | inr h0 => exact (sin_pos_of_pos_of_lt_pi h0 hx₂).ne',
+  fun h => by simp [h]⟩
 #align real.sin_eq_zero_iff_of_lt_of_lt Real.sin_eq_zero_iff_of_lt_of_lt
 
 theorem sin_eq_zero_iff {x : ℝ} : sin x = 0 ↔ ∃ n : ℤ, (n : ℝ) * π = x :=
@@ -736,24 +733,23 @@ theorem cos_pi_over_two_pow : ∀ n : ℕ, cos (π / 2 ^ (n + 1)) = sqrtTwoAddSe
   | 0 => by simp
   | n + 1 => by
     have : (2 : ℝ) ≠ 0 := two_ne_zero
-    symm; rw [div_eq_iff_mul_eq this]; symm
-    rw [sqrtTwoAddSeries, sqrt_eq_iff_sq_eq, mul_pow, cos_sq, ← mul_div_assoc, Nat.add_succ,
-      pow_succ, mul_div_mul_left _ _ this, cos_pi_over_two_pow _, add_mul]
-    congr; · norm_num
-    rw [mul_comm, sq, mul_assoc, ← mul_div_assoc, mul_div_cancel_left, ← mul_div_assoc,
-        mul_div_cancel_left] <;>
-      try exact this
-    apply add_nonneg; norm_num; apply sqrtTwoAddSeries_zero_nonneg; norm_num
-    apply le_of_lt; apply cos_pos_of_mem_Ioo ⟨_, _⟩
+    rw [eq_div_iff_mul_eq this, eq_comm, sqrtTwoAddSeries, sqrt_eq_iff_sq_eq, mul_pow, cos_sq,
+      ← mul_div_assoc, pow_succ, mul_div_mul_left _ _ this, cos_pi_over_two_pow _, add_mul]
+    · congr
+      · norm_num
+      · rw [mul_comm, sq, mul_assoc, ← mul_div_assoc, mul_div_cancel_left _ this, ← mul_div_assoc,
+          mul_div_cancel_left _ this]
+    · exact add_nonneg two_pos.le (sqrtTwoAddSeries_zero_nonneg _)
+    refine le_of_lt <| mul_pos (cos_pos_of_mem_Ioo ⟨?_, ?_⟩) two_pos
     · trans (0 : ℝ)
-      rw [neg_lt_zero]
-      apply pi_div_two_pos
-      apply div_pos pi_pos
-      apply pow_pos
-      norm_num
-    apply div_lt_div' (le_refl π) _ pi_pos _
+      · rw [neg_lt_zero]
+        exact pi_div_two_pos
+      · exact div_pos pi_pos <| pow_pos two_pos _
+    apply div_lt_div' (le_refl π) _ pi_pos two_pos
     refine' lt_of_le_of_lt (le_of_eq (pow_one _).symm) _
-    apply pow_lt_pow; norm_num; apply Nat.succ_lt_succ; apply Nat.succ_pos; all_goals norm_num
+    apply pow_lt_pow
+    · norm_num
+    · exact Nat.succ_lt_succ n.succ_pos
 #align real.cos_pi_over_two_pow Real.cos_pi_over_two_pow
 
 theorem sin_sq_pi_over_two_pow (n : ℕ) :
@@ -764,90 +760,92 @@ theorem sin_sq_pi_over_two_pow (n : ℕ) :
 theorem sin_sq_pi_over_two_pow_succ (n : ℕ) :
     sin (π / 2 ^ (n + 2)) ^ 2 = 1 / 2 - sqrtTwoAddSeries 0 n / 4 := by
   rw [sin_sq_pi_over_two_pow, sqrtTwoAddSeries, div_pow, sq_sqrt, add_div, ← sub_sub]
-  congr; norm_num; norm_num; apply add_nonneg; norm_num; apply sqrtTwoAddSeries_zero_nonneg
+  congr
+  · norm_num
+  · norm_num
+  · exact add_nonneg two_pos.le (sqrtTwoAddSeries_zero_nonneg _)
 #align real.sin_sq_pi_over_two_pow_succ Real.sin_sq_pi_over_two_pow_succ
 
