Changes since the initial port

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

Changes in mathlib3

f2ce6086

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

c2092722

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -49,7 +49,7 @@ theorem tan_add' {x y : ℝ}
 #print Real.tan_two_mul /-
 theorem tan_two_mul {x : ℝ} : tan (2 * x) = 2 * tan x / (1 - tan x ^ 2) := by
   simpa only [← Complex.ofReal_inj, Complex.ofReal_sub, Complex.ofReal_div, Complex.ofReal_pow,
-    Complex.ofReal_mul, Complex.ofReal_tan, Complex.ofReal_bit0, Complex.ofReal_one] using
+    Complex.ofReal_mul, Complex.ofReal_tan, Complex.of_real_bit0, Complex.ofReal_one] using
     Complex.tan_two_mul
 #align real.tan_two_mul Real.tan_two_mul
 -/
@@ -220,7 +220,7 @@ theorem arctan_eq_arcsin (x : ℝ) : arctan x = arcsin (x / sqrt (1 + x ^ 2)) :=
 #print Real.arcsin_eq_arctan /-
 theorem arcsin_eq_arctan {x : ℝ} (h : x ∈ Ioo (-(1 : ℝ)) 1) :
     arcsin x = arctan (x / sqrt (1 - x ^ 2)) := by
-  rw [arctan_eq_arcsin, div_pow, sq_sqrt, one_add_div, div_div, ← sqrt_mul, mul_div_cancel',
+  rw [arctan_eq_arcsin, div_pow, sq_sqrt, one_add_div, div_div, ← sqrt_mul, mul_div_cancel₀,
       sub_add_cancel, sqrt_one, div_one] <;>
     nlinarith [h.1, h.2]
 #align real.arcsin_eq_arctan Real.arcsin_eq_arctan
@@ -257,7 +257,7 @@ theorem arctan_eq_arccos {x : ℝ} (h : 0 ≤ x) : arctan x = arccos (sqrt (1 +
   by
   rw [arctan_eq_arcsin, arccos_eq_arcsin]; swap; · exact inv_nonneg.2 (sqrt_nonneg _)
   congr 1
-  rw [← sqrt_inv, sq_sqrt, ← one_div, one_sub_div, add_sub_cancel', sqrt_div, sqrt_sq h]
+  rw [← sqrt_inv, sq_sqrt, ← one_div, one_sub_div, add_sub_cancel_left, sqrt_div, sqrt_sq h]
   all_goals positivity
 #align real.arctan_eq_arccos Real.arctan_eq_arccos
 -/

c2092722

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -78,7 +78,7 @@ theorem continuousOn_tan : ContinuousOn tan {x | cos x ≠ 0} :=
   suffices ContinuousOn (fun x => sin x / cos x) {x | cos x ≠ 0}
     by
     have h_eq : (fun x => sin x / cos x) = tan := by ext1 x; rw [tan_eq_sin_div_cos]
-    rwa [h_eq] at this 
+    rwa [h_eq] at this
   exact continuous_on_sin.div continuous_on_cos fun x => id
 #align real.continuous_on_tan Real.continuousOn_tan
 -/
@@ -98,15 +98,15 @@ theorem continuousOn_tan_Ioo : ContinuousOn tan (Ioo (-(π / 2)) (π / 2)) :=
   rw [cos_eq_zero_iff]
   rintro hx_gt hx_lt ⟨r, hxr_eq⟩
   cases le_or_lt 0 r
-  · rw [lt_iff_not_ge] at hx_lt 
+  · rw [lt_iff_not_ge] at hx_lt
     refine' hx_lt _
     rw [hxr_eq, ← one_mul (π / 2), mul_div_assoc, ge_iff_le, mul_le_mul_right (half_pos pi_pos)]
     simp [h]
-  · rw [lt_iff_not_ge] at hx_gt 
+  · rw [lt_iff_not_ge] at hx_gt
     refine' hx_gt _
     rw [hxr_eq, ← one_mul (π / 2), mul_div_assoc, ge_iff_le, neg_mul_eq_neg_mul,
       mul_le_mul_right (half_pos pi_pos)]
-    have hr_le : r ≤ -1 := by rwa [Int.lt_iff_add_one_le, ← le_neg_iff_add_nonpos_right] at h 
+    have hr_le : r ≤ -1 := by rwa [Int.lt_iff_add_one_le, ← le_neg_iff_add_nonpos_right] at h
     rw [← le_sub_iff_add_le, mul_comm, ← le_div_iff]
     · norm_num; rw [← Int.cast_one, ← Int.cast_neg]; norm_cast; exact hr_le
     · exact zero_lt_two

c2092722

bump to nightly-2023-12-13-12

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

19154cfe

Diff

@@ -287,9 +287,9 @@ theorem continuousAt_arctan {x : ℝ} : ContinuousAt arctan x :=
 #align real.continuous_at_arctan Real.continuousAt_arctan
 -/
 
-#print Real.tanLocalHomeomorph /-
+#print Real.tanPartialHomeomorph /-
 /-- `real.tan` as a `local_homeomorph` between `(-(π / 2), π / 2)` and the whole line. -/
-def tanLocalHomeomorph : LocalHomeomorph ℝ ℝ
+def tanPartialHomeomorph : PartialHomeomorph ℝ ℝ
     where
   toFun := tan
   invFun := arctan
@@ -303,21 +303,21 @@ def tanLocalHomeomorph : LocalHomeomorph ℝ ℝ
   open_target := isOpen_univ
   continuous_toFun := continuousOn_tan_Ioo
   continuous_invFun := continuous_arctan.ContinuousOn
-#align real.tan_local_homeomorph Real.tanLocalHomeomorph
+#align real.tan_local_homeomorph Real.tanPartialHomeomorph
 -/
 
-#print Real.coe_tanLocalHomeomorph /-
+#print Real.coe_tanPartialHomeomorph /-
 @[simp]
-theorem coe_tanLocalHomeomorph : ⇑tanLocalHomeomorph = tan :=
+theorem coe_tanPartialHomeomorph : ⇑tanPartialHomeomorph = tan :=
   rfl
-#align real.coe_tan_local_homeomorph Real.coe_tanLocalHomeomorph
+#align real.coe_tan_local_homeomorph Real.coe_tanPartialHomeomorph
 -/
 
-#print Real.coe_tanLocalHomeomorph_symm /-
+#print Real.coe_tanPartialHomeomorph_symm /-
 @[simp]
-theorem coe_tanLocalHomeomorph_symm : ⇑tanLocalHomeomorph.symm = arctan :=
+theorem coe_tanPartialHomeomorph_symm : ⇑tanPartialHomeomorph.symm = arctan :=
   rfl
-#align real.coe_tan_local_homeomorph_symm Real.coe_tanLocalHomeomorph_symm
+#align real.coe_tan_local_homeomorph_symm Real.coe_tanPartialHomeomorph_symm
 -/
 
 end Real

c2092722

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -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.Trigonometric.Complex
+import Analysis.SpecialFunctions.Trigonometric.Complex
 
 #align_import analysis.special_functions.trigonometric.arctan from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"

c2092722

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -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.arctan
-! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecialFunctions.Trigonometric.Complex
 
+#align_import analysis.special_functions.trigonometric.arctan from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
 /-!
 # The `arctan` function.

c2092722

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -29,6 +29,7 @@ open Set Filter
 
 open scoped Topology Real
 
+#print Real.tan_add /-
 theorem tan_add {x y : ℝ}
     (h :
       ((∀ k : ℤ, x ≠ (2 * k + 1) * π / 2) ∧ ∀ l : ℤ, y ≠ (2 * l + 1) * π / 2) ∨
@@ -38,12 +39,15 @@ theorem tan_add {x y : ℝ}
     Complex.ofReal_mul, Complex.ofReal_tan] using
     @Complex.tan_add (x : ℂ) (y : ℂ) (by convert h <;> norm_cast)
 #align real.tan_add Real.tan_add
+-/
 
