analysis.special_functions.sqrt | 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

575b4ea3

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Analysis.Calculus.ContDiff
+import Analysis.Calculus.ContDiff.Basic
 
 #align_import analysis.special_functions.sqrt from "leanprover-community/mathlib"@"575b4ea3738b017e30fb205cb9b4a8742e5e82b6"

575b4ea3

bump to nightly-2023-12-13-12

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

19154cfe

Diff

@@ -28,10 +28,10 @@ open scoped Topology
 
 namespace Real
 
-#print Real.sqLocalHomeomorph /-
+#print Real.sqPartialHomeomorph /-
 /-- Local homeomorph between `(0, +∞)` and `(0, +∞)` with `to_fun = λ x, x ^ 2` and
 `inv_fun = sqrt`. -/
-noncomputable def sqLocalHomeomorph : LocalHomeomorph ℝ ℝ
+noncomputable def sqPartialHomeomorph : PartialHomeomorph ℝ ℝ
     where
   toFun x := x ^ 2
   invFun := sqrt
@@ -45,7 +45,7 @@ noncomputable def sqLocalHomeomorph : LocalHomeomorph ℝ ℝ
   open_target := isOpen_Ioi
   continuous_toFun := (continuous_pow 2).ContinuousOn
   continuous_invFun := continuousOn_id.sqrt
-#align real.sq_local_homeomorph Real.sqLocalHomeomorph
+#align real.sq_local_homeomorph Real.sqPartialHomeomorph
 -/
 
 #print Real.deriv_sqrt_aux /-

575b4ea3

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) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Mathbin.Analysis.Calculus.ContDiff
+import Analysis.Calculus.ContDiff
 
 #align_import analysis.special_functions.sqrt from "leanprover-community/mathlib"@"575b4ea3738b017e30fb205cb9b4a8742e5e82b6"

575b4ea3

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) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module analysis.special_functions.sqrt
-! leanprover-community/mathlib commit 575b4ea3738b017e30fb205cb9b4a8742e5e82b6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.ContDiff
 
+#align_import analysis.special_functions.sqrt from "leanprover-community/mathlib"@"575b4ea3738b017e30fb205cb9b4a8742e5e82b6"
+
 /-!
 # Smoothness of `real.sqrt`

575b4ea3

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -51,6 +51,7 @@ noncomputable def sqLocalHomeomorph : LocalHomeomorph ℝ ℝ
 #align real.sq_local_homeomorph Real.sqLocalHomeomorph
 -/
 
+#print Real.deriv_sqrt_aux /-
 theorem deriv_sqrt_aux {x : ℝ} (hx : x ≠ 0) :
     HasStrictDerivAt sqrt (1 / (2 * sqrt x)) x ∧ ∀ n, ContDiffAt ℝ n sqrt x :=
   by
@@ -68,18 +69,25 @@ theorem deriv_sqrt_aux {x : ℝ} (hx : x ≠ 0) :
         sq_local_homeomorph.cont_diff_at_symm_deriv this hx (hasDerivAt_pow 2 (sqrt x))
           (cont_diff_at_id.pow 2)
 #align real.deriv_sqrt_aux Real.deriv_sqrt_aux
+-/
 
+#print Real.hasStrictDerivAt_sqrt /-
 theorem hasStrictDerivAt_sqrt {x : ℝ} (hx : x ≠ 0) : HasStrictDerivAt sqrt (1 / (2 * sqrt x)) x :=
   (deriv_sqrt_aux hx).1
 #align real.has_strict_deriv_at_sqrt Real.hasStrictDerivAt_sqrt
+-/
 
+#print Real.contDiffAt_sqrt /-
 theorem contDiffAt_sqrt {x : ℝ} {n : ℕ∞} (hx : x ≠ 0) : ContDiffAt ℝ n sqrt x :=
   (deriv_sqrt_aux hx).2 n
 #align real.cont_diff_at_sqrt Real.contDiffAt_sqrt
+-/
 
+#print Real.hasDerivAt_sqrt /-
 theorem hasDerivAt_sqrt {x : ℝ} (hx : x ≠ 0) : HasDerivAt sqrt (1 / (2 * sqrt x)) x :=
   (hasStrictDerivAt_sqrt hx).HasDerivAt
 #align real.has_deriv_at_sqrt Real.hasDerivAt_sqrt
+-/
 
 end Real
 
@@ -89,33 +97,43 @@ section deriv
 
 variable {f : ℝ → ℝ} {s : Set ℝ} {f' x : ℝ}
 
+#print HasDerivWithinAt.sqrt /-
 theorem HasDerivWithinAt.sqrt (hf : HasDerivWithinAt f f' s x) (hx : f x ≠ 0) :
     HasDerivWithinAt (fun y => sqrt (f y)) (f' / (2 * sqrt (f x))) s x := by
   simpa only [(· ∘ ·), div_eq_inv_mul, mul_one] using
     (has_deriv_at_sqrt hx).comp_hasDerivWithinAt x hf
 #align has_deriv_within_at.sqrt HasDerivWithinAt.sqrt
+-/
 