 @[simp]
 theorem sin_pi_over_two_pow_succ (n : ℕ) :
     sin (π / 2 ^ (n + 2)) = sqrt (2 - sqrtTwoAddSeries 0 n) / 2 := by
-  symm; rw [div_eq_iff_mul_eq]; symm
-  rw [sqrt_eq_iff_sq_eq, mul_pow, sin_sq_pi_over_two_pow_succ, sub_mul]
+  rw [eq_div_iff_mul_eq two_ne_zero, eq_comm, sqrt_eq_iff_sq_eq, mul_pow,
+    sin_sq_pi_over_two_pow_succ, sub_mul]
   · congr <;> norm_num
   · rw [sub_nonneg]
-    apply le_of_lt
-    apply sqrtTwoAddSeries_lt_two
-  apply le_of_lt; apply mul_pos; apply sin_pos_of_pos_of_lt_pi
-  · apply div_pos pi_pos
-    apply pow_pos
-    norm_num
-  refine' lt_of_lt_of_le _ (le_of_eq (div_one _)); rw [div_lt_div_left]
+    exact (sqrtTwoAddSeries_lt_two _).le
+  refine le_of_lt <| mul_pos (sin_pos_of_pos_of_lt_pi ?_ ?_) two_pos
+  · exact div_pos pi_pos <| pow_pos two_pos _
+  refine' lt_of_lt_of_le _ (le_of_eq (div_one _))
+  rw [div_lt_div_left pi_pos (pow_pos two_pos _) one_pos]
   refine' lt_of_le_of_lt (le_of_eq (pow_zero 2).symm) _
-  apply pow_lt_pow; norm_num; apply Nat.succ_pos; apply pi_pos
-  apply pow_pos; all_goals norm_num
+  apply pow_lt_pow
+  · norm_num
+  · apply Nat.succ_pos
 #align real.sin_pi_over_two_pow_succ Real.sin_pi_over_two_pow_succ
 
 @[simp]
 theorem cos_pi_div_four : cos (π / 4) = sqrt 2 / 2 := by
   trans cos (π / 2 ^ 2)
-  congr
-  norm_num
-  simp
+  · congr
+    norm_num
+  · simp
 #align real.cos_pi_div_four Real.cos_pi_div_four
 
 @[simp]
 theorem sin_pi_div_four : sin (π / 4) = sqrt 2 / 2 := by
   trans sin (π / 2 ^ 2)
-  congr
-  norm_num
-  simp
+  · congr
+    norm_num
+  · simp
 #align real.sin_pi_div_four Real.sin_pi_div_four
 
 @[simp]
 theorem cos_pi_div_eight : cos (π / 8) = sqrt (2 + sqrt 2) / 2 := by
   trans cos (π / 2 ^ 3)
-  congr
-  norm_num
-  simp
+  · congr
+    norm_num
+  · simp
 #align real.cos_pi_div_eight Real.cos_pi_div_eight
 
 @[simp]
 theorem sin_pi_div_eight : sin (π / 8) = sqrt (2 - sqrt 2) / 2 := by
   trans sin (π / 2 ^ 3)
-  congr
-  norm_num
-  simp
+  · congr
+    norm_num
+  · simp
 #align real.sin_pi_div_eight Real.sin_pi_div_eight
 
 @[simp]
 theorem cos_pi_div_sixteen : cos (π / 16) = sqrt (2 + sqrt (2 + sqrt 2)) / 2 := by
   trans cos (π / 2 ^ 4)
-  congr
-  norm_num
-  simp
+  · congr
+    norm_num
+  · simp
 #align real.cos_pi_div_sixteen Real.cos_pi_div_sixteen
 
 @[simp]
 theorem sin_pi_div_sixteen : sin (π / 16) = sqrt (2 - sqrt (2 + sqrt 2)) / 2 := by
   trans sin (π / 2 ^ 4)
-  congr
-  norm_num
-  simp
+  · congr
+    norm_num
+  · simp
 #align real.sin_pi_div_sixteen Real.sin_pi_div_sixteen
 
 @[simp]
 theorem cos_pi_div_thirty_two : cos (π / 32) = sqrt (2 + sqrt (2 + sqrt (2 + sqrt 2))) / 2 := by
   trans cos (π / 2 ^ 5)
-  congr
-  norm_num
-  simp
+  · congr
+    norm_num
+  · simp
 #align real.cos_pi_div_thirty_two Real.cos_pi_div_thirty_two
 
 @[simp]
 theorem sin_pi_div_thirty_two : sin (π / 32) = sqrt (2 - sqrt (2 + sqrt (2 + sqrt 2))) / 2 := by
   trans sin (π / 2 ^ 5)
-  congr
-  norm_num
-  simp
+  · congr
+    norm_num
+  · simp
 #align real.sin_pi_div_thirty_two Real.sin_pi_div_thirty_two
 
 -- This section is also a convenient location for other explicit values of `sin` and `cos`.
@@ -862,7 +860,7 @@ theorem cos_pi_div_three : cos (π / 3) = 1 / 2 := by
   cases' mul_eq_zero.mp h₁ with h h
   · linarith [pow_eq_zero h]
   · have : cos π < cos (π / 3) := by
-      refine' cos_lt_cos_of_nonneg_of_le_pi _ rfl.ge _ <;> linarith [pi_pos]
+      refine' cos_lt_cos_of_nonneg_of_le_pi _ le_rfl _ <;> linarith [pi_pos]
     linarith [cos_pi]
 #align real.cos_pi_div_three Real.cos_pi_div_three
 
