analysis.special_functions.arsinh | Mathlib porting status

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

36938f77

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -82,7 +82,7 @@ theorem arsinh_neg (x : ℝ) : arsinh (-x) = -arsinh x :=
   by
   rw [← NormedSpace.exp_eq_exp, exp_arsinh, NormedSpace.exp_neg, exp_arsinh]
   apply eq_inv_of_mul_eq_one_left
-  rw [neg_sq, neg_add_eq_sub, add_comm x, mul_comm, ← sq_sub_sq, sq_sqrt, add_sub_cancel]
+  rw [neg_sq, neg_add_eq_sub, add_comm x, mul_comm, ← sq_sub_sq, sq_sqrt, add_sub_cancel_right]
   exact add_nonneg zero_le_one (sq_nonneg _)
 #align real.arsinh_neg Real.arsinh_neg
 -/

36938f77

bump to nightly-2023-11-29-11

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

049e2cad

Diff

@@ -80,7 +80,7 @@ theorem arsinh_zero : arsinh 0 = 0 := by simp [arsinh]
 @[simp]
 theorem arsinh_neg (x : ℝ) : arsinh (-x) = -arsinh x :=
   by
-  rw [← exp_eq_exp, exp_arsinh, exp_neg, exp_arsinh]
+  rw [← NormedSpace.exp_eq_exp, exp_arsinh, NormedSpace.exp_neg, exp_arsinh]
   apply eq_inv_of_mul_eq_one_left
   rw [neg_sq, neg_add_eq_sub, add_comm x, mul_comm, ← sq_sub_sq, sq_sqrt, add_sub_cancel]
   exact add_nonneg zero_le_one (sq_nonneg _)

36938f77

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 James Arthur. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: James Arthur, Chris Hughes, Shing Tak Lam
 -/
-import Mathbin.Analysis.SpecialFunctions.Trigonometric.Deriv
-import Mathbin.Analysis.SpecialFunctions.Log.Basic
+import Analysis.SpecialFunctions.Trigonometric.Deriv
+import Analysis.SpecialFunctions.Log.Basic
 
 #align_import analysis.special_functions.arsinh from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"

36938f77

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 James Arthur. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: James Arthur, Chris Hughes, Shing Tak Lam
-
-! This file was ported from Lean 3 source module analysis.special_functions.arsinh
-! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecialFunctions.Trigonometric.Deriv
 import Mathbin.Analysis.SpecialFunctions.Log.Basic
 
+#align_import analysis.special_functions.arsinh from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
+
 /-!
 # Inverse of the sinh function

36938f77

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -62,6 +62,7 @@ def arsinh (x : ℝ) :=
 #align real.arsinh Real.arsinh
 -/
 
+#print Real.exp_arsinh /-
 theorem exp_arsinh (x : ℝ) : exp (arsinh x) = x + sqrt (1 + x ^ 2) :=
   by
   apply exp_log
@@ -70,11 +71,15 @@ theorem exp_arsinh (x : ℝ) : exp (arsinh x) = x + sqrt (1 + x ^ 2) :=
     -x ≤ sqrt (x ^ 2) := le_sqrt_of_sq_le (neg_pow_bit0 _ _).le
     _ < sqrt (1 + x ^ 2) := sqrt_lt_sqrt (sq_nonneg _) (lt_one_add _)
 #align real.exp_arsinh Real.exp_arsinh
+-/
 
+#print Real.arsinh_zero /-
 @[simp]
 theorem arsinh_zero : arsinh 0 = 0 := by simp [arsinh]
 #align real.arsinh_zero Real.arsinh_zero
+-/
 
+#print Real.arsinh_neg /-
 @[simp]
 theorem arsinh_neg (x : ℝ) : arsinh (-x) = -arsinh x :=
   by
@@ -83,6 +88,7 @@ theorem arsinh_neg (x : ℝ) : arsinh (-x) = -arsinh x :=
   rw [neg_sq, neg_add_eq_sub, add_comm x, mul_comm, ← sq_sub_sq, sq_sqrt, add_sub_cancel]
   exact add_nonneg zero_le_one (sq_nonneg _)
 #align real.arsinh_neg Real.arsinh_neg
+-/
 
 #print Real.sinh_arsinh /-
 /-- `arsinh` is the right inverse of `sinh`. -/
@@ -92,10 +98,12 @@ theorem sinh_arsinh (x : ℝ) : sinh (arsinh x) = x := by
 #align real.sinh_arsinh Real.sinh_arsinh
 -/
 
+#print Real.cosh_arsinh /-
 @[simp]
 theorem cosh_arsinh (x : ℝ) : cosh (arsinh x) = sqrt (1 + x ^ 2) := by
   rw [← sqrt_sq (cosh_pos _).le, cosh_sq', sinh_arsinh]
 #align real.cosh_arsinh Real.cosh_arsinh
+-/
 