+#print HasDerivAt.sqrt /-
 theorem HasDerivAt.sqrt (hf : HasDerivAt f f' x) (hx : f x ≠ 0) :
     HasDerivAt (fun y => sqrt (f y)) (f' / (2 * sqrt (f x))) x := by
   simpa only [(· ∘ ·), div_eq_inv_mul, mul_one] using (has_deriv_at_sqrt hx).comp x hf
 #align has_deriv_at.sqrt HasDerivAt.sqrt
+-/
 
+#print HasStrictDerivAt.sqrt /-
 theorem HasStrictDerivAt.sqrt (hf : HasStrictDerivAt f f' x) (hx : f x ≠ 0) :
     HasStrictDerivAt (fun t => sqrt (f t)) (f' / (2 * sqrt (f x))) x := by
   simpa only [(· ∘ ·), div_eq_inv_mul, mul_one] using (has_strict_deriv_at_sqrt hx).comp x hf
 #align has_strict_deriv_at.sqrt HasStrictDerivAt.sqrt
+-/
 
+#print derivWithin_sqrt /-
 theorem derivWithin_sqrt (hf : DifferentiableWithinAt ℝ f s x) (hx : f x ≠ 0)
     (hxs : UniqueDiffWithinAt ℝ s x) :
     derivWithin (fun x => sqrt (f x)) s x = derivWithin f s x / (2 * sqrt (f x)) :=
   (hf.HasDerivWithinAt.sqrt hx).derivWithin hxs
 #align deriv_within_sqrt derivWithin_sqrt
+-/
 
+#print deriv_sqrt /-
 @[simp]
 theorem deriv_sqrt (hf : DifferentiableAt ℝ f x) (hx : f x ≠ 0) :
     deriv (fun x => sqrt (f x)) x = deriv f x / (2 * sqrt (f x)) :=
   (hf.HasDerivAt.sqrt hx).deriv
 #align deriv_sqrt deriv_sqrt
+-/
 
 end deriv
 
@@ -124,68 +142,94 @@ section fderiv
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {f : E → ℝ} {n : ℕ∞} {s : Set E}
   {x : E} {f' : E →L[ℝ] ℝ}
 
+#print HasFDerivAt.sqrt /-
 theorem HasFDerivAt.sqrt (hf : HasFDerivAt f f' x) (hx : f x ≠ 0) :
     HasFDerivAt (fun y => sqrt (f y)) ((1 / (2 * sqrt (f x))) • f') x :=
   (hasDerivAt_sqrt hx).comp_hasFDerivAt x hf
 #align has_fderiv_at.sqrt HasFDerivAt.sqrt
+-/
 
+#print HasStrictFDerivAt.sqrt /-
 theorem HasStrictFDerivAt.sqrt (hf : HasStrictFDerivAt f f' x) (hx : f x ≠ 0) :
     HasStrictFDerivAt (fun y => sqrt (f y)) ((1 / (2 * sqrt (f x))) • f') x :=
   (hasStrictDerivAt_sqrt hx).comp_hasStrictFDerivAt x hf
 #align has_strict_fderiv_at.sqrt HasStrictFDerivAt.sqrt
+-/
 
+#print HasFDerivWithinAt.sqrt /-
 theorem HasFDerivWithinAt.sqrt (hf : HasFDerivWithinAt f f' s x) (hx : f x ≠ 0) :
     HasFDerivWithinAt (fun y => sqrt (f y)) ((1 / (2 * sqrt (f x))) • f') s x :=
   (hasDerivAt_sqrt hx).comp_hasFDerivWithinAt x hf
 #align has_fderiv_within_at.sqrt HasFDerivWithinAt.sqrt
+-/
 
+#print DifferentiableWithinAt.sqrt /-
 theorem DifferentiableWithinAt.sqrt (hf : DifferentiableWithinAt ℝ f s x) (hx : f x ≠ 0) :
     DifferentiableWithinAt ℝ (fun y => sqrt (f y)) s x :=
   (hf.HasFDerivWithinAt.sqrt hx).DifferentiableWithinAt
 #align differentiable_within_at.sqrt DifferentiableWithinAt.sqrt
+-/
 
+#print DifferentiableAt.sqrt /-
 theorem DifferentiableAt.sqrt (hf : DifferentiableAt ℝ f x) (hx : f x ≠ 0) :
     DifferentiableAt ℝ (fun y => sqrt (f y)) x :=
   (hf.HasFDerivAt.sqrt hx).DifferentiableAt
 #align differentiable_at.sqrt DifferentiableAt.sqrt
+-/
 
+#print DifferentiableOn.sqrt /-
 theorem DifferentiableOn.sqrt (hf : DifferentiableOn ℝ f s) (hs : ∀ x ∈ s, f x ≠ 0) :
     DifferentiableOn ℝ (fun y => sqrt (f y)) s := fun x hx => (hf x hx).sqrt (hs x hx)
 #align differentiable_on.sqrt DifferentiableOn.sqrt
+-/
 
+#print Differentiable.sqrt /-
 theorem Differentiable.sqrt (hf : Differentiable ℝ f) (hs : ∀ x, f x ≠ 0) :
     Differentiable ℝ fun y => sqrt (f y) := fun x => (hf x).sqrt (hs x)
 #align differentiable.sqrt Differentiable.sqrt
+-/
 