+#print Real.tan_add' /-
 theorem tan_add' {x y : ℝ}
     (h : (∀ k : ℤ, x ≠ (2 * k + 1) * π / 2) ∧ ∀ l : ℤ, y ≠ (2 * l + 1) * π / 2) :
     tan (x + y) = (tan x + tan y) / (1 - tan x * tan y) :=
   tan_add (Or.inl h)
 #align real.tan_add' Real.tan_add'
+-/
 
 #print Real.tan_two_mul /-
 theorem tan_two_mul {x : ℝ} : tan (2 * x) = 2 * tan x / (1 - tan x ^ 2) := by
@@ -53,13 +57,17 @@ theorem tan_two_mul {x : ℝ} : tan (2 * x) = 2 * tan x / (1 - tan x ^ 2) := by
 #align real.tan_two_mul Real.tan_two_mul
 -/
 
+#print Real.tan_ne_zero_iff /-
 theorem tan_ne_zero_iff {θ : ℝ} : tan θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π / 2 := by
   rw [← Complex.ofReal_ne_zero, Complex.ofReal_tan, Complex.tan_ne_zero_iff] <;> norm_cast
 #align real.tan_ne_zero_iff Real.tan_ne_zero_iff
+-/
 
+#print Real.tan_eq_zero_iff /-
 theorem tan_eq_zero_iff {θ : ℝ} : tan θ = 0 ↔ ∃ k : ℤ, θ = k * π / 2 := by
   rw [← not_iff_not, not_exists, ← Ne, tan_ne_zero_iff]
 #align real.tan_eq_zero_iff Real.tan_eq_zero_iff
+-/
 
 #print Real.tan_int_mul_pi_div_two /-
 theorem tan_int_mul_pi_div_two (n : ℤ) : tan (n * π / 2) = 0 :=
@@ -67,6 +75,7 @@ theorem tan_int_mul_pi_div_two (n : ℤ) : tan (n * π / 2) = 0 :=
 #align real.tan_int_mul_pi_div_two Real.tan_int_mul_pi_div_two
 -/
 
+#print Real.continuousOn_tan /-
 theorem continuousOn_tan : ContinuousOn tan {x | cos x ≠ 0} :=
   by
   suffices ContinuousOn (fun x => sin x / cos x) {x | cos x ≠ 0}
@@ -75,12 +84,16 @@ theorem continuousOn_tan : ContinuousOn tan {x | cos x ≠ 0} :=
     rwa [h_eq] at this 
   exact continuous_on_sin.div continuous_on_cos fun x => id
 #align real.continuous_on_tan Real.continuousOn_tan
+-/
 
+#print Real.continuous_tan /-
 @[continuity]
 theorem continuous_tan : Continuous fun x : {x | cos x ≠ 0} => tan x :=
   continuousOn_iff_continuous_restrict.1 continuousOn_tan
 #align real.continuous_tan Real.continuous_tan
+-/
 
+#print Real.continuousOn_tan_Ioo /-
 theorem continuousOn_tan_Ioo : ContinuousOn tan (Ioo (-(π / 2)) (π / 2)) :=
   by
   refine' ContinuousOn.mono continuous_on_tan fun x => _
@@ -101,27 +114,34 @@ theorem continuousOn_tan_Ioo : ContinuousOn tan (Ioo (-(π / 2)) (π / 2)) :=
     · norm_num; rw [← Int.cast_one, ← Int.cast_neg]; norm_cast; exact hr_le
     · exact zero_lt_two
 #align real.continuous_on_tan_Ioo Real.continuousOn_tan_Ioo
+-/
 
+#print Real.surjOn_tan /-
 theorem surjOn_tan : SurjOn tan (Ioo (-(π / 2)) (π / 2)) univ :=
   have := neg_lt_self pi_div_two_pos
   continuousOn_tan_Ioo.surjOn_of_tendsto (nonempty_Ioo.2 this)
     (by simp [tendsto_tan_neg_pi_div_two, this]) (by simp [tendsto_tan_pi_div_two, this])
 #align real.surj_on_tan Real.surjOn_tan
+-/
 
 #print Real.tan_surjective /-
 theorem tan_surjective : Function.Surjective tan := fun x => surjOn_tan.subset_range trivial
 #align real.tan_surjective Real.tan_surjective
 -/
 
+#print Real.image_tan_Ioo /-
 theorem image_tan_Ioo : tan '' Ioo (-(π / 2)) (π / 2) = univ :=
   univ_subset_iff.1 surjOn_tan
 #align real.image_tan_Ioo Real.image_tan_Ioo
+-/
 
+#print Real.tanOrderIso /-
 /-- `real.tan` as an `order_iso` between `(-(π / 2), π / 2)` and `ℝ`. -/
 def tanOrderIso : Ioo (-(π / 2)) (π / 2) ≃o ℝ :=
   (strictMonoOn_tan.OrderIso _ _).trans <|
     (OrderIso.setCongr _ _ image_tan_Ioo).trans OrderIso.Set.univ
 #align real.tan_order_iso Real.tanOrderIso
+-/
 
 #print Real.arctan /-
 /-- Inverse of the `tan` function, returns values in the range `-π / 2 < arctan x` and
@@ -139,72 +159,103 @@ theorem tan_arctan (x : ℝ) : tan (arctan x) = x :=
 #align real.tan_arctan Real.tan_arctan
 -/
 
+#print Real.arctan_mem_Ioo /-
 theorem arctan_mem_Ioo (x : ℝ) : arctan x ∈ Ioo (-(π / 2)) (π / 2) :=
   Subtype.coe_prop _
 #align real.arctan_mem_Ioo Real.arctan_mem_Ioo
+-/
 
+#print Real.range_arctan /-
 @[simp]
 theorem range_arctan : range arctan = Ioo (-(π / 2)) (π / 2) :=
   ((EquivLike.surjective _).range_comp _).trans Subtype.range_coe
 #align real.range_arctan Real.range_arctan
+-/
 
+#print Real.arctan_tan /-
 theorem arctan_tan {x : ℝ} (hx₁ : -(π / 2) < x) (hx₂ : x < π / 2) : arctan (tan x) = x :=
   Subtype.ext_iff.1 <| tanOrderIso.symm_apply_apply ⟨x, hx₁, hx₂⟩
 #align real.arctan_tan Real.arctan_tan
+-/
 
+#print Real.cos_arctan_pos /-
 theorem cos_arctan_pos (x : ℝ) : 0 < cos (arctan x) :=
   cos_pos_of_mem_Ioo <| arctan_mem_Ioo x
 #align real.cos_arctan_pos Real.cos_arctan_pos
+-/
 
+#print Real.cos_sq_arctan /-
 theorem cos_sq_arctan (x : ℝ) : cos (arctan x) ^ 2 = 1 / (1 + x ^ 2) := by
   rw [one_div, ← inv_one_add_tan_sq (cos_arctan_pos x).ne', tan_arctan]
 #align real.cos_sq_arctan Real.cos_sq_arctan
+-/
 
+#print Real.sin_arctan /-
 theorem sin_arctan (x : ℝ) : sin (arctan x) = x / sqrt (1 + x ^ 2) := by
   rw [← tan_div_sqrt_one_add_tan_sq (cos_arctan_pos x), tan_arctan]
 #align real.sin_arctan Real.sin_arctan
+-/
 
+#print Real.cos_arctan /-
 theorem cos_arctan (x : ℝ) : cos (arctan x) = 1 / sqrt (1 + x ^ 2) := by
   rw [one_div, ← inv_sqrt_one_add_tan_sq (cos_arctan_pos x), tan_arctan]
 #align real.cos_arctan Real.cos_arctan
+-/
 