 #print Real.sinh_surjective /-
 /-- `sinh` is surjective, `∀ b, ∃ a, sinh a = b`. In this case, we use `a = arsinh b`. -/
@@ -130,12 +138,14 @@ def sinhEquiv : ℝ ≃ ℝ where
 #align real.sinh_equiv Real.sinhEquiv
 -/
 
+#print Real.sinhOrderIso /-
 /-- `real.sinh` as an `order_iso`. -/
 @[simps (config := { fullyApplied := false })]
 def sinhOrderIso : ℝ ≃o ℝ where
   toEquiv := sinhEquiv
   map_rel_iff' := @sinh_le_sinh
 #align real.sinh_order_iso Real.sinhOrderIso
+-/
 
 #print Real.sinhHomeomorph /-
 /-- `real.sinh` as a `homeomorph`. -/
@@ -176,39 +186,54 @@ theorem arsinh_inj : arsinh x = arsinh y ↔ x = y :=
 #align real.arsinh_inj Real.arsinh_inj
 -/
 
+#print Real.arsinh_le_arsinh /-
 @[simp]
 theorem arsinh_le_arsinh : arsinh x ≤ arsinh y ↔ x ≤ y :=
   sinhOrderIso.symm.le_iff_le
 #align real.arsinh_le_arsinh Real.arsinh_le_arsinh
+-/
 
+#print Real.arsinh_lt_arsinh /-
 @[simp]
 theorem arsinh_lt_arsinh : arsinh x < arsinh y ↔ x < y :=
   sinhOrderIso.symm.lt_iff_lt
 #align real.arsinh_lt_arsinh Real.arsinh_lt_arsinh
+-/
 
+#print Real.arsinh_eq_zero_iff /-
 @[simp]
 theorem arsinh_eq_zero_iff : arsinh x = 0 ↔ x = 0 :=
   arsinh_injective.eq_iff' arsinh_zero
 #align real.arsinh_eq_zero_iff Real.arsinh_eq_zero_iff
+-/
 
+#print Real.arsinh_nonneg_iff /-
 @[simp]
 theorem arsinh_nonneg_iff : 0 ≤ arsinh x ↔ 0 ≤ x := by rw [← sinh_le_sinh, sinh_zero, sinh_arsinh]
 #align real.arsinh_nonneg_iff Real.arsinh_nonneg_iff
+-/
 
+#print Real.arsinh_nonpos_iff /-
 @[simp]
 theorem arsinh_nonpos_iff : arsinh x ≤ 0 ↔ x ≤ 0 := by rw [← sinh_le_sinh, sinh_zero, sinh_arsinh]
 #align real.arsinh_nonpos_iff Real.arsinh_nonpos_iff
+-/
 
+#print Real.arsinh_pos_iff /-
 @[simp]
 theorem arsinh_pos_iff : 0 < arsinh x ↔ 0 < x :=
   lt_iff_lt_of_le_iff_le arsinh_nonpos_iff
 #align real.arsinh_pos_iff Real.arsinh_pos_iff
+-/
 
+#print Real.arsinh_neg_iff /-
 @[simp]
 theorem arsinh_neg_iff : arsinh x < 0 ↔ x < 0 :=
   lt_iff_lt_of_le_iff_le arsinh_nonneg_iff
 #align real.arsinh_neg_iff Real.arsinh_neg_iff
+-/
 
+#print Real.hasStrictDerivAt_arsinh /-
 theorem hasStrictDerivAt_arsinh (x : ℝ) : HasStrictDerivAt arsinh (sqrt (1 + x ^ 2))⁻¹ x :=
   by
   convert
@@ -216,10 +241,13 @@ theorem hasStrictDerivAt_arsinh (x : ℝ) : HasStrictDerivAt arsinh (sqrt (1 + x
       (has_strict_deriv_at_sinh _)
   exact (cosh_arsinh _).symm
 #align real.has_strict_deriv_at_arsinh Real.hasStrictDerivAt_arsinh
+-/
 
+#print Real.hasDerivAt_arsinh /-
 theorem hasDerivAt_arsinh (x : ℝ) : HasDerivAt arsinh (sqrt (1 + x ^ 2))⁻¹ x :=
   (hasStrictDerivAt_arsinh x).HasDerivAt
 #align real.has_deriv_at_arsinh Real.hasDerivAt_arsinh
+-/
 
 #print Real.differentiable_arsinh /-
 theorem differentiable_arsinh : Differentiable ℝ arsinh := fun x =>
@@ -287,20 +315,26 @@ section fderiv
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {f : E → ℝ} {s : Set E} {a : E}
   {f' : E →L[ℝ] ℝ} {n : ℕ∞}
 
+#print HasStrictFDerivAt.arsinh /-
 theorem HasStrictFDerivAt.arsinh (hf : HasStrictFDerivAt f f' a) :
     HasStrictFDerivAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') a :=
   (hasStrictDerivAt_arsinh _).comp_hasStrictFDerivAt a hf
 #align has_strict_fderiv_at.arsinh HasStrictFDerivAt.arsinh
+-/
 