+#print fderivWithin_sqrt /-
 theorem fderivWithin_sqrt (hf : DifferentiableWithinAt ℝ f s x) (hx : f x ≠ 0)
     (hxs : UniqueDiffWithinAt ℝ s x) :
     fderivWithin ℝ (fun x => sqrt (f x)) s x = (1 / (2 * sqrt (f x))) • fderivWithin ℝ f s x :=
   (hf.HasFDerivWithinAt.sqrt hx).fderivWithin hxs
 #align fderiv_within_sqrt fderivWithin_sqrt
+-/
 
+#print fderiv_sqrt /-
 @[simp]
 theorem fderiv_sqrt (hf : DifferentiableAt ℝ f x) (hx : f x ≠ 0) :
     fderiv ℝ (fun x => sqrt (f x)) x = (1 / (2 * sqrt (f x))) • fderiv ℝ f x :=
   (hf.HasFDerivAt.sqrt hx).fderiv
 #align fderiv_sqrt fderiv_sqrt
+-/
 
+#print ContDiffAt.sqrt /-
 theorem ContDiffAt.sqrt (hf : ContDiffAt ℝ n f x) (hx : f x ≠ 0) :
     ContDiffAt ℝ n (fun y => sqrt (f y)) x :=
   (contDiffAt_sqrt hx).comp x hf
 #align cont_diff_at.sqrt ContDiffAt.sqrt
+-/
 
+#print ContDiffWithinAt.sqrt /-
 theorem ContDiffWithinAt.sqrt (hf : ContDiffWithinAt ℝ n f s x) (hx : f x ≠ 0) :
     ContDiffWithinAt ℝ n (fun y => sqrt (f y)) s x :=
   (contDiffAt_sqrt hx).comp_contDiffWithinAt x hf
 #align cont_diff_within_at.sqrt ContDiffWithinAt.sqrt
+-/
 
+#print ContDiffOn.sqrt /-
 theorem ContDiffOn.sqrt (hf : ContDiffOn ℝ n f s) (hs : ∀ x ∈ s, f x ≠ 0) :
     ContDiffOn ℝ n (fun y => sqrt (f y)) s := fun x hx => (hf x hx).sqrt (hs x hx)
 #align cont_diff_on.sqrt ContDiffOn.sqrt
+-/
 
+#print ContDiff.sqrt /-
 theorem ContDiff.sqrt (hf : ContDiff ℝ n f) (h : ∀ x, f x ≠ 0) : ContDiff ℝ n fun y => sqrt (f y) :=
   contDiff_iff_contDiffAt.2 fun x => hf.ContDiffAt.sqrt (h x)
 #align cont_diff.sqrt ContDiff.sqrt
+-/
 
 end fderiv

575b4ea3

bump to nightly-2023-06-06-03

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

90f9e14f

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.special_functions.sqrt
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 575b4ea3738b017e30fb205cb9b4a8742e5e82b6
 ! 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.Calculus.ContDiff
 /-!
 # Smoothness of `real.sqrt`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove that `real.sqrt` is infinitely smooth at all points `x ≠ 0` and provide some
 dot-notation lemmas.

f2ce6086

bump to nightly-2023-06-04-22

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

3d1af1b2

Diff

@@ -28,6 +28,7 @@ open scoped Topology
 
 namespace Real
 
+#print Real.sqLocalHomeomorph /-
 /-- Local homeomorph between `(0, +∞)` and `(0, +∞)` with `to_fun = λ x, x ^ 2` and
 `inv_fun = sqrt`. -/
 noncomputable def sqLocalHomeomorph : LocalHomeomorph ℝ ℝ
@@ -45,6 +46,7 @@ noncomputable def sqLocalHomeomorph : LocalHomeomorph ℝ ℝ
   continuous_toFun := (continuous_pow 2).ContinuousOn
   continuous_invFun := continuousOn_id.sqrt
 #align real.sq_local_homeomorph Real.sqLocalHomeomorph
+-/
 
 theorem deriv_sqrt_aux {x : ℝ} (hx : x ≠ 0) :
     HasStrictDerivAt sqrt (1 / (2 * sqrt x)) x ∧ ∀ n, ContDiffAt ℝ n sqrt x :=

f2ce6086

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -24,7 +24,7 @@ sqrt, differentiable
 
 open Set
 
-open Topology
+open scoped Topology
 
 namespace Real

f2ce6086

bump to nightly-2023-05-22-01

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

a4206c98

Diff

@@ -119,29 +119,29 @@ section fderiv
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {f : E → ℝ} {n : ℕ∞} {s : Set E}
   {x : E} {f' : E →L[ℝ] ℝ}
 
-theorem HasFderivAt.sqrt (hf : HasFderivAt f f' x) (hx : f x ≠ 0) :
-    HasFderivAt (fun y => sqrt (f y)) ((1 / (2 * sqrt (f x))) • f') x :=
-  (hasDerivAt_sqrt hx).comp_hasFderivAt x hf
-#align has_fderiv_at.sqrt HasFderivAt.sqrt
+theorem HasFDerivAt.sqrt (hf : HasFDerivAt f f' x) (hx : f x ≠ 0) :
+    HasFDerivAt (fun y => sqrt (f y)) ((1 / (2 * sqrt (f x))) • f') x :=
+  (hasDerivAt_sqrt hx).comp_hasFDerivAt x hf
+#align has_fderiv_at.sqrt HasFDerivAt.sqrt
 