+#print Real.arctan_lt_pi_div_two /-
 theorem arctan_lt_pi_div_two (x : ℝ) : arctan x < π / 2 :=
   (arctan_mem_Ioo x).2
 #align real.arctan_lt_pi_div_two Real.arctan_lt_pi_div_two
+-/
 
+#print Real.neg_pi_div_two_lt_arctan /-
 theorem neg_pi_div_two_lt_arctan (x : ℝ) : -(π / 2) < arctan x :=
   (arctan_mem_Ioo x).1
 #align real.neg_pi_div_two_lt_arctan Real.neg_pi_div_two_lt_arctan
+-/
 
+#print Real.arctan_eq_arcsin /-
 theorem arctan_eq_arcsin (x : ℝ) : arctan x = arcsin (x / sqrt (1 + x ^ 2)) :=
   Eq.symm <| arcsin_eq_of_sin_eq (sin_arctan x) (mem_Icc_of_Ioo <| arctan_mem_Ioo x)
 #align real.arctan_eq_arcsin Real.arctan_eq_arcsin
+-/
 
+#print Real.arcsin_eq_arctan /-
 theorem arcsin_eq_arctan {x : ℝ} (h : x ∈ Ioo (-(1 : ℝ)) 1) :
     arcsin x = arctan (x / sqrt (1 - x ^ 2)) := by
   rw [arctan_eq_arcsin, div_pow, sq_sqrt, one_add_div, div_div, ← sqrt_mul, mul_div_cancel',
       sub_add_cancel, sqrt_one, div_one] <;>
     nlinarith [h.1, h.2]
 #align real.arcsin_eq_arctan Real.arcsin_eq_arctan
+-/
 
+#print Real.arctan_zero /-
 @[simp]
 theorem arctan_zero : arctan 0 = 0 := by simp [arctan_eq_arcsin]
 #align real.arctan_zero Real.arctan_zero
+-/
 
+#print Real.arctan_eq_of_tan_eq /-
 theorem arctan_eq_of_tan_eq {x y : ℝ} (h : tan x = y) (hx : x ∈ Ioo (-(π / 2)) (π / 2)) :
     arctan y = x :=
   injOn_tan (arctan_mem_Ioo _) hx (by rw [tan_arctan, h])
 #align real.arctan_eq_of_tan_eq Real.arctan_eq_of_tan_eq
+-/
 
+#print Real.arctan_one /-
 @[simp]
 theorem arctan_one : arctan 1 = π / 4 :=
   arctan_eq_of_tan_eq tan_pi_div_four <| by constructor <;> linarith [pi_pos]
 #align real.arctan_one Real.arctan_one
+-/
 
+#print Real.arctan_neg /-
 @[simp]
 theorem arctan_neg (x : ℝ) : arctan (-x) = -arctan x := by simp [arctan_eq_arcsin, neg_div]
 #align real.arctan_neg Real.arctan_neg
+-/
 
+#print Real.arctan_eq_arccos /-
 theorem arctan_eq_arccos {x : ℝ} (h : 0 ≤ x) : arctan x = arccos (sqrt (1 + x ^ 2))⁻¹ :=
   by
   rw [arctan_eq_arcsin, arccos_eq_arcsin]; swap; · exact inv_nonneg.2 (sqrt_nonneg _)
@@ -212,7 +263,9 @@ theorem arctan_eq_arccos {x : ℝ} (h : 0 ≤ x) : arctan x = arccos (sqrt (1 +
   rw [← sqrt_inv, sq_sqrt, ← one_div, one_sub_div, add_sub_cancel', sqrt_div, sqrt_sq h]
   all_goals positivity
 #align real.arctan_eq_arccos Real.arctan_eq_arccos
+-/
 
+#print Real.arccos_eq_arctan /-
 -- The junk values for `arccos` and `sqrt` make this true even for `1 < x`.
 theorem arccos_eq_arctan {x : ℝ} (h : 0 < x) : arccos x = arctan (sqrt (1 - x ^ 2) / x) :=
   by
@@ -222,6 +275,7 @@ theorem arccos_eq_arctan {x : ℝ} (h : 0 < x) : arccos x = arctan (sqrt (1 - x
   · linarith only [arcsin_le_pi_div_two x, pi_pos]
   · linarith only [arcsin_pos.2 h]
 #align real.arccos_eq_arctan Real.arccos_eq_arctan
+-/
 
 #print Real.continuous_arctan /-
 @[continuity]

c2092722

bump to nightly-2023-06-08-03

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

8f04dc2b

Diff

@@ -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.arctan
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
 ! 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.Trigonometric.Complex
 /-!
 # The `arctan` function.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Inequalities, derivatives,
 and `real.tan` as a `local_homeomorph` between `(-(π / 2), π / 2)` and the whole line.
 -/

f2ce6086

bump to nightly-2023-06-06-23

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

23748742

Diff

@@ -42,11 +42,13 @@ theorem tan_add' {x y : ℝ}
   tan_add (Or.inl h)
 #align real.tan_add' Real.tan_add'
 
+#print Real.tan_two_mul /-
 theorem tan_two_mul {x : ℝ} : tan (2 * x) = 2 * tan x / (1 - tan x ^ 2) := by
   simpa only [← Complex.ofReal_inj, Complex.ofReal_sub, Complex.ofReal_div, Complex.ofReal_pow,
     Complex.ofReal_mul, Complex.ofReal_tan, Complex.ofReal_bit0, Complex.ofReal_one] using
     Complex.tan_two_mul
 #align real.tan_two_mul Real.tan_two_mul
+-/
 
 theorem tan_ne_zero_iff {θ : ℝ} : tan θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π / 2 := by
   rw [← Complex.ofReal_ne_zero, Complex.ofReal_tan, Complex.tan_ne_zero_iff] <;> norm_cast
@@ -56,9 +58,11 @@ theorem tan_eq_zero_iff {θ : ℝ} : tan θ = 0 ↔ ∃ k : ℤ, θ = k * π / 2
   rw [← not_iff_not, not_exists, ← Ne, tan_ne_zero_iff]
 #align real.tan_eq_zero_iff Real.tan_eq_zero_iff
 
+#print Real.tan_int_mul_pi_div_two /-
 theorem tan_int_mul_pi_div_two (n : ℤ) : tan (n * π / 2) = 0 :=
   tan_eq_zero_iff.mpr (by use n)
 #align real.tan_int_mul_pi_div_two Real.tan_int_mul_pi_div_two
+-/
 
 theorem continuousOn_tan : ContinuousOn tan {x | cos x ≠ 0} :=
   by
@@ -101,8 +105,10 @@ theorem surjOn_tan : SurjOn tan (Ioo (-(π / 2)) (π / 2)) univ :=
     (by simp [tendsto_tan_neg_pi_div_two, this]) (by simp [tendsto_tan_pi_div_two, this])
 #align real.surj_on_tan Real.surjOn_tan
 
+#print Real.tan_surjective /-
 theorem tan_surjective : Function.Surjective tan := fun x => surjOn_tan.subset_range trivial
 #align real.tan_surjective Real.tan_surjective
+-/
 
 theorem image_tan_Ioo : tan '' Ioo (-(π / 2)) (π / 2) = univ :=
   univ_subset_iff.1 surjOn_tan
@@ -114,17 +120,21 @@ def tanOrderIso : Ioo (-(π / 2)) (π / 2) ≃o ℝ :=
     (OrderIso.setCongr _ _ image_tan_Ioo).trans OrderIso.Set.univ
 #align real.tan_order_iso Real.tanOrderIso
 