@@ -882,8 +880,7 @@ theorem sq_cos_pi_div_six : cos (π / 6) ^ 2 = 3 / 4 := by
 @[simp]
 theorem cos_pi_div_six : cos (π / 6) = sqrt 3 / 2 := by
   suffices sqrt 3 = cos (π / 6) * 2 by
-    field_simp [(by norm_num : 0 ≠ 2)]
-    exact this.symm
+    field_simp [(by norm_num : 0 ≠ 2), ← this]
   rw [sqrt_eq_iff_sq_eq]
   · have h1 := (mul_right_inj' (by norm_num : (4 : ℝ) ≠ 0)).mpr sq_cos_pi_div_six
     rw [← sub_eq_zero] at h1 ⊢

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>

@@ -4,6 +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
 -/
 import Mathlib.Analysis.SpecialFunctions.Exp
+import Mathlib.Tactic.Positivity.Core
 
 #align_import analysis.special_functions.trigonometric.basic from "leanprover-community/mathlib"@"2c1d8ca2812b64f88992a5294ea3dba144755cd1"
 
@@ -163,6 +164,17 @@ theorem pi_pos : 0 < π :=
   lt_of_lt_of_le (by norm_num) two_le_pi
 #align real.pi_pos Real.pi_pos
 
+namespace Mathlib.Meta.Positivity
+open Lean.Meta Qq
+
+/-- Extension for the `positivity` tactic: `π` is always positive. -/
+@[positivity π]
+def evalExp : Mathlib.Meta.Positivity.PositivityExt where eval {_ _} _ _ _ := do
+  pure (.positive (q(Real.pi_pos) : Lean.Expr))
+
+end Mathlib.Meta.Positivity
+
+
 theorem pi_ne_zero : π ≠ 0 :=
   ne_of_gt pi_pos
 #align real.pi_ne_zero Real.pi_ne_zero

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).

@@ -520,7 +520,7 @@ theorem sin_ne_zero_iff {x : ℝ} : sin x ≠ 0 ↔ ∀ n : ℤ, (n : ℝ) * π
 
 theorem sin_eq_zero_iff_cos_eq {x : ℝ} : sin x = 0 ↔ cos x = 1 ∨ cos x = -1 := by
   rw [← mul_self_eq_one_iff, ← sin_sq_add_cos_sq x, sq, sq, ← sub_eq_iff_eq_add, sub_self]
-  exact ⟨fun h => by rw [h, MulZeroClass.mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
+  exact ⟨fun h => by rw [h, mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
 #align real.sin_eq_zero_iff_cos_eq Real.sin_eq_zero_iff_cos_eq
 
 theorem cos_eq_one_iff (x : ℝ) : cos x = 1 ↔ ∃ n : ℤ, (n : ℝ) * (2 * π) = x :=
@@ -1098,7 +1098,7 @@ open Real
 
 theorem sin_eq_zero_iff_cos_eq {z : ℂ} : sin z = 0 ↔ cos z = 1 ∨ cos z = -1 := by
   rw [← mul_self_eq_one_iff, ← sin_sq_add_cos_sq, sq, sq, ← sub_eq_iff_eq_add, sub_self]
-  exact ⟨fun h => by rw [h, MulZeroClass.mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
+  exact ⟨fun h => by rw [h, mul_zero], eq_zero_of_mul_self_eq_zero ∘ Eq.symm⟩
 #align complex.sin_eq_zero_iff_cos_eq Complex.sin_eq_zero_iff_cos_eq
 
 @[simp]

• depends on: #5966

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

@@ -2,14 +2,11 @@
 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.basic
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.SpecialFunctions.Exp
 
+#align_import analysis.special_functions.trigonometric.basic from "leanprover-community/mathlib"@"2c1d8ca2812b64f88992a5294ea3dba144755cd1"
+
 /-!
 # Trigonometric functions
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -730,7 +730,7 @@ theorem cos_pi_over_two_pow : ∀ n : ℕ, cos (π / 2 ^ (n + 1)) = sqrtTwoAddSe
     symm; rw [div_eq_iff_mul_eq this]; symm
     rw [sqrtTwoAddSeries, sqrt_eq_iff_sq_eq, mul_pow, cos_sq, ← mul_div_assoc, Nat.add_succ,
       pow_succ, mul_div_mul_left _ _ this, cos_pi_over_two_pow _, add_mul]
-    congr ; · norm_num
+    congr; · norm_num
     rw [mul_comm, sq, mul_assoc, ← mul_div_assoc, mul_div_cancel_left, ← mul_div_assoc,
         mul_div_cancel_left] <;>
       try exact this
@@ -755,7 +755,7 @@ theorem sin_sq_pi_over_two_pow (n : ℕ) :
 theorem sin_sq_pi_over_two_pow_succ (n : ℕ) :
     sin (π / 2 ^ (n + 2)) ^ 2 = 1 / 2 - sqrtTwoAddSeries 0 n / 4 := by
   rw [sin_sq_pi_over_two_pow, sqrtTwoAddSeries, div_pow, sq_sqrt, add_div, ← sub_sub]
-  congr ; norm_num; norm_num; apply add_nonneg; norm_num; apply sqrtTwoAddSeries_zero_nonneg
+  congr; norm_num; norm_num; apply add_nonneg; norm_num; apply sqrtTwoAddSeries_zero_nonneg
 #align real.sin_sq_pi_over_two_pow_succ Real.sin_sq_pi_over_two_pow_succ
 