+#print HasFDerivAt.arsinh /-
 theorem HasFDerivAt.arsinh (hf : HasFDerivAt f f' a) :
     HasFDerivAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') a :=
   (hasDerivAt_arsinh _).comp_hasFDerivAt a hf
 #align has_fderiv_at.arsinh HasFDerivAt.arsinh
+-/
 
+#print HasFDerivWithinAt.arsinh /-
 theorem HasFDerivWithinAt.arsinh (hf : HasFDerivWithinAt f f' s a) :
     HasFDerivWithinAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') s a :=
   (hasDerivAt_arsinh _).comp_hasFDerivWithinAt a hf
 #align has_fderiv_within_at.arsinh HasFDerivWithinAt.arsinh
+-/
 
 #print DifferentiableAt.arsinh /-
 theorem DifferentiableAt.arsinh (h : DifferentiableAt ℝ f a) :
@@ -359,20 +393,26 @@ section deriv
 
 variable {f : ℝ → ℝ} {s : Set ℝ} {a f' : ℝ}
 
+#print HasStrictDerivAt.arsinh /-
 theorem HasStrictDerivAt.arsinh (hf : HasStrictDerivAt f f' a) :
     HasStrictDerivAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') a :=
   (hasStrictDerivAt_arsinh _).comp a hf
 #align has_strict_deriv_at.arsinh HasStrictDerivAt.arsinh
+-/
 
+#print HasDerivAt.arsinh /-
 theorem HasDerivAt.arsinh (hf : HasDerivAt f f' a) :
     HasDerivAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') a :=
   (hasDerivAt_arsinh _).comp a hf
 #align has_deriv_at.arsinh HasDerivAt.arsinh
+-/
 
+#print HasDerivWithinAt.arsinh /-
 theorem HasDerivWithinAt.arsinh (hf : HasDerivWithinAt f f' s a) :
     HasDerivWithinAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') s a :=
   (hasDerivAt_arsinh _).comp_hasDerivWithinAt a hf
 #align has_deriv_within_at.arsinh HasDerivWithinAt.arsinh
+-/
 
 end deriv

36938f77

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -69,7 +69,6 @@ theorem exp_arsinh (x : ℝ) : exp (arsinh x) = x + sqrt (1 + x ^ 2) :=
   calc
     -x ≤ sqrt (x ^ 2) := le_sqrt_of_sq_le (neg_pow_bit0 _ _).le
     _ < sqrt (1 + x ^ 2) := sqrt_lt_sqrt (sq_nonneg _) (lt_one_add _)
-    
 #align real.exp_arsinh Real.exp_arsinh
 
 @[simp]

36938f77

bump to nightly-2023-06-07-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

831e78ce

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: James Arthur, Chris Hughes, Shing Tak Lam
 
 ! This file was ported from Lean 3 source module analysis.special_functions.arsinh
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.SpecialFunctions.Log.Basic
 /-!
 # Inverse of the sinh function
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove that sinh is bijective and hence has an
 inverse, arsinh.

f2ce6086

bump to nightly-2023-06-05-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725

62cd60d3

Diff

@@ -51,11 +51,13 @@ namespace Real
 
 variable {x y : ℝ}
 
+#print Real.arsinh /-
 /-- `arsinh` is defined using a logarithm, `arsinh x = log (x + sqrt(1 + x^2))`. -/
 @[pp_nodot]
 def arsinh (x : ℝ) :=
   log (x + sqrt (1 + x ^ 2))
 #align real.arsinh Real.arsinh
+-/
 
 theorem exp_arsinh (x : ℝ) : exp (arsinh x) = x + sqrt (1 + x ^ 2) :=
   by
@@ -80,33 +82,42 @@ theorem arsinh_neg (x : ℝ) : arsinh (-x) = -arsinh x :=
   exact add_nonneg zero_le_one (sq_nonneg _)
 #align real.arsinh_neg Real.arsinh_neg
 
+#print Real.sinh_arsinh /-
 /-- `arsinh` is the right inverse of `sinh`. -/
 @[simp]
 theorem sinh_arsinh (x : ℝ) : sinh (arsinh x) = x := by
   rw [sinh_eq, ← arsinh_neg, exp_arsinh, exp_arsinh, neg_sq]; field_simp
 #align real.sinh_arsinh Real.sinh_arsinh
+-/
 
 @[simp]
 theorem cosh_arsinh (x : ℝ) : cosh (arsinh x) = sqrt (1 + x ^ 2) := by
   rw [← sqrt_sq (cosh_pos _).le, cosh_sq', sinh_arsinh]
 #align real.cosh_arsinh Real.cosh_arsinh
 
+#print Real.sinh_surjective /-
 /-- `sinh` is surjective, `∀ b, ∃ a, sinh a = b`. In this case, we use `a = arsinh b`. -/
 theorem sinh_surjective : Surjective sinh :=
   LeftInverse.surjective sinh_arsinh
 #align real.sinh_surjective Real.sinh_surjective
+-/
 