+#print Real.arctan /-
 /-- Inverse of the `tan` function, returns values in the range `-π / 2 < arctan x` and
 `arctan x < π / 2` -/
 @[pp_nodot]
 noncomputable def arctan (x : ℝ) : ℝ :=
   tanOrderIso.symm x
 #align real.arctan Real.arctan
+-/
 
+#print Real.tan_arctan /-
 @[simp]
 theorem tan_arctan (x : ℝ) : tan (arctan x) = x :=
   tanOrderIso.apply_symm_apply x
 #align real.tan_arctan Real.tan_arctan
+-/
 
 theorem arctan_mem_Ioo (x : ℝ) : arctan x ∈ Ioo (-(π / 2)) (π / 2) :=
   Subtype.coe_prop _
@@ -210,15 +220,20 @@ theorem arccos_eq_arctan {x : ℝ} (h : 0 < x) : arccos x = arctan (sqrt (1 - x
   · linarith only [arcsin_pos.2 h]
 #align real.arccos_eq_arctan Real.arccos_eq_arctan
 
+#print Real.continuous_arctan /-
 @[continuity]
 theorem continuous_arctan : Continuous arctan :=
   continuous_subtype_val.comp tanOrderIso.toHomeomorph.continuous_invFun
 #align real.continuous_arctan Real.continuous_arctan
+-/
 
+#print Real.continuousAt_arctan /-
 theorem continuousAt_arctan {x : ℝ} : ContinuousAt arctan x :=
   continuous_arctan.ContinuousAt
 #align real.continuous_at_arctan Real.continuousAt_arctan
+-/
 
+#print Real.tanLocalHomeomorph /-
 /-- `real.tan` as a `local_homeomorph` between `(-(π / 2), π / 2)` and the whole line. -/
 def tanLocalHomeomorph : LocalHomeomorph ℝ ℝ
     where
@@ -235,16 +250,21 @@ def tanLocalHomeomorph : LocalHomeomorph ℝ ℝ
   continuous_toFun := continuousOn_tan_Ioo
   continuous_invFun := continuous_arctan.ContinuousOn
 #align real.tan_local_homeomorph Real.tanLocalHomeomorph
+-/
 
+#print Real.coe_tanLocalHomeomorph /-
 @[simp]
 theorem coe_tanLocalHomeomorph : ⇑tanLocalHomeomorph = tan :=
   rfl
 #align real.coe_tan_local_homeomorph Real.coe_tanLocalHomeomorph
+-/
 
+#print Real.coe_tanLocalHomeomorph_symm /-
 @[simp]
 theorem coe_tanLocalHomeomorph_symm : ⇑tanLocalHomeomorph.symm = arctan :=
   rfl
 #align real.coe_tan_local_homeomorph_symm Real.coe_tanLocalHomeomorph_symm
+-/
 
 end Real

f2ce6086

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -60,9 +60,9 @@ theorem tan_int_mul_pi_div_two (n : ℤ) : tan (n * π / 2) = 0 :=
   tan_eq_zero_iff.mpr (by use n)
 #align real.tan_int_mul_pi_div_two Real.tan_int_mul_pi_div_two
 
-theorem continuousOn_tan : ContinuousOn tan { x | cos x ≠ 0 } :=
+theorem continuousOn_tan : ContinuousOn tan {x | cos x ≠ 0} :=
   by
-  suffices ContinuousOn (fun x => sin x / cos x) { x | cos x ≠ 0 }
+  suffices ContinuousOn (fun x => sin x / cos x) {x | cos x ≠ 0}
     by
     have h_eq : (fun x => sin x / cos x) = tan := by ext1 x; rw [tan_eq_sin_div_cos]
     rwa [h_eq] at this 
@@ -70,7 +70,7 @@ theorem continuousOn_tan : ContinuousOn tan { x | cos x ≠ 0 } :=
 #align real.continuous_on_tan Real.continuousOn_tan
 
 @[continuity]
-theorem continuous_tan : Continuous fun x : { x | cos x ≠ 0 } => tan x :=
+theorem continuous_tan : Continuous fun x : {x | cos x ≠ 0} => tan x :=
   continuousOn_iff_continuous_restrict.1 continuousOn_tan
 #align real.continuous_tan Real.continuous_tan

f2ce6086

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -65,7 +65,7 @@ theorem continuousOn_tan : ContinuousOn tan { x | cos x ≠ 0 } :=
   suffices ContinuousOn (fun x => sin x / cos x) { x | cos x ≠ 0 }
     by
     have h_eq : (fun x => sin x / cos x) = tan := by ext1 x; rw [tan_eq_sin_div_cos]
-    rwa [h_eq] at this
+    rwa [h_eq] at this 
   exact continuous_on_sin.div continuous_on_cos fun x => id
 #align real.continuous_on_tan Real.continuousOn_tan
 
@@ -81,15 +81,15 @@ theorem continuousOn_tan_Ioo : ContinuousOn tan (Ioo (-(π / 2)) (π / 2)) :=
   rw [cos_eq_zero_iff]
   rintro hx_gt hx_lt ⟨r, hxr_eq⟩
   cases le_or_lt 0 r
-  · rw [lt_iff_not_ge] at hx_lt
+  · rw [lt_iff_not_ge] at hx_lt 
     refine' hx_lt _
     rw [hxr_eq, ← one_mul (π / 2), mul_div_assoc, ge_iff_le, mul_le_mul_right (half_pos pi_pos)]
     simp [h]
-  · rw [lt_iff_not_ge] at hx_gt
+  · rw [lt_iff_not_ge] at hx_gt 
     refine' hx_gt _
     rw [hxr_eq, ← one_mul (π / 2), mul_div_assoc, ge_iff_le, neg_mul_eq_neg_mul,
       mul_le_mul_right (half_pos pi_pos)]
-    have hr_le : r ≤ -1 := by rwa [Int.lt_iff_add_one_le, ← le_neg_iff_add_nonpos_right] at h
+    have hr_le : r ≤ -1 := by rwa [Int.lt_iff_add_one_le, ← le_neg_iff_add_nonpos_right] at h 
     rw [← le_sub_iff_add_le, mul_comm, ← le_div_iff]
     · norm_num; rw [← Int.cast_one, ← Int.cast_neg]; norm_cast; exact hr_le
     · exact zero_lt_two

f2ce6086

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -24,7 +24,7 @@ namespace Real
 
 open Set Filter
 
-open Topology Real
+open scoped Topology Real
 
 theorem tan_add {x y : ℝ}
     (h :

f2ce6086

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -64,10 +64,7 @@ theorem continuousOn_tan : ContinuousOn tan { x | cos x ≠ 0 } :=
   by
   suffices ContinuousOn (fun x => sin x / cos x) { x | cos x ≠ 0 }
     by
-    have h_eq : (fun x => sin x / cos x) = tan :=
-      by
-      ext1 x
-      rw [tan_eq_sin_div_cos]
+    have h_eq : (fun x => sin x / cos x) = tan := by ext1 x; rw [tan_eq_sin_div_cos]
     rwa [h_eq] at this
   exact continuous_on_sin.div continuous_on_cos fun x => id
 #align real.continuous_on_tan Real.continuousOn_tan
@@ -94,10 +91,7 @@ theorem continuousOn_tan_Ioo : ContinuousOn tan (Ioo (-(π / 2)) (π / 2)) :=
       mul_le_mul_right (half_pos pi_pos)]
     have hr_le : r ≤ -1 := by rwa [Int.lt_iff_add_one_le, ← le_neg_iff_add_nonpos_right] at h
     rw [← le_sub_iff_add_le, mul_comm, ← le_div_iff]
-    · norm_num
-      rw [← Int.cast_one, ← Int.cast_neg]
-      norm_cast
-      exact hr_le
+    · norm_num; rw [← Int.cast_one, ← Int.cast_neg]; norm_cast; exact hr_le
     · exact zero_lt_two
 #align real.continuous_on_tan_Ioo Real.continuousOn_tan_Ioo

f2ce6086

bump to nightly-2023-03-15-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

da6bb02a

Diff

@@ -32,7 +32,7 @@ theorem tan_add {x y : ℝ}
         (∃ k : ℤ, x = (2 * k + 1) * π / 2) ∧ ∃ l : ℤ, y = (2 * l + 1) * π / 2) :
     tan (x + y) = (tan x + tan y) / (1 - tan x * tan y) := by
   simpa only [← Complex.ofReal_inj, Complex.ofReal_sub, Complex.ofReal_add, Complex.ofReal_div,
-    Complex.ofReal_mul, Complex.of_real_tan] using
+    Complex.ofReal_mul, Complex.ofReal_tan] using
     @Complex.tan_add (x : ℂ) (y : ℂ) (by convert h <;> norm_cast)
 #align real.tan_add Real.tan_add
 