-theorem HasStrictFderivAt.sqrt (hf : HasStrictFderivAt f f' x) (hx : f x ≠ 0) :
-    HasStrictFderivAt (fun y => sqrt (f y)) ((1 / (2 * sqrt (f x))) • f') x :=
-  (hasStrictDerivAt_sqrt hx).comp_hasStrictFderivAt x hf
-#align has_strict_fderiv_at.sqrt HasStrictFderivAt.sqrt
+theorem HasStrictFDerivAt.sqrt (hf : HasStrictFDerivAt f f' x) (hx : f x ≠ 0) :
+    HasStrictFDerivAt (fun y => sqrt (f y)) ((1 / (2 * sqrt (f x))) • f') x :=
+  (hasStrictDerivAt_sqrt hx).comp_hasStrictFDerivAt x hf
+#align has_strict_fderiv_at.sqrt HasStrictFDerivAt.sqrt
 
-theorem HasFderivWithinAt.sqrt (hf : HasFderivWithinAt f f' s x) (hx : f x ≠ 0) :
-    HasFderivWithinAt (fun y => sqrt (f y)) ((1 / (2 * sqrt (f x))) • f') s x :=
-  (hasDerivAt_sqrt hx).comp_hasFderivWithinAt x hf
-#align has_fderiv_within_at.sqrt HasFderivWithinAt.sqrt
+theorem HasFDerivWithinAt.sqrt (hf : HasFDerivWithinAt f f' s x) (hx : f x ≠ 0) :
+    HasFDerivWithinAt (fun y => sqrt (f y)) ((1 / (2 * sqrt (f x))) • f') s x :=
+  (hasDerivAt_sqrt hx).comp_hasFDerivWithinAt x hf
+#align has_fderiv_within_at.sqrt HasFDerivWithinAt.sqrt
 
 theorem DifferentiableWithinAt.sqrt (hf : DifferentiableWithinAt ℝ f s x) (hx : f x ≠ 0) :
     DifferentiableWithinAt ℝ (fun y => sqrt (f y)) s x :=
-  (hf.HasFderivWithinAt.sqrt hx).DifferentiableWithinAt
+  (hf.HasFDerivWithinAt.sqrt hx).DifferentiableWithinAt
 #align differentiable_within_at.sqrt DifferentiableWithinAt.sqrt
 
 theorem DifferentiableAt.sqrt (hf : DifferentiableAt ℝ f x) (hx : f x ≠ 0) :
     DifferentiableAt ℝ (fun y => sqrt (f y)) x :=
-  (hf.HasFderivAt.sqrt hx).DifferentiableAt
+  (hf.HasFDerivAt.sqrt hx).DifferentiableAt
 #align differentiable_at.sqrt DifferentiableAt.sqrt
 
 theorem DifferentiableOn.sqrt (hf : DifferentiableOn ℝ f s) (hs : ∀ x ∈ s, f x ≠ 0) :
@@ -155,13 +155,13 @@ theorem Differentiable.sqrt (hf : Differentiable ℝ f) (hs : ∀ x, f x ≠ 0)
 theorem fderivWithin_sqrt (hf : DifferentiableWithinAt ℝ f s x) (hx : f x ≠ 0)
     (hxs : UniqueDiffWithinAt ℝ s x) :
     fderivWithin ℝ (fun x => sqrt (f x)) s x = (1 / (2 * sqrt (f x))) • fderivWithin ℝ f s x :=
-  (hf.HasFderivWithinAt.sqrt hx).fderivWithin hxs
+  (hf.HasFDerivWithinAt.sqrt hx).fderivWithin hxs
 #align fderiv_within_sqrt fderivWithin_sqrt
 
 @[simp]
 theorem fderiv_sqrt (hf : DifferentiableAt ℝ f x) (hx : f x ≠ 0) :
     fderiv ℝ (fun x => sqrt (f x)) x = (1 / (2 * sqrt (f x))) • fderiv ℝ f x :=
-  (hf.HasFderivAt.sqrt hx).fderiv
+  (hf.HasFDerivAt.sqrt hx).fderiv
 #align fderiv_sqrt fderiv_sqrt
 
 theorem ContDiffAt.sqrt (hf : ContDiffAt ℝ n f x) (hx : f x ≠ 0) :

f2ce6086

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -50,7 +50,7 @@ theorem deriv_sqrt_aux {x : ℝ} (hx : x ≠ 0) :
     HasStrictDerivAt sqrt (1 / (2 * sqrt x)) x ∧ ∀ n, ContDiffAt ℝ n sqrt x :=
   by
   cases' hx.lt_or_lt with hx hx
-  · rw [sqrt_eq_zero_of_nonpos hx.le, mul_zero, div_zero]
+  · rw [sqrt_eq_zero_of_nonpos hx.le, MulZeroClass.mul_zero, div_zero]
     have : sqrt =ᶠ[𝓝 x] fun _ => 0 := (gt_mem_nhds hx).mono fun x hx => sqrt_eq_zero_of_nonpos hx.le
     exact
       ⟨(hasStrictDerivAt_const x (0 : ℝ)).congr_of_eventuallyEq this.symm, fun n =>