 @[simp]

@@ -1406,10 +1406,10 @@ $$\left|exp^{a\left(e^{z}+e^{-z}\right)}\right| \le e^{a\cos b \exp^{|re z|}}.$$
 -/
 theorem abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le {a b : ℝ} (ha : a ≤ 0) {z : ℂ} (hz : |z.im| ≤ b)
     (hb : b ≤ π / 2) :
-    abs (exp (a * (exp z + exp (-z)))) ≤ Real.exp (a * Real.cos b * Real.exp (|z.re|)) := by
+    abs (exp (a * (exp z + exp (-z)))) ≤ Real.exp (a * Real.cos b * Real.exp |z.re|) := by
   simp only [abs_exp, Real.exp_le_exp, ofReal_mul_re, add_re, exp_re, neg_im, Real.cos_neg, ←
     add_mul, mul_assoc, mul_comm (Real.cos b), neg_re, ← Real.cos_abs z.im]
-  have : Real.exp (|z.re|) ≤ Real.exp z.re + Real.exp (-z.re) :=
+  have : Real.exp |z.re| ≤ Real.exp z.re + Real.exp (-z.re) :=
     apply_abs_le_add_of_nonneg (fun x => (Real.exp_pos x).le) z.re
   refine' mul_le_mul_of_nonpos_left (mul_le_mul this _ _ ((Real.exp_pos _).le.trans this)) ha
   · exact

Changes are of the form

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

@@ -548,7 +548,7 @@ theorem cos_eq_one_iff_of_lt_of_lt {x : ℝ} (hx₁ : -(2 * π) < x) (hx₂ : x
     rcases(cos_eq_one_iff _).1 h with ⟨n, rfl⟩
     rw [mul_lt_iff_lt_one_left two_pi_pos] at hx₂
     rw [neg_lt, neg_mul_eq_neg_mul, mul_lt_iff_lt_one_left two_pi_pos] at hx₁
-    norm_cast  at hx₁ hx₂
+    norm_cast at hx₁ hx₂
     obtain rfl : n = 0 := le_antisymm (by linarith) (by linarith)
     simp, fun h => by simp [h]⟩
 #align real.cos_eq_one_iff_of_lt_of_lt Real.cos_eq_one_iff_of_lt_of_lt
@@ -864,7 +864,7 @@ theorem sq_cos_pi_div_six : cos (π / 6) ^ 2 = 3 / 4 := by
     convert cos_sq (π / 6) using 3
     have h2 : 2 * (π / 6) = π / 3 := by linarith
     rw [h2, cos_pi_div_three]
-  rw [← sub_eq_zero] at h1⊢
+  rw [← sub_eq_zero] at h1 ⊢
   convert h1 using 1
   ring
 #align real.sq_cos_pi_div_six Real.sq_cos_pi_div_six
@@ -877,7 +877,7 @@ theorem cos_pi_div_six : cos (π / 6) = sqrt 3 / 2 := by
     exact this.symm
   rw [sqrt_eq_iff_sq_eq]
   · have h1 := (mul_right_inj' (by norm_num : (4 : ℝ) ≠ 0)).mpr sq_cos_pi_div_six
-    rw [← sub_eq_zero] at h1⊢
+    rw [← sub_eq_zero] at h1 ⊢
     convert h1 using 1
     ring
   · norm_num

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

@@ -1003,6 +1003,10 @@ theorem tan_periodic : Function.Periodic tan π := by
   simpa only [Function.Periodic, tan_eq_sin_div_cos] using sin_antiperiodic.div cos_antiperiodic
 #align real.tan_periodic Real.tan_periodic
 
+-- Porting note: added
+@[simp]
+theorem tan_pi : tan π = 0 := by rw [tan_periodic.eq, tan_zero]
+
 theorem tan_add_pi (x : ℝ) : tan (x + π) = tan x :=
   tan_periodic x
 #align real.tan_add_pi Real.tan_add_pi

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>