@@ -44,12 +44,12 @@ theorem tan_add' {x y : ℝ}
 
 theorem tan_two_mul {x : ℝ} : tan (2 * x) = 2 * tan x / (1 - tan x ^ 2) := by
   simpa only [← Complex.ofReal_inj, Complex.ofReal_sub, Complex.ofReal_div, Complex.ofReal_pow,
-    Complex.ofReal_mul, Complex.of_real_tan, Complex.ofReal_bit0, Complex.ofReal_one] using
+    Complex.ofReal_mul, Complex.ofReal_tan, Complex.ofReal_bit0, Complex.ofReal_one] using
     Complex.tan_two_mul
 #align real.tan_two_mul Real.tan_two_mul
 
 theorem tan_ne_zero_iff {θ : ℝ} : tan θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π / 2 := by
-  rw [← Complex.ofReal_ne_zero, Complex.of_real_tan, Complex.tan_ne_zero_iff] <;> norm_cast
+  rw [← Complex.ofReal_ne_zero, Complex.ofReal_tan, Complex.tan_ne_zero_iff] <;> norm_cast
 #align real.tan_ne_zero_iff Real.tan_ne_zero_iff
 
 theorem tan_eq_zero_iff {θ : ℝ} : tan θ = 0 ↔ ∃ k : ℤ, θ = k * π / 2 := by

f2ce6086

bump to nightly-2023-03-10-14

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

24f14899

Diff

@@ -31,8 +31,8 @@ theorem tan_add {x y : ℝ}
       ((∀ k : ℤ, x ≠ (2 * k + 1) * π / 2) ∧ ∀ l : ℤ, y ≠ (2 * l + 1) * π / 2) ∨
         (∃ k : ℤ, x = (2 * k + 1) * π / 2) ∧ ∃ l : ℤ, y = (2 * l + 1) * π / 2) :
     tan (x + y) = (tan x + tan y) / (1 - tan x * tan y) := by
-  simpa only [← Complex.of_real_inj, Complex.of_real_sub, Complex.of_real_add, Complex.of_real_div,
-    Complex.of_real_mul, Complex.of_real_tan] using
+  simpa only [← Complex.ofReal_inj, Complex.ofReal_sub, Complex.ofReal_add, Complex.ofReal_div,
+    Complex.ofReal_mul, Complex.of_real_tan] using
     @Complex.tan_add (x : ℂ) (y : ℂ) (by convert h <;> norm_cast)
 #align real.tan_add Real.tan_add
 
@@ -43,13 +43,13 @@ theorem tan_add' {x y : ℝ}
 #align real.tan_add' Real.tan_add'
 
 theorem tan_two_mul {x : ℝ} : tan (2 * x) = 2 * tan x / (1 - tan x ^ 2) := by
-  simpa only [← Complex.of_real_inj, Complex.of_real_sub, Complex.of_real_div, Complex.of_real_pow,
-    Complex.of_real_mul, Complex.of_real_tan, Complex.of_real_bit0, Complex.of_real_one] using
+  simpa only [← Complex.ofReal_inj, Complex.ofReal_sub, Complex.ofReal_div, Complex.ofReal_pow,
+    Complex.ofReal_mul, Complex.of_real_tan, Complex.ofReal_bit0, Complex.ofReal_one] using
     Complex.tan_two_mul
 #align real.tan_two_mul Real.tan_two_mul
 
 theorem tan_ne_zero_iff {θ : ℝ} : tan θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π / 2 := by
-  rw [← Complex.of_real_ne_zero, Complex.of_real_tan, Complex.tan_ne_zero_iff] <;> norm_cast
+  rw [← Complex.ofReal_ne_zero, Complex.of_real_tan, Complex.tan_ne_zero_iff] <;> norm_cast
 #align real.tan_ne_zero_iff Real.tan_ne_zero_iff
 
 theorem tan_eq_zero_iff {θ : ℝ} : tan θ = 0 ↔ ∃ k : ℤ, θ = k * π / 2 := by

f2ce6086

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

f2ce6086

feat: add notation for Real.sqrt (#12056)

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>

8640948c

Diff

@@ -139,11 +139,11 @@ theorem cos_sq_arctan (x : ℝ) : cos (arctan x) ^ 2 = 1 / (1 + x ^ 2) := by
   rw_mod_cast [one_div, ← inv_one_add_tan_sq (cos_arctan_pos x).ne', tan_arctan]
 #align real.cos_sq_arctan Real.cos_sq_arctan
 
-theorem sin_arctan (x : ℝ) : sin (arctan x) = x / sqrt (1 + x ^ 2) := by
+theorem sin_arctan (x : ℝ) : sin (arctan x) = x / √(1 + x ^ 2) := by
   rw_mod_cast [← tan_div_sqrt_one_add_tan_sq (cos_arctan_pos x), tan_arctan]
 #align real.sin_arctan Real.sin_arctan
 
-theorem cos_arctan (x : ℝ) : cos (arctan x) = 1 / sqrt (1 + x ^ 2) := by
+theorem cos_arctan (x : ℝ) : cos (arctan x) = 1 / √(1 + x ^ 2) := by
   rw_mod_cast [one_div, ← inv_sqrt_one_add_tan_sq (cos_arctan_pos x), tan_arctan]
 #align real.cos_arctan Real.cos_arctan
 
@@ -155,12 +155,12 @@ theorem neg_pi_div_two_lt_arctan (x : ℝ) : -(π / 2) < arctan x :=
   (arctan_mem_Ioo x).1
 #align real.neg_pi_div_two_lt_arctan Real.neg_pi_div_two_lt_arctan
 
-theorem arctan_eq_arcsin (x : ℝ) : arctan x = arcsin (x / sqrt (1 + x ^ 2)) :=
+theorem arctan_eq_arcsin (x : ℝ) : arctan x = arcsin (x / √(1 + x ^ 2)) :=
   Eq.symm <| arcsin_eq_of_sin_eq (sin_arctan x) (mem_Icc_of_Ioo <| arctan_mem_Ioo x)
 #align real.arctan_eq_arcsin Real.arctan_eq_arcsin
 
 theorem arcsin_eq_arctan {x : ℝ} (h : x ∈ Ioo (-(1 : ℝ)) 1) :
-    arcsin x = arctan (x / sqrt (1 - x ^ 2)) := by
+    arcsin x = arctan (x / √(1 - x ^ 2)) := by
   rw_mod_cast [arctan_eq_arcsin, div_pow, sq_sqrt, one_add_div, div_div, ← sqrt_mul,
     mul_div_cancel₀, sub_add_cancel, sqrt_one, div_one] <;> simp at h <;> nlinarith [h.1, h.2]
 #align real.arcsin_eq_arctan Real.arcsin_eq_arctan
@@ -198,7 +198,7 @@ theorem arctan_one : arctan 1 = π / 4 :=
 theorem arctan_neg (x : ℝ) : arctan (-x) = -arctan x := by simp [arctan_eq_arcsin, neg_div]
 #align real.arctan_neg Real.arctan_neg
 