+#print Real.sinh_bijective /-
 /-- `sinh` is bijective, both injective and surjective. -/
 theorem sinh_bijective : Bijective sinh :=
   ⟨sinh_injective, sinh_surjective⟩
 #align real.sinh_bijective Real.sinh_bijective
+-/
 
+#print Real.arsinh_sinh /-
 /-- `arsinh` is the left inverse of `sinh`. -/
 @[simp]
 theorem arsinh_sinh (x : ℝ) : arsinh (sinh x) = x :=
   rightInverse_of_injective_of_leftInverse sinh_injective sinh_arsinh x
 #align real.arsinh_sinh Real.arsinh_sinh
+-/
 
+#print Real.sinhEquiv /-
 /-- `real.sinh` as an `equiv`. -/
 @[simps]
 def sinhEquiv : ℝ ≃ ℝ where
@@ -115,6 +126,7 @@ def sinhEquiv : ℝ ≃ ℝ where
   left_inv := arsinh_sinh
   right_inv := sinh_arsinh
 #align real.sinh_equiv Real.sinhEquiv
+-/
 
 /-- `real.sinh` as an `order_iso`. -/
 @[simps (config := { fullyApplied := false })]
@@ -123,32 +135,44 @@ def sinhOrderIso : ℝ ≃o ℝ where
   map_rel_iff' := @sinh_le_sinh
 #align real.sinh_order_iso Real.sinhOrderIso
 
+#print Real.sinhHomeomorph /-
 /-- `real.sinh` as a `homeomorph`. -/
 @[simps (config := { fullyApplied := false })]
 def sinhHomeomorph : ℝ ≃ₜ ℝ :=
   sinhOrderIso.toHomeomorph
 #align real.sinh_homeomorph Real.sinhHomeomorph
+-/
 
+#print Real.arsinh_bijective /-
 theorem arsinh_bijective : Bijective arsinh :=
   sinhEquiv.symm.Bijective
 #align real.arsinh_bijective Real.arsinh_bijective
+-/
 
+#print Real.arsinh_injective /-
 theorem arsinh_injective : Injective arsinh :=
   sinhEquiv.symm.Injective
 #align real.arsinh_injective Real.arsinh_injective
+-/
 
+#print Real.arsinh_surjective /-
 theorem arsinh_surjective : Surjective arsinh :=
   sinhEquiv.symm.Surjective
 #align real.arsinh_surjective Real.arsinh_surjective
+-/
 
+#print Real.arsinh_strictMono /-
 theorem arsinh_strictMono : StrictMono arsinh :=
   sinhOrderIso.symm.StrictMono
 #align real.arsinh_strict_mono Real.arsinh_strictMono
+-/
 
+#print Real.arsinh_inj /-
 @[simp]
 theorem arsinh_inj : arsinh x = arsinh y ↔ x = y :=
   arsinh_injective.eq_iff
 #align real.arsinh_inj Real.arsinh_inj
+-/
 
 @[simp]
 theorem arsinh_le_arsinh : arsinh x ≤ arsinh y ↔ x ≤ y :=
@@ -195,48 +219,64 @@ theorem hasDerivAt_arsinh (x : ℝ) : HasDerivAt arsinh (sqrt (1 + x ^ 2))⁻¹
   (hasStrictDerivAt_arsinh x).HasDerivAt
 #align real.has_deriv_at_arsinh Real.hasDerivAt_arsinh
 
+#print Real.differentiable_arsinh /-
 theorem differentiable_arsinh : Differentiable ℝ arsinh := fun x =>
   (hasDerivAt_arsinh x).DifferentiableAt
 #align real.differentiable_arsinh Real.differentiable_arsinh
+-/
 
+#print Real.contDiff_arsinh /-
 theorem contDiff_arsinh {n : ℕ∞} : ContDiff ℝ n arsinh :=
   sinhHomeomorph.contDiff_symm_deriv (fun x => (cosh_pos x).ne') hasDerivAt_sinh contDiff_sinh
 #align real.cont_diff_arsinh Real.contDiff_arsinh
+-/
 
+#print Real.continuous_arsinh /-
 @[continuity]
 theorem continuous_arsinh : Continuous arsinh :=
   sinhHomeomorph.symm.Continuous
 #align real.continuous_arsinh Real.continuous_arsinh
+-/
 
 end Real
 
 open Real
 
+#print Filter.Tendsto.arsinh /-
 theorem Filter.Tendsto.arsinh {α : Type _} {l : Filter α} {f : α → ℝ} {a : ℝ}
     (h : Tendsto f l (𝓝 a)) : Tendsto (fun x => arsinh (f x)) l (𝓝 (arsinh a)) :=
   (continuous_arsinh.Tendsto _).comp h
 #align filter.tendsto.arsinh Filter.Tendsto.arsinh
+-/
 
 section Continuous
 
 variable {X : Type _} [TopologicalSpace X] {f : X → ℝ} {s : Set X} {a : X}
 
+#print ContinuousAt.arsinh /-
 theorem ContinuousAt.arsinh (h : ContinuousAt f a) : ContinuousAt (fun x => arsinh (f x)) a :=
   h.arsinh
 #align continuous_at.arsinh ContinuousAt.arsinh
+-/
 