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

@@ -30,7 +30,7 @@ namespace Real
 `invFun = Real.sqrt`. -/
 noncomputable def sqPartialHomeomorph : PartialHomeomorph ℝ ℝ where
   toFun x := x ^ 2
-  invFun := sqrt
+  invFun := (√·)
   source := Ioi 0
   target := Ioi 0
   map_source' _ h := mem_Ioi.2 (pow_pos (mem_Ioi.1 h) _)
@@ -44,29 +44,29 @@ noncomputable def sqPartialHomeomorph : PartialHomeomorph ℝ ℝ where
 #align real.sq_local_homeomorph Real.sqPartialHomeomorph
 
 theorem deriv_sqrt_aux {x : ℝ} (hx : x ≠ 0) :
-    HasStrictDerivAt sqrt (1 / (2 * sqrt x)) x ∧ ∀ n, ContDiffAt ℝ n sqrt x := by
+    HasStrictDerivAt (√·) (1 / (2 * √x)) x ∧ ∀ n, ContDiffAt ℝ n (√·) x := by
   cases' hx.lt_or_lt with hx hx
   · rw [sqrt_eq_zero_of_nonpos hx.le, mul_zero, div_zero]
-    have : sqrt =ᶠ[𝓝 x] fun _ => 0 := (gt_mem_nhds hx).mono fun x hx => sqrt_eq_zero_of_nonpos hx.le
+    have : (√·) =ᶠ[𝓝 x] fun _ => 0 := (gt_mem_nhds hx).mono fun x hx => sqrt_eq_zero_of_nonpos hx.le
     exact
       ⟨(hasStrictDerivAt_const x (0 : ℝ)).congr_of_eventuallyEq this.symm, fun n =>
         contDiffAt_const.congr_of_eventuallyEq this⟩
-  · have : ↑2 * sqrt x ^ (2 - 1) ≠ 0 := by simp [(sqrt_pos.2 hx).ne', @two_ne_zero ℝ]
+  · have : ↑2 * √x ^ (2 - 1) ≠ 0 := by simp [(sqrt_pos.2 hx).ne', @two_ne_zero ℝ]
     constructor
     · simpa using sqPartialHomeomorph.hasStrictDerivAt_symm hx this (hasStrictDerivAt_pow 2 _)
-    · exact fun n => sqPartialHomeomorph.contDiffAt_symm_deriv this hx (hasDerivAt_pow 2 (sqrt x))
+    · exact fun n => sqPartialHomeomorph.contDiffAt_symm_deriv this hx (hasDerivAt_pow 2 (√x))
         (contDiffAt_id.pow 2)
 #align real.deriv_sqrt_aux Real.deriv_sqrt_aux
 
-theorem hasStrictDerivAt_sqrt {x : ℝ} (hx : x ≠ 0) : HasStrictDerivAt sqrt (1 / (2 * sqrt x)) x :=
+theorem hasStrictDerivAt_sqrt {x : ℝ} (hx : x ≠ 0) : HasStrictDerivAt (√·) (1 / (2 * √x)) x :=
   (deriv_sqrt_aux hx).1
 #align real.has_strict_deriv_at_sqrt Real.hasStrictDerivAt_sqrt
 
-theorem contDiffAt_sqrt {x : ℝ} {n : ℕ∞} (hx : x ≠ 0) : ContDiffAt ℝ n sqrt x :=
+theorem contDiffAt_sqrt {x : ℝ} {n : ℕ∞} (hx : x ≠ 0) : ContDiffAt ℝ n (√·) x :=
   (deriv_sqrt_aux hx).2 n
 #align real.cont_diff_at_sqrt Real.contDiffAt_sqrt
 
-theorem hasDerivAt_sqrt {x : ℝ} (hx : x ≠ 0) : HasDerivAt sqrt (1 / (2 * sqrt x)) x :=
+theorem hasDerivAt_sqrt {x : ℝ} (hx : x ≠ 0) : HasDerivAt (√·) (1 / (2 * √x)) x :=
   (hasStrictDerivAt_sqrt hx).hasDerivAt
 #align real.has_deriv_at_sqrt Real.hasDerivAt_sqrt
 
@@ -79,30 +79,30 @@ section deriv
 variable {f : ℝ → ℝ} {s : Set ℝ} {f' x : ℝ}
 
 theorem HasDerivWithinAt.sqrt (hf : HasDerivWithinAt f f' s x) (hx : f x ≠ 0) :
-    HasDerivWithinAt (fun y => sqrt (f y)) (f' / (2 * sqrt (f x))) s x := by
+    HasDerivWithinAt (fun y => √(f y)) (f' / (2 * √(f x))) s x := by
   simpa only [(· ∘ ·), div_eq_inv_mul, mul_one] using
     (hasDerivAt_sqrt hx).comp_hasDerivWithinAt x hf
 #align has_deriv_within_at.sqrt HasDerivWithinAt.sqrt
 
 theorem HasDerivAt.sqrt (hf : HasDerivAt f f' x) (hx : f x ≠ 0) :
-    HasDerivAt (fun y => sqrt (f y)) (f' / (2 * sqrt (f x))) x := by
+    HasDerivAt (fun y => √(f y)) (f' / (2 * √(f x))) x := by
   simpa only [(· ∘ ·), div_eq_inv_mul, mul_one] using (hasDerivAt_sqrt hx).comp x hf
 #align has_deriv_at.sqrt HasDerivAt.sqrt
 
 theorem HasStrictDerivAt.sqrt (hf : HasStrictDerivAt f f' x) (hx : f x ≠ 0) :
-    HasStrictDerivAt (fun t => sqrt (f t)) (f' / (2 * sqrt (f x))) x := by
+    HasStrictDerivAt (fun t => √(f t)) (f' / (2 * √(f x))) x := by
   simpa only [(· ∘ ·), div_eq_inv_mul, mul_one] using (hasStrictDerivAt_sqrt hx).comp x hf
 #align has_strict_deriv_at.sqrt HasStrictDerivAt.sqrt
 
 theorem derivWithin_sqrt (hf : DifferentiableWithinAt ℝ f s x) (hx : f x ≠ 0)
     (hxs : UniqueDiffWithinAt ℝ s x) :
-    derivWithin (fun x => sqrt (f x)) s x = derivWithin f s x / (2 * sqrt (f x)) :=
+    derivWithin (fun x => √(f x)) s x = derivWithin f s x / (2 * √(f x)) :=
   (hf.hasDerivWithinAt.sqrt hx).derivWithin hxs
 #align deriv_within_sqrt derivWithin_sqrt
 
 @[simp]
 theorem deriv_sqrt (hf : DifferentiableAt ℝ f x) (hx : f x ≠ 0) :
-    deriv (fun x => sqrt (f x)) x = deriv f x / (2 * sqrt (f x)) :=
+    deriv (fun x => √(f x)) x = deriv f x / (2 * √(f x)) :=
   (hf.hasDerivAt.sqrt hx).deriv
 #align deriv_sqrt deriv_sqrt
 
@@ -114,65 +114,65 @@ variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] {f : E → ℝ}
   {x : E} {f' : E →L[ℝ] ℝ}
 
 theorem HasFDerivAt.sqrt (hf : HasFDerivAt f f' x) (hx : f x ≠ 0) :
-    HasFDerivAt (fun y => sqrt (f y)) ((1 / (2 * sqrt (f x))) • f') x :=
+    HasFDerivAt (fun y => √(f y)) ((1 / (2 * √(f x))) • f') x :=
   (hasDerivAt_sqrt hx).comp_hasFDerivAt x hf
 #align has_fderiv_at.sqrt HasFDerivAt.sqrt
 
 theorem HasStrictFDerivAt.sqrt (hf : HasStrictFDerivAt f f' x) (hx : f x ≠ 0) :
-    HasStrictFDerivAt (fun y => sqrt (f y)) ((1 / (2 * sqrt (f x))) • f') x :=
+    HasStrictFDerivAt (fun y => √(f y)) ((1 / (2 * √(f x))) • f') x :=
   (hasStrictDerivAt_sqrt hx).comp_hasStrictFDerivAt x hf
 #align has_strict_fderiv_at.sqrt HasStrictFDerivAt.sqrt
 
 theorem HasFDerivWithinAt.sqrt (hf : HasFDerivWithinAt f f' s x) (hx : f x ≠ 0) :
-    HasFDerivWithinAt (fun y => sqrt (f y)) ((1 / (2 * sqrt (f x))) • f') s x :=
+    HasFDerivWithinAt (fun y => √(f y)) ((1 / (2 * √(f x))) • f') s x :=
   (hasDerivAt_sqrt hx).comp_hasFDerivWithinAt x hf
 #align has_fderiv_within_at.sqrt HasFDerivWithinAt.sqrt
 
 theorem DifferentiableWithinAt.sqrt (hf : DifferentiableWithinAt ℝ f s x) (hx : f x ≠ 0) :
-    DifferentiableWithinAt ℝ (fun y => sqrt (f y)) s x :=
+    DifferentiableWithinAt ℝ (fun y => √(f y)) s x :=
   (hf.hasFDerivWithinAt.sqrt hx).differentiableWithinAt
 #align differentiable_within_at.sqrt DifferentiableWithinAt.sqrt
 
 theorem DifferentiableAt.sqrt (hf : DifferentiableAt ℝ f x) (hx : f x ≠ 0) :
-    DifferentiableAt ℝ (fun y => sqrt (f y)) x :=
+    DifferentiableAt ℝ (fun y => √(f y)) x :=
   (hf.hasFDerivAt.sqrt hx).differentiableAt
 #align differentiable_at.sqrt DifferentiableAt.sqrt
 
 theorem DifferentiableOn.sqrt (hf : DifferentiableOn ℝ f s) (hs : ∀ x ∈ s, f x ≠ 0) :
-    DifferentiableOn ℝ (fun y => sqrt (f y)) s := fun x hx => (hf x hx).sqrt (hs x hx)
+    DifferentiableOn ℝ (fun y => √(f y)) s := fun x hx => (hf x hx).sqrt (hs x hx)
 #align differentiable_on.sqrt DifferentiableOn.sqrt
 