-theorem arctan_eq_arccos {x : ℝ} (h : 0 ≤ x) : arctan x = arccos (sqrt (1 + x ^ 2))⁻¹ := by
+theorem arctan_eq_arccos {x : ℝ} (h : 0 ≤ x) : arctan x = arccos (√(1 + x ^ 2))⁻¹ := by
   rw [arctan_eq_arcsin, arccos_eq_arcsin]; swap; · exact inv_nonneg.2 (sqrt_nonneg _)
   congr 1
   rw_mod_cast [← sqrt_inv, sq_sqrt, ← one_div, one_sub_div, add_sub_cancel_left, sqrt_div,
@@ -207,7 +207,7 @@ theorem arctan_eq_arccos {x : ℝ} (h : 0 ≤ x) : arctan x = arccos (sqrt (1 +
 #align real.arctan_eq_arccos Real.arctan_eq_arccos
 
 -- The junk values for `arccos` and `sqrt` make this true even for `1 < x`.
-theorem arccos_eq_arctan {x : ℝ} (h : 0 < x) : arccos x = arctan (sqrt (1 - x ^ 2) / x) := by
+theorem arccos_eq_arctan {x : ℝ} (h : 0 < x) : arccos x = arctan (√(1 - x ^ 2) / x) := by
   rw [arccos, eq_comm]
   refine' arctan_eq_of_tan_eq _ ⟨_, _⟩
   · rw_mod_cast [tan_pi_div_two_sub, tan_arcsin, inv_div]

f2ce6086

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -67,7 +67,7 @@ theorem continuous_tan : Continuous fun x : {x | cos x ≠ 0} => tan x :=
 
 theorem continuousOn_tan_Ioo : ContinuousOn tan (Ioo (-(π / 2)) (π / 2)) := by
   refine' ContinuousOn.mono continuousOn_tan fun x => _
-  simp only [and_imp, mem_Ioo, mem_setOf_eq, Ne.def]
+  simp only [and_imp, mem_Ioo, mem_setOf_eq, Ne]
   rw [cos_eq_zero_iff]
   rintro hx_gt hx_lt ⟨r, hxr_eq⟩
   rcases le_or_lt 0 r with h | h

f2ce6086

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

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

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

4ea4a86a

Diff

@@ -162,7 +162,7 @@ theorem arctan_eq_arcsin (x : ℝ) : arctan x = arcsin (x / sqrt (1 + x ^ 2)) :=
 theorem arcsin_eq_arctan {x : ℝ} (h : x ∈ Ioo (-(1 : ℝ)) 1) :
     arcsin x = arctan (x / sqrt (1 - x ^ 2)) := by
   rw_mod_cast [arctan_eq_arcsin, div_pow, sq_sqrt, one_add_div, div_div, ← sqrt_mul,
-    mul_div_cancel', sub_add_cancel, sqrt_one, div_one] <;> simp at h <;> nlinarith [h.1, h.2]
+    mul_div_cancel₀, sub_add_cancel, sqrt_one, div_one] <;> simp at h <;> nlinarith [h.1, h.2]
 #align real.arcsin_eq_arctan Real.arcsin_eq_arctan
 
 @[simp]
@@ -201,7 +201,8 @@ theorem arctan_neg (x : ℝ) : arctan (-x) = -arctan x := by simp [arctan_eq_arc
 theorem arctan_eq_arccos {x : ℝ} (h : 0 ≤ x) : arctan x = arccos (sqrt (1 + x ^ 2))⁻¹ := by
   rw [arctan_eq_arcsin, arccos_eq_arcsin]; swap; · exact inv_nonneg.2 (sqrt_nonneg _)
   congr 1
-  rw_mod_cast [← sqrt_inv, sq_sqrt, ← one_div, one_sub_div, add_sub_cancel', sqrt_div, sqrt_sq h]
+  rw_mod_cast [← sqrt_inv, sq_sqrt, ← one_div, one_sub_div, add_sub_cancel_left, sqrt_div,
+    sqrt_sq h]
   all_goals positivity
 #align real.arctan_eq_arccos Real.arctan_eq_arccos

f2ce6086

chore: move Mathlib to v4.7.0-rc1 (#11162)

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

fa48894a

Diff

@@ -81,7 +81,8 @@ theorem continuousOn_tan_Ioo : ContinuousOn tan (Ioo (-(π / 2)) (π / 2)) := by
       mul_le_mul_right (half_pos pi_pos)]
     have hr_le : r ≤ -1 := by rwa [Int.lt_iff_add_one_le, ← le_neg_iff_add_nonpos_right] at h
     rw [← le_sub_iff_add_le, mul_comm, ← le_div_iff]
-    · norm_num; rw [← Int.cast_one, ← Int.cast_neg]; norm_cast
+    · set_option tactic.skipAssignedInstances false in norm_num
+      rw [← Int.cast_one, ← Int.cast_neg]; norm_cast
     · exact zero_lt_two
 #align real.continuous_on_tan_Ioo Real.continuousOn_tan_Ioo

f2ce6086

feat: improper integrals of 1/(1 + x^2) (#10234)

Co-authored-by: L Lllvvuu <git@llllvvuu.dev>

6ec9e85b

Diff

@@ -168,6 +168,21 @@ theorem arcsin_eq_arctan {x : ℝ} (h : x ∈ Ioo (-(1 : ℝ)) 1) :
 theorem arctan_zero : arctan 0 = 0 := by simp [arctan_eq_arcsin]
 #align real.arctan_zero Real.arctan_zero
 
+@[mono]
+theorem arctan_strictMono : StrictMono arctan := tanOrderIso.symm.strictMono
+
+theorem arctan_injective : arctan.Injective := arctan_strictMono.injective
+
+@[simp]
+theorem arctan_eq_zero_iff {x : ℝ} : arctan x = 0 ↔ x = 0 :=
+  .trans (by rw [arctan_zero]) arctan_injective.eq_iff
+
+theorem tendsto_arctan_atTop : Tendsto arctan atTop (𝓝[<] (π / 2)) :=
+  tendsto_Ioo_atTop.mp tanOrderIso.symm.tendsto_atTop
+
+theorem tendsto_arctan_atBot : Tendsto arctan atBot (𝓝[>] (-(π / 2))) :=
+  tendsto_Ioo_atBot.mp tanOrderIso.symm.tendsto_atBot
+
 theorem arctan_eq_of_tan_eq {x y : ℝ} (h : tan x = y) (hx : x ∈ Ioo (-(π / 2)) (π / 2)) :
     arctan y = x :=
   injOn_tan (arctan_mem_Ioo _) hx (by rw [tan_arctan, h])

f2ce6086

feat: arctangent addition and Machin's formula for π (#9847)

four_mul_arctan_inv_5_sub_arctan_inv_239 is theorem 1 in my own #6091.

b4adfe72

Diff

@@ -10,8 +10,14 @@ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex
 /-!
 # The `arctan` function.
 