+#print ContinuousWithinAt.arsinh /-
 theorem ContinuousWithinAt.arsinh (h : ContinuousWithinAt f s a) :
     ContinuousWithinAt (fun x => arsinh (f x)) s a :=
   h.arsinh
 #align continuous_within_at.arsinh ContinuousWithinAt.arsinh
+-/
 
+#print ContinuousOn.arsinh /-
 theorem ContinuousOn.arsinh (h : ContinuousOn f s) : ContinuousOn (fun x => arsinh (f x)) s :=
   fun x hx => (h x hx).arsinh
 #align continuous_on.arsinh ContinuousOn.arsinh
+-/
 
+#print Continuous.arsinh /-
 theorem Continuous.arsinh (h : Continuous f) : Continuous fun x => arsinh (f x) :=
   continuous_arsinh.comp h
 #align continuous.arsinh Continuous.arsinh
+-/
 
 end Continuous
 
@@ -260,40 +300,56 @@ theorem HasFDerivWithinAt.arsinh (hf : HasFDerivWithinAt f f' s a) :
   (hasDerivAt_arsinh _).comp_hasFDerivWithinAt a hf
 #align has_fderiv_within_at.arsinh HasFDerivWithinAt.arsinh
 
+#print DifferentiableAt.arsinh /-
 theorem DifferentiableAt.arsinh (h : DifferentiableAt ℝ f a) :
     DifferentiableAt ℝ (fun x => arsinh (f x)) a :=
   (differentiable_arsinh _).comp a h
 #align differentiable_at.arsinh DifferentiableAt.arsinh
+-/
 
+#print DifferentiableWithinAt.arsinh /-
 theorem DifferentiableWithinAt.arsinh (h : DifferentiableWithinAt ℝ f s a) :
     DifferentiableWithinAt ℝ (fun x => arsinh (f x)) s a :=
   (differentiable_arsinh _).comp_differentiableWithinAt a h
 #align differentiable_within_at.arsinh DifferentiableWithinAt.arsinh
+-/
 
+#print DifferentiableOn.arsinh /-
 theorem DifferentiableOn.arsinh (h : DifferentiableOn ℝ f s) :
     DifferentiableOn ℝ (fun x => arsinh (f x)) s := fun x hx => (h x hx).arsinh
 #align differentiable_on.arsinh DifferentiableOn.arsinh
+-/
 
+#print Differentiable.arsinh /-
 theorem Differentiable.arsinh (h : Differentiable ℝ f) : Differentiable ℝ fun x => arsinh (f x) :=
   differentiable_arsinh.comp h
 #align differentiable.arsinh Differentiable.arsinh
+-/
 
+#print ContDiffAt.arsinh /-
 theorem ContDiffAt.arsinh (h : ContDiffAt ℝ n f a) : ContDiffAt ℝ n (fun x => arsinh (f x)) a :=
   contDiff_arsinh.ContDiffAt.comp a h
 #align cont_diff_at.arsinh ContDiffAt.arsinh
+-/
 
+#print ContDiffWithinAt.arsinh /-
 theorem ContDiffWithinAt.arsinh (h : ContDiffWithinAt ℝ n f s a) :
     ContDiffWithinAt ℝ n (fun x => arsinh (f x)) s a :=
   contDiff_arsinh.ContDiffAt.comp_contDiffWithinAt a h
 #align cont_diff_within_at.arsinh ContDiffWithinAt.arsinh
+-/
 
+#print ContDiff.arsinh /-
 theorem ContDiff.arsinh (h : ContDiff ℝ n f) : ContDiff ℝ n fun x => arsinh (f x) :=
   contDiff_arsinh.comp h
 #align cont_diff.arsinh ContDiff.arsinh
+-/
 
+#print ContDiffOn.arsinh /-
 theorem ContDiffOn.arsinh (h : ContDiffOn ℝ n f s) : ContDiffOn ℝ n (fun x => arsinh (f x)) s :=
   fun x hx => (h x hx).arsinh
 #align cont_diff_on.arsinh ContDiffOn.arsinh
+-/
 
 end fderiv

f2ce6086

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -185,7 +185,8 @@ theorem arsinh_neg_iff : arsinh x < 0 ↔ x < 0 :=
 
 theorem hasStrictDerivAt_arsinh (x : ℝ) : HasStrictDerivAt arsinh (sqrt (1 + x ^ 2))⁻¹ x :=
   by
-  convert sinh_homeomorph.to_local_homeomorph.has_strict_deriv_at_symm (mem_univ x) (cosh_pos _).ne'
+  convert
+    sinh_homeomorph.to_local_homeomorph.has_strict_deriv_at_symm (mem_univ x) (cosh_pos _).ne'
       (has_strict_deriv_at_sinh _)
   exact (cosh_arsinh _).symm
 #align real.has_strict_deriv_at_arsinh Real.hasStrictDerivAt_arsinh

f2ce6086

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -45,7 +45,7 @@ noncomputable section
 
 open Function Filter Set
 
-open Topology
+open scoped Topology
 
 namespace Real

f2ce6086

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -82,10 +82,8 @@ theorem arsinh_neg (x : ℝ) : arsinh (-x) = -arsinh x :=
 
 /-- `arsinh` is the right inverse of `sinh`. -/
 @[simp]
-theorem sinh_arsinh (x : ℝ) : sinh (arsinh x) = x :=
-  by
-  rw [sinh_eq, ← arsinh_neg, exp_arsinh, exp_arsinh, neg_sq]
-  field_simp
+theorem sinh_arsinh (x : ℝ) : sinh (arsinh x) = x := by
+  rw [sinh_eq, ← arsinh_neg, exp_arsinh, exp_arsinh, neg_sq]; field_simp
 #align real.sinh_arsinh Real.sinh_arsinh
 
 @[simp]

f2ce6086

bump to nightly-2023-05-22-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

a4206c98

Diff

@@ -246,20 +246,20 @@ section fderiv
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {f : E → ℝ} {s : Set E} {a : E}
   {f' : E →L[ℝ] ℝ} {n : ℕ∞}
 
-theorem HasStrictFderivAt.arsinh (hf : HasStrictFderivAt f f' a) :
-    HasStrictFderivAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') a :=
-  (hasStrictDerivAt_arsinh _).comp_hasStrictFderivAt a hf
-#align has_strict_fderiv_at.arsinh HasStrictFderivAt.arsinh
-
-theorem HasFderivAt.arsinh (hf : HasFderivAt f f' a) :
-    HasFderivAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') a :=
-  (hasDerivAt_arsinh _).comp_hasFderivAt a hf
-#align has_fderiv_at.arsinh HasFderivAt.arsinh
-
-theorem HasFderivWithinAt.arsinh (hf : HasFderivWithinAt f f' s a) :
-    HasFderivWithinAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') s a :=
-  (hasDerivAt_arsinh _).comp_hasFderivWithinAt a hf
-#align has_fderiv_within_at.arsinh HasFderivWithinAt.arsinh
+theorem HasStrictFDerivAt.arsinh (hf : HasStrictFDerivAt f f' a) :
+    HasStrictFDerivAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') a :=
+  (hasStrictDerivAt_arsinh _).comp_hasStrictFDerivAt a hf
+#align has_strict_fderiv_at.arsinh HasStrictFDerivAt.arsinh
+
+theorem HasFDerivAt.arsinh (hf : HasFDerivAt f f' a) :
+    HasFDerivAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') a :=
+  (hasDerivAt_arsinh _).comp_hasFDerivAt a hf
+#align has_fderiv_at.arsinh HasFDerivAt.arsinh
+
+theorem HasFDerivWithinAt.arsinh (hf : HasFDerivWithinAt f f' s a) :
+    HasFDerivWithinAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') s a :=
+  (hasDerivAt_arsinh _).comp_hasFDerivWithinAt a hf
+#align has_fderiv_within_at.arsinh HasFDerivWithinAt.arsinh
 
 theorem DifferentiableAt.arsinh (h : DifferentiableAt ℝ f a) :
     DifferentiableAt ℝ (fun x => arsinh (f x)) a :=

f2ce6086

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -187,8 +187,7 @@ theorem arsinh_neg_iff : arsinh x < 0 ↔ x < 0 :=
 
 theorem hasStrictDerivAt_arsinh (x : ℝ) : HasStrictDerivAt arsinh (sqrt (1 + x ^ 2))⁻¹ x :=
   by
-  convert
-    sinh_homeomorph.to_local_homeomorph.has_strict_deriv_at_symm (mem_univ x) (cosh_pos _).ne'
+  convert sinh_homeomorph.to_local_homeomorph.has_strict_deriv_at_symm (mem_univ x) (cosh_pos _).ne'
       (has_strict_deriv_at_sinh _)
   exact (cosh_arsinh _).symm
 #align real.has_strict_deriv_at_arsinh Real.hasStrictDerivAt_arsinh

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

@@ -51,10 +51,10 @@ variable {x y : ℝ}
 /-- `arsinh` is defined using a logarithm, `arsinh x = log (x + sqrt(1 + x^2))`. -/
 -- @[pp_nodot] is no longer needed
 def arsinh (x : ℝ) :=
-  log (x + sqrt (1 + x ^ 2))
+  log (x + √(1 + x ^ 2))
 #align real.arsinh Real.arsinh
 
-theorem exp_arsinh (x : ℝ) : exp (arsinh x) = x + sqrt (1 + x ^ 2) := by
+theorem exp_arsinh (x : ℝ) : exp (arsinh x) = x + √(1 + x ^ 2) := by
   apply exp_log
   rw [← neg_lt_iff_pos_add']
   apply lt_sqrt_of_sq_lt
@@ -80,7 +80,7 @@ theorem sinh_arsinh (x : ℝ) : sinh (arsinh x) = x := by
 #align real.sinh_arsinh Real.sinh_arsinh
 
 @[simp]
-theorem cosh_arsinh (x : ℝ) : cosh (arsinh x) = sqrt (1 + x ^ 2) := by
+theorem cosh_arsinh (x : ℝ) : cosh (arsinh x) = √(1 + x ^ 2) := by
   rw [← sqrt_sq (cosh_pos _).le, cosh_sq', sinh_arsinh]
 #align real.cosh_arsinh Real.cosh_arsinh
 
@@ -178,13 +178,13 @@ theorem arsinh_neg_iff : arsinh x < 0 ↔ x < 0 :=
   lt_iff_lt_of_le_iff_le arsinh_nonneg_iff
 #align real.arsinh_neg_iff Real.arsinh_neg_iff
 
-theorem hasStrictDerivAt_arsinh (x : ℝ) : HasStrictDerivAt arsinh (sqrt (1 + x ^ 2))⁻¹ x := by
+theorem hasStrictDerivAt_arsinh (x : ℝ) : HasStrictDerivAt arsinh (√(1 + x ^ 2))⁻¹ x := by
   convert sinhHomeomorph.toPartialHomeomorph.hasStrictDerivAt_symm (mem_univ x) (cosh_pos _).ne'
     (hasStrictDerivAt_sinh _) using 2
   exact (cosh_arsinh _).symm
 #align real.has_strict_deriv_at_arsinh Real.hasStrictDerivAt_arsinh
 
-theorem hasDerivAt_arsinh (x : ℝ) : HasDerivAt arsinh (sqrt (1 + x ^ 2))⁻¹ x :=
+theorem hasDerivAt_arsinh (x : ℝ) : HasDerivAt arsinh (√(1 + x ^ 2))⁻¹ x :=
   (hasStrictDerivAt_arsinh x).hasDerivAt
 #align real.has_deriv_at_arsinh Real.hasDerivAt_arsinh
 
@@ -240,17 +240,17 @@ variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] {f : E → ℝ}
   {f' : E →L[ℝ] ℝ} {n : ℕ∞}
 
 theorem HasStrictFDerivAt.arsinh (hf : HasStrictFDerivAt f f' a) :
-    HasStrictFDerivAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') a :=
+    HasStrictFDerivAt (fun x => arsinh (f x)) ((√(1 + f a ^ 2))⁻¹ • f') a :=
   (hasStrictDerivAt_arsinh _).comp_hasStrictFDerivAt a hf
 #align has_strict_fderiv_at.arsinh HasStrictFDerivAt.arsinh
 
 theorem HasFDerivAt.arsinh (hf : HasFDerivAt f f' a) :
-    HasFDerivAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') a :=
+    HasFDerivAt (fun x => arsinh (f x)) ((√(1 + f a ^ 2))⁻¹ • f') a :=
   (hasDerivAt_arsinh _).comp_hasFDerivAt a hf
 #align has_fderiv_at.arsinh HasFDerivAt.arsinh
 
 theorem HasFDerivWithinAt.arsinh (hf : HasFDerivWithinAt f f' s a) :
-    HasFDerivWithinAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') s a :=
+    HasFDerivWithinAt (fun x => arsinh (f x)) ((√(1 + f a ^ 2))⁻¹ • f') s a :=
   (hasDerivAt_arsinh _).comp_hasFDerivWithinAt a hf
 #align has_fderiv_within_at.arsinh HasFDerivWithinAt.arsinh
 
@@ -296,17 +296,17 @@ section deriv
 variable {f : ℝ → ℝ} {s : Set ℝ} {a f' : ℝ}
 
 theorem HasStrictDerivAt.arsinh (hf : HasStrictDerivAt f f' a) :
-    HasStrictDerivAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') a :=
+    HasStrictDerivAt (fun x => arsinh (f x)) ((√(1 + f a ^ 2))⁻¹ • f') a :=
   (hasStrictDerivAt_arsinh _).comp a hf
 #align has_strict_deriv_at.arsinh HasStrictDerivAt.arsinh
 
 theorem HasDerivAt.arsinh (hf : HasDerivAt f f' a) :
-    HasDerivAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') a :=
+    HasDerivAt (fun x => arsinh (f x)) ((√(1 + f a ^ 2))⁻¹ • f') a :=
   (hasDerivAt_arsinh _).comp a hf
 #align has_deriv_at.arsinh HasDerivAt.arsinh
 
 theorem HasDerivWithinAt.arsinh (hf : HasDerivWithinAt f f' s a) :
-    HasDerivWithinAt (fun x => arsinh (f x)) ((sqrt (1 + f a ^ 2))⁻¹ • f') s a :=
+    HasDerivWithinAt (fun x => arsinh (f x)) ((√(1 + f a ^ 2))⁻¹ • f') s a :=
   (hasDerivAt_arsinh _).comp_hasDerivWithinAt a hf
 #align has_deriv_within_at.arsinh HasDerivWithinAt.arsinh

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

@@ -69,7 +69,7 @@ theorem arsinh_zero : arsinh 0 = 0 := by simp [arsinh]
 theorem arsinh_neg (x : ℝ) : arsinh (-x) = -arsinh x := by
   rw [← exp_eq_exp, exp_arsinh, exp_neg, exp_arsinh]
   apply eq_inv_of_mul_eq_one_left
-  rw [neg_sq, neg_add_eq_sub, add_comm x, mul_comm, ← sq_sub_sq, sq_sqrt, add_sub_cancel]
+  rw [neg_sq, neg_add_eq_sub, add_comm x, mul_comm, ← sq_sub_sq, sq_sqrt, add_sub_cancel_right]
   exact add_nonneg zero_le_one (sq_nonneg _)
 #align real.arsinh_neg Real.arsinh_neg

f2ce6086

chore: Rename monotonicity of / lemmas (#10634)

The new names and argument orders match the corresponding * lemmas, which I already took care of in a previous PR.

From LeanAPAP

c8e50e0c

Diff

@@ -148,6 +148,8 @@ theorem arsinh_le_arsinh : arsinh x ≤ arsinh y ↔ x ≤ y :=
   sinhOrderIso.symm.le_iff_le
 #align real.arsinh_le_arsinh Real.arsinh_le_arsinh
 
+@[gcongr] protected alias ⟨_, GCongr.arsinh_le_arsinh⟩ := arsinh_le_arsinh
+
 @[simp]
 theorem arsinh_lt_arsinh : arsinh x < arsinh y ↔ x < y :=
   sinhOrderIso.symm.lt_iff_lt

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

@@ -177,7 +177,7 @@ theorem arsinh_neg_iff : arsinh x < 0 ↔ x < 0 :=
 #align real.arsinh_neg_iff Real.arsinh_neg_iff
 
 theorem hasStrictDerivAt_arsinh (x : ℝ) : HasStrictDerivAt arsinh (sqrt (1 + x ^ 2))⁻¹ x := by
-  convert sinhHomeomorph.toLocalHomeomorph.hasStrictDerivAt_symm (mem_univ x) (cosh_pos _).ne'
+  convert sinhHomeomorph.toPartialHomeomorph.hasStrictDerivAt_symm (mem_univ x) (cosh_pos _).ne'
     (hasStrictDerivAt_sinh _) using 2
   exact (cosh_arsinh _).symm
 #align real.has_strict_deriv_at_arsinh Real.hasStrictDerivAt_arsinh

f2ce6086

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -203,14 +203,14 @@ end Real
 
 open Real
 
-theorem Filter.Tendsto.arsinh {α : Type _} {l : Filter α} {f : α → ℝ} {a : ℝ}
+theorem Filter.Tendsto.arsinh {α : Type*} {l : Filter α} {f : α → ℝ} {a : ℝ}
     (h : Tendsto f l (𝓝 a)) : Tendsto (fun x => arsinh (f x)) l (𝓝 (arsinh a)) :=
   (continuous_arsinh.tendsto _).comp h
 #align filter.tendsto.arsinh Filter.Tendsto.arsinh
 
 section Continuous
 
-variable {X : Type _} [TopologicalSpace X] {f : X → ℝ} {s : Set X} {a : X}
+variable {X : Type*} [TopologicalSpace X] {f : X → ℝ} {s : Set X} {a : X}
 
 nonrec theorem ContinuousAt.arsinh (h : ContinuousAt f a) :
     ContinuousAt (fun x => arsinh (f x)) a :=
@@ -234,7 +234,7 @@ end Continuous
 
 section fderiv
 
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {f : E → ℝ} {s : Set E} {a : E}
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] {f : E → ℝ} {s : Set E} {a : E}
   {f' : E →L[ℝ] ℝ} {n : ℕ∞}
 
 theorem HasStrictFDerivAt.arsinh (hf : HasStrictFDerivAt f f' a) :

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 James Arthur. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: James Arthur, Chris Hughes, Shing Tak Lam
-
-! This file was ported from Lean 3 source module analysis.special_functions.arsinh
-! 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.Deriv
 import Mathlib.Analysis.SpecialFunctions.Log.Basic
 
+#align_import analysis.special_functions.arsinh from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Inverse of the sinh function

f2ce6086

feat: port Analysis.SpecialFunctions.Arsinh (#4674)

311c2413

`analysis.special_functions.arsinh` ⟷ `Mathlib.Analysis.SpecialFunctions.Arsinh`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 901

analysis.special_functions.arsinh ⟷ Mathlib.Analysis.SpecialFunctions.Arsinh

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 901

`analysis.special_functions.arsinh` ⟷ `Mathlib.Analysis.SpecialFunctions.Arsinh`