 theorem Differentiable.sqrt (hf : Differentiable ℝ f) (hs : ∀ x, f x ≠ 0) :
-    Differentiable ℝ fun y => sqrt (f y) := fun x => (hf x).sqrt (hs x)
+    Differentiable ℝ fun y => √(f y) := fun x => (hf x).sqrt (hs x)
 #align differentiable.sqrt Differentiable.sqrt
 
 theorem fderivWithin_sqrt (hf : DifferentiableWithinAt ℝ f s x) (hx : f x ≠ 0)
     (hxs : UniqueDiffWithinAt ℝ s x) :
-    fderivWithin ℝ (fun x => sqrt (f x)) s x = (1 / (2 * sqrt (f x))) • fderivWithin ℝ f s x :=
+    fderivWithin ℝ (fun x => √(f x)) s x = (1 / (2 * √(f x))) • fderivWithin ℝ f s x :=
   (hf.hasFDerivWithinAt.sqrt hx).fderivWithin hxs
 #align fderiv_within_sqrt fderivWithin_sqrt
 
 @[simp]
 theorem fderiv_sqrt (hf : DifferentiableAt ℝ f x) (hx : f x ≠ 0) :
-    fderiv ℝ (fun x => sqrt (f x)) x = (1 / (2 * sqrt (f x))) • fderiv ℝ f x :=
+    fderiv ℝ (fun x => √(f x)) x = (1 / (2 * √(f x))) • fderiv ℝ f x :=
   (hf.hasFDerivAt.sqrt hx).fderiv
 #align fderiv_sqrt fderiv_sqrt
 
 theorem ContDiffAt.sqrt (hf : ContDiffAt ℝ n f x) (hx : f x ≠ 0) :
-    ContDiffAt ℝ n (fun y => sqrt (f y)) x :=
+    ContDiffAt ℝ n (fun y => √(f y)) x :=
   (contDiffAt_sqrt hx).comp x hf
 #align cont_diff_at.sqrt ContDiffAt.sqrt
 
 theorem ContDiffWithinAt.sqrt (hf : ContDiffWithinAt ℝ n f s x) (hx : f x ≠ 0) :
-    ContDiffWithinAt ℝ n (fun y => sqrt (f y)) s x :=
+    ContDiffWithinAt ℝ n (fun y => √(f y)) s x :=
   (contDiffAt_sqrt hx).comp_contDiffWithinAt x hf
 #align cont_diff_within_at.sqrt ContDiffWithinAt.sqrt
 
 theorem ContDiffOn.sqrt (hf : ContDiffOn ℝ n f s) (hs : ∀ x ∈ s, f x ≠ 0) :
-    ContDiffOn ℝ n (fun y => sqrt (f y)) s := fun x hx => (hf x hx).sqrt (hs x hx)
+    ContDiffOn ℝ n (fun y => √(f y)) s := fun x hx => (hf x hx).sqrt (hs x hx)
 #align cont_diff_on.sqrt ContDiffOn.sqrt
 
-theorem ContDiff.sqrt (hf : ContDiff ℝ n f) (h : ∀ x, f x ≠ 0) : ContDiff ℝ n fun y => sqrt (f y) :=
+theorem ContDiff.sqrt (hf : ContDiff ℝ n f) (h : ∀ x, f x ≠ 0) : ContDiff ℝ n fun y => √(f y) :=
   contDiff_iff_contDiffAt.2 fun x => hf.contDiffAt.sqrt (h x)
 #align cont_diff.sqrt ContDiff.sqrt

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

@@ -28,7 +28,7 @@ namespace Real
 
 /-- Local homeomorph between `(0, +∞)` and `(0, +∞)` with `toFun = (· ^ 2)` and
 `invFun = Real.sqrt`. -/
-noncomputable def sqLocalHomeomorph : LocalHomeomorph ℝ ℝ where
+noncomputable def sqPartialHomeomorph : PartialHomeomorph ℝ ℝ where
   toFun x := x ^ 2
   invFun := sqrt
   source := Ioi 0
@@ -41,7 +41,7 @@ noncomputable def sqLocalHomeomorph : LocalHomeomorph ℝ ℝ where
   open_target := isOpen_Ioi
   continuousOn_toFun := (continuous_pow 2).continuousOn
   continuousOn_invFun := continuousOn_id.sqrt
-#align real.sq_local_homeomorph Real.sqLocalHomeomorph
+#align real.sq_local_homeomorph Real.sqPartialHomeomorph
 
 theorem deriv_sqrt_aux {x : ℝ} (hx : x ≠ 0) :
     HasStrictDerivAt sqrt (1 / (2 * sqrt x)) x ∧ ∀ n, ContDiffAt ℝ n sqrt x := by
@@ -53,8 +53,8 @@ theorem deriv_sqrt_aux {x : ℝ} (hx : x ≠ 0) :
         contDiffAt_const.congr_of_eventuallyEq this⟩
   · have : ↑2 * sqrt x ^ (2 - 1) ≠ 0 := by simp [(sqrt_pos.2 hx).ne', @two_ne_zero ℝ]
     constructor
-    · simpa using sqLocalHomeomorph.hasStrictDerivAt_symm hx this (hasStrictDerivAt_pow 2 _)
-    · exact fun n => sqLocalHomeomorph.contDiffAt_symm_deriv this hx (hasDerivAt_pow 2 (sqrt x))
+    · simpa using sqPartialHomeomorph.hasStrictDerivAt_symm hx this (hasStrictDerivAt_pow 2 _)
+    · exact fun n => sqPartialHomeomorph.contDiffAt_symm_deriv this hx (hasDerivAt_pow 2 (sqrt x))
         (contDiffAt_id.pow 2)
 #align real.deriv_sqrt_aux Real.deriv_sqrt_aux

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

@@ -39,8 +39,8 @@ noncomputable def sqLocalHomeomorph : LocalHomeomorph ℝ ℝ where
   right_inv' _ h := sq_sqrt (le_of_lt h)
   open_source := isOpen_Ioi
   open_target := isOpen_Ioi
-  continuous_toFun := (continuous_pow 2).continuousOn
-  continuous_invFun := continuousOn_id.sqrt
+  continuousOn_toFun := (continuous_pow 2).continuousOn
+  continuousOn_invFun := continuousOn_id.sqrt
 #align real.sq_local_homeomorph Real.sqLocalHomeomorph
 
 theorem deriv_sqrt_aux {x : ℝ} (hx : x ≠ 0) :

f2ce6086

chore: move Analysis/ContDiff to Analysis/ContDiff/Basic to make room for splitting (#8337)

No changes to content, or splitting, just a rename so there is room for more files.

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

7766bcc4

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Mathlib.Analysis.Calculus.ContDiff
+import Mathlib.Analysis.Calculus.ContDiff.Basic
 import Mathlib.Analysis.Calculus.Deriv.Pow
 
 #align_import analysis.special_functions.sqrt from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
@@ -177,4 +177,3 @@ theorem ContDiff.sqrt (hf : ContDiff ℝ n f) (h : ∀ x, f x ≠ 0) : ContDiff
 #align cont_diff.sqrt ContDiff.sqrt
 
 end fderiv
-

f2ce6086

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

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

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

277dea95

Diff

@@ -46,7 +46,7 @@ noncomputable def sqLocalHomeomorph : LocalHomeomorph ℝ ℝ where
 theorem deriv_sqrt_aux {x : ℝ} (hx : x ≠ 0) :
     HasStrictDerivAt sqrt (1 / (2 * sqrt x)) x ∧ ∀ n, ContDiffAt ℝ n sqrt x := by
   cases' hx.lt_or_lt with hx hx
-  · rw [sqrt_eq_zero_of_nonpos hx.le, MulZeroClass.mul_zero, div_zero]
+  · rw [sqrt_eq_zero_of_nonpos hx.le, mul_zero, div_zero]
     have : sqrt =ᶠ[𝓝 x] fun _ => 0 := (gt_mem_nhds hx).mono fun x hx => sqrt_eq_zero_of_nonpos hx.le
     exact
       ⟨(hasStrictDerivAt_const x (0 : ℝ)).congr_of_eventuallyEq this.symm, fun n =>

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

@@ -110,7 +110,7 @@ end deriv
 
 section fderiv
 
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {f : E → ℝ} {n : ℕ∞} {s : Set E}
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] {f : E → ℝ} {n : ℕ∞} {s : Set E}
   {x : E} {f' : E →L[ℝ] ℝ}
 
 theorem HasFDerivAt.sqrt (hf : HasFDerivAt f f' x) (hx : f x ≠ 0) :

f2ce6086

refactor: split Analysis.Calculus.LocalExtr (#5944)

Also make f/f' arguments implicit in all versions of Rolle's Theorem.

Fixes #4830

API changes

exists_Ioo_extr_on_Icc:
- generalize from functions f : ℝ → ℝ to functions from a conditionally complete linear order to a linear order.
- make f implicit;
exists_local_extr_Ioo:
- rename to exists_isLocalExtr_Ioo;
- generalize as above;
- make f implicit;
exists_isExtrOn_Ioo_of_tendsto, exists_isLocalExtr_Ioo_of_tendsto: new lemmas extracted from the proof of exists_hasDerivAt_eq_zero';
exists_hasDerivAt_eq_zero, exists_hasDerivAt_eq_zero': make f and f' implicit;
exists_deriv_eq_zero, exists_deriv_eq_zero': make f implicit.

eec218b4

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
 import Mathlib.Analysis.Calculus.ContDiff
+import Mathlib.Analysis.Calculus.Deriv.Pow
 
 #align_import analysis.special_functions.sqrt from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"

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) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module analysis.special_functions.sqrt
-! 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.Calculus.ContDiff
 
+#align_import analysis.special_functions.sqrt from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Smoothness of `Real.sqrt`

f2ce6086

feat: port Analysis.SpecialFunctions.Sqrt (#4529)

04d916cc

`analysis.special_functions.sqrt` ⟷ `Mathlib.Analysis.SpecialFunctions.Sqrt`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

API changes

Dependencies 12 + 873

analysis.special_functions.sqrt ⟷ Mathlib.Analysis.SpecialFunctions.Sqrt

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

API changes

Dependencies 12 + 873

`analysis.special_functions.sqrt` ⟷ `Mathlib.Analysis.SpecialFunctions.Sqrt`