-Inequalities, derivatives,
-and `Real.tan` as a `PartialHomeomorph` between `(-(π / 2), π / 2)` and the whole line.
+Inequalities, identities and `Real.tan` as a `PartialHomeomorph` between `(-(π / 2), π / 2)`
+and the whole line.
+
+The result of `arctan x + arctan y` is given by `arctan_add`, `arctan_add_eq_add_pi` or
+`arctan_add_eq_sub_pi` depending on whether `x * y < 1` and `0 < x`. As an application of
+`arctan_add` we give four Machin-like formulas (linear combinations of arctangents equal to
+`π / 4 = arctan 1`), including John Machin's original one at
+`four_mul_arctan_inv_5_sub_arctan_inv_239`.
 -/
 
 
@@ -192,6 +198,94 @@ theorem arccos_eq_arctan {x : ℝ} (h : 0 < x) : arccos x = arctan (sqrt (1 - x
   · linarith only [arcsin_pos.2 h]
 #align real.arccos_eq_arctan Real.arccos_eq_arctan
 
+theorem arctan_inv_of_pos {x : ℝ} (h : 0 < x) : arctan x⁻¹ = π / 2 - arctan x := by
+  rw [← arctan_tan (x := _ - _), tan_pi_div_two_sub, tan_arctan]
+  · norm_num
+    exact (arctan_lt_pi_div_two x).trans (half_lt_self_iff.mpr pi_pos)
+  · rw [sub_lt_self_iff, ← arctan_zero]
+    exact tanOrderIso.symm.strictMono h
+
+theorem arctan_inv_of_neg {x : ℝ} (h : x < 0) : arctan x⁻¹ = -(π / 2) - arctan x := by
+  have := arctan_inv_of_pos (neg_pos.mpr h)
+  rwa [inv_neg, arctan_neg, neg_eq_iff_eq_neg, neg_sub', arctan_neg, neg_neg] at this
+
+section ArctanAdd
+
+lemma arctan_ne_mul_pi_div_two {x : ℝ} : ∀ (k : ℤ), arctan x ≠ (2 * k + 1) * π / 2 := by
+  by_contra!
+  obtain ⟨k, h⟩ := this
+  obtain ⟨lb, ub⟩ := arctan_mem_Ioo x
+  rw [h, neg_eq_neg_one_mul, mul_div_assoc, mul_lt_mul_right (by positivity)] at lb
+  rw [h, ← one_mul (π / 2), mul_div_assoc, mul_lt_mul_right (by positivity)] at ub
+  norm_cast at lb ub; change -1 < _ at lb; omega
+
+lemma arctan_add_arctan_lt_pi_div_two {x y : ℝ} (h : x * y < 1) : arctan x + arctan y < π / 2 := by
+  cases' le_or_lt y 0 with hy hy
+  · rw [← add_zero (π / 2), ← arctan_zero]
+    exact add_lt_add_of_lt_of_le (arctan_lt_pi_div_two _) (tanOrderIso.symm.monotone hy)
+  · rw [← lt_div_iff hy, ← inv_eq_one_div] at h
+    replace h : arctan x < arctan y⁻¹ := tanOrderIso.symm.strictMono h
+    rwa [arctan_inv_of_pos hy, lt_tsub_iff_right] at h
+
+theorem arctan_add {x y : ℝ} (h : x * y < 1) :
+    arctan x + arctan y = arctan ((x + y) / (1 - x * y)) := by
+  rw [← arctan_tan (x := _ + _)]
+  · congr
+    conv_rhs => rw [← tan_arctan x, ← tan_arctan y]
+    exact tan_add' ⟨arctan_ne_mul_pi_div_two, arctan_ne_mul_pi_div_two⟩
+  · rw [neg_lt, neg_add, ← arctan_neg, ← arctan_neg]
+    rw [← neg_mul_neg] at h
+    exact arctan_add_arctan_lt_pi_div_two h
+  · exact arctan_add_arctan_lt_pi_div_two h
+
+theorem arctan_add_eq_add_pi {x y : ℝ} (h : 1 < x * y) (hx : 0 < x) :
+    arctan x + arctan y = arctan ((x + y) / (1 - x * y)) + π := by
+  have hy : 0 < y := by
+    have := mul_pos_iff.mp (zero_lt_one.trans h)
+    simpa [hx, hx.asymm]
+  have k := arctan_add (mul_inv x y ▸ inv_lt_one h)
+  rw [arctan_inv_of_pos hx, arctan_inv_of_pos hy, show _ + _ = π - (arctan x + arctan y) by ring,
+    sub_eq_iff_eq_add, ← sub_eq_iff_eq_add', sub_eq_add_neg, ← arctan_neg, add_comm] at k
+  convert k.symm using 3
+  field_simp
+  rw [show -x + -y = -(x + y) by ring, show x * y - 1 = -(1 - x * y) by ring, neg_div_neg_eq]
+
+theorem arctan_add_eq_sub_pi {x y : ℝ} (h : 1 < x * y) (hx : x < 0) :
+    arctan x + arctan y = arctan ((x + y) / (1 - x * y)) - π := by
+  rw [← neg_mul_neg] at h
+  have k := arctan_add_eq_add_pi h (neg_pos.mpr hx)
+  rw [show _ / _ = -((x + y) / (1 - x * y)) by ring, ← neg_inj] at k
+  simp only [arctan_neg, neg_add, neg_neg, ← sub_eq_add_neg _ π] at k
+  exact k
+
+theorem two_mul_arctan {x : ℝ} (h₁ : -1 < x) (h₂ : x < 1) :
+    2 * arctan x = arctan (2 * x / (1 - x ^ 2)) := by
+  rw [two_mul, arctan_add (by nlinarith)]; congr 1; ring
+
+theorem two_mul_arctan_add_pi {x : ℝ} (h : 1 < x) :
+    2 * arctan x = arctan (2 * x / (1 - x ^ 2)) + π := by
+  rw [two_mul, arctan_add_eq_add_pi (by nlinarith) (by linarith)]; congr 2; ring
+
+theorem two_mul_arctan_sub_pi {x : ℝ} (h : x < -1) :
+    2 * arctan x = arctan (2 * x / (1 - x ^ 2)) - π := by
+  rw [two_mul, arctan_add_eq_sub_pi (by nlinarith) (by linarith)]; congr 2; ring
+
+theorem arctan_inv_2_add_arctan_inv_3 : arctan 2⁻¹ + arctan 3⁻¹ = π / 4 := by
+  rw [arctan_add] <;> norm_num
+
+theorem two_mul_arctan_inv_2_sub_arctan_inv_7 : 2 * arctan 2⁻¹ - arctan 7⁻¹ = π / 4 := by
+  rw [two_mul_arctan, ← arctan_one, sub_eq_iff_eq_add, arctan_add] <;> norm_num
+
+theorem two_mul_arctan_inv_3_add_arctan_inv_7 : 2 * arctan 3⁻¹ + arctan 7⁻¹ = π / 4 := by
+  rw [two_mul_arctan, arctan_add] <;> norm_num
+
+/-- **John Machin's 1706 formula**, which he used to compute π to 100 decimal places. -/
+theorem four_mul_arctan_inv_5_sub_arctan_inv_239 : 4 * arctan 5⁻¹ - arctan 239⁻¹ = π / 4 := by
+  rw [show 4 * arctan _ = 2 * (2 * _) by ring, two_mul_arctan, two_mul_arctan, ← arctan_one,
+    sub_eq_iff_eq_add, arctan_add] <;> norm_num
+
+end ArctanAdd
+
 @[continuity]
 theorem continuous_arctan : Continuous arctan :=
   continuous_subtype_val.comp tanOrderIso.toHomeomorph.continuous_invFun

f2ce6086

feat(Trigonometric): add Complex.tan_eq_zero_iff' (#9877)

This version assumes that the cosine is not zero.

a05375f7

Diff

@@ -43,14 +43,6 @@ theorem tan_two_mul {x : ℝ} : tan (2 * x) = 2 * tan x / (1 - tan x ^ 2) := by
   norm_cast at *
 #align real.tan_two_mul Real.tan_two_mul
 
-theorem tan_ne_zero_iff {θ : ℝ} : tan θ ≠ 0 ↔ ∀ k : ℤ, θ ≠ k * π / 2 := by
-  rw [← Complex.ofReal_ne_zero, Complex.ofReal_tan, Complex.tan_ne_zero_iff]; norm_cast
-#align real.tan_ne_zero_iff Real.tan_ne_zero_iff
-
-theorem tan_eq_zero_iff {θ : ℝ} : tan θ = 0 ↔ ∃ k : ℤ, θ = k * π / 2 := by
-  rw [← not_iff_not, not_exists, ← Ne, tan_ne_zero_iff]
-#align real.tan_eq_zero_iff Real.tan_eq_zero_iff
-
 theorem tan_int_mul_pi_div_two (n : ℤ) : tan (n * π / 2) = 0 :=
   tan_eq_zero_iff.mpr (by use n)
 #align real.tan_int_mul_pi_div_two Real.tan_int_mul_pi_div_two

f2ce6086

chore: remove uses of cases' (#9171)

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

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

3fca282c

Diff

@@ -72,7 +72,7 @@ theorem continuousOn_tan_Ioo : ContinuousOn tan (Ioo (-(π / 2)) (π / 2)) := by
   simp only [and_imp, mem_Ioo, mem_setOf_eq, Ne.def]
   rw [cos_eq_zero_iff]
   rintro hx_gt hx_lt ⟨r, hxr_eq⟩
-  cases' le_or_lt 0 r with h h
+  rcases le_or_lt 0 r with h | h
   · rw [lt_iff_not_ge] at hx_lt
     refine' hx_lt _
     rw [hxr_eq, ← one_mul (π / 2), mul_div_assoc, ge_iff_le, mul_le_mul_right (half_pos pi_pos)]

f2ce6086

chore: rename LocalHomeomorph to PartialHomeomorph (#8982)

LocalHomeomorph evokes a "local homeomorphism": this is not what this means. Instead, this is a homeomorphism on an open set of the domain (extended to the whole space, by the junk value pattern). Hence, partial homeomorphism is more appropriate, and avoids confusion with IsLocallyHomeomorph.

A future PR will rename LocalEquiv to PartialEquiv.

Zulip discussion

bbc6e56d

Diff

@@ -11,7 +11,7 @@ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex
 # The `arctan` function.
 
 Inequalities, derivatives,
-and `Real.tan` as a `LocalHomeomorph` between `(-(π / 2), π / 2)` and the whole line.
+and `Real.tan` as a `PartialHomeomorph` between `(-(π / 2), π / 2)` and the whole line.
 -/
 
 
@@ -209,8 +209,8 @@ theorem continuousAt_arctan {x : ℝ} : ContinuousAt arctan x :=
   continuous_arctan.continuousAt
 #align real.continuous_at_arctan Real.continuousAt_arctan
 
-/-- `Real.tan` as a `LocalHomeomorph` between `(-(π / 2), π / 2)` and the whole line. -/
-def tanLocalHomeomorph : LocalHomeomorph ℝ ℝ where
+/-- `Real.tan` as a `PartialHomeomorph` between `(-(π / 2), π / 2)` and the whole line. -/
+def tanPartialHomeomorph : PartialHomeomorph ℝ ℝ where
   toFun := tan
   invFun := arctan
   source := Ioo (-(π / 2)) (π / 2)
@@ -223,16 +223,16 @@ def tanLocalHomeomorph : LocalHomeomorph ℝ ℝ where
   open_target := isOpen_univ
   continuousOn_toFun := continuousOn_tan_Ioo
   continuousOn_invFun := continuous_arctan.continuousOn
-#align real.tan_local_homeomorph Real.tanLocalHomeomorph
+#align real.tan_local_homeomorph Real.tanPartialHomeomorph
 
 @[simp]
-theorem coe_tanLocalHomeomorph : ⇑tanLocalHomeomorph = tan :=
+theorem coe_tanPartialHomeomorph : ⇑tanPartialHomeomorph = tan :=
   rfl
-#align real.coe_tan_local_homeomorph Real.coe_tanLocalHomeomorph
+#align real.coe_tan_local_homeomorph Real.coe_tanPartialHomeomorph
 
 @[simp]
-theorem coe_tanLocalHomeomorph_symm : ⇑tanLocalHomeomorph.symm = arctan :=
+theorem coe_tanPartialHomeomorph_symm : ⇑tanPartialHomeomorph.symm = arctan :=
   rfl
-#align real.coe_tan_local_homeomorph_symm Real.coe_tanLocalHomeomorph_symm
+#align real.coe_tan_local_homeomorph_symm Real.coe_tanPartialHomeomorph_symm
 
 end Real

f2ce6086

chore: rename {LocalHomeomorph,ChartedSpace}.continuous_{to,inv}Fun fields to continuousOn_{to,inv}Fun (#8848)

They have type ContinuousOn ..., hence should be named accordingly. Suggested by @fpvandoorn in #8736.

d10d71d7

Diff

@@ -221,8 +221,8 @@ def tanLocalHomeomorph : LocalHomeomorph ℝ ℝ where
   right_inv' y _ := tan_arctan y
   open_source := isOpen_Ioo
   open_target := isOpen_univ
-  continuous_toFun := continuousOn_tan_Ioo
-  continuous_invFun := continuous_arctan.continuousOn
+  continuousOn_toFun := continuousOn_tan_Ioo
+  continuousOn_invFun := continuous_arctan.continuousOn
 #align real.tan_local_homeomorph Real.tanLocalHomeomorph
 
 @[simp]

f2ce6086

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

PR contents

This is the supremum of

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

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

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

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

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

We can get rid of all the

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

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

leanprover/lean4#2722

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

leanprover/lean4#2783

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

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

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

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

40b64f79

Diff

@@ -17,8 +17,6 @@ and `Real.tan` as a `LocalHomeomorph` between `(-(π / 2), π / 2)` and the whol
 
 noncomputable section
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 namespace Real
 
 open Set Filter

f2ce6086

chore: regularize HPow.hPow porting notes (#6465)

0f85d19f

Diff

@@ -17,7 +17,7 @@ and `Real.tan` as a `LocalHomeomorph` between `(-(π / 2), π / 2)` and the whol
 
 noncomputable section
 
-local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 namespace Real

f2ce6086

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +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.arctan
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex
 
+#align_import analysis.special_functions.trigonometric.arctan from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # The `arctan` function.

f2ce6086

chore: tidy various files (#5355)

0d584e40

Diff

@@ -14,7 +14,7 @@ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex
 # The `arctan` function.
 
 Inequalities, derivatives,
-and `real.tan` as a `local_homeomorph` between `(-(π / 2), π / 2)` and the whole line.
+and `Real.tan` as a `LocalHomeomorph` between `(-(π / 2), π / 2)` and the whole line.
 -/
 
 
@@ -214,7 +214,7 @@ theorem continuousAt_arctan {x : ℝ} : ContinuousAt arctan x :=
   continuous_arctan.continuousAt
 #align real.continuous_at_arctan Real.continuousAt_arctan
 
-/-- `real.tan` as a `local_homeomorph` between `(-(π / 2), π / 2)` and the whole line. -/
+/-- `Real.tan` as a `LocalHomeomorph` between `(-(π / 2), π / 2)` and the whole line. -/
 def tanLocalHomeomorph : LocalHomeomorph ℝ ℝ where
   toFun := tan
   invFun := arctan

f2ce6086

feat: port Analysis.SpecialFunctions.Trigonometric.Arctan (#4750)

03e1c2fa

`analysis.special_functions.trigonometric.arctan` ⟷ `Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 12 + 947

analysis.special_functions.trigonometric.arctan ⟷ Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 12 + 947

`analysis.special_functions.trigonometric.arctan` ⟷ `Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan`