analysis.complex.schwarz ⟷ Mathlib.Analysis.Complex.Schwarz

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

@@ -110,7 +110,7 @@ theorem norm_dslope_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R
   calc
     ‖dslope f c z‖ = ‖dslope (g ∘ f) c z‖ :=
       by
-      rw [g.dslope_comp, hgf, IsROrC.norm_ofReal, abs_norm]
+      rw [g.dslope_comp, hgf, RCLike.norm_ofReal, abs_norm]
       exact fun _ => hd.differentiable_at (ball_mem_nhds _ hR₁)
     _ ≤ R₂ / R₁ :=
       by

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

@@ -74,7 +74,7 @@ theorem schwarz_aux {f : ℂ → ℂ} (hd : DifferentiableOn ℂ f (ball c R₁)
     by
     refine' ge_of_tendsto _ this
     exact (tendsto_const_nhds.div tendsto_id hR₁.ne').mono_left nhdsWithin_le_nhds
-  rw [mem_ball] at hz 
+  rw [mem_ball] at hz
   filter_upwards [Ioo_mem_nhdsWithin_Iio ⟨hz, le_rfl⟩] with r hr
   have hr₀ : 0 < r := dist_nonneg.trans_lt hr.1
   replace hd : DiffContOnCl ℂ (dslope f c) (ball c r)

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 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.Complex.AbsMax
-import Mathbin.Analysis.Complex.RemovableSingularity
+import Analysis.Complex.AbsMax
+import Analysis.Complex.RemovableSingularity
 
 #align_import analysis.complex.schwarz from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 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.complex.schwarz
-! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Complex.AbsMax
 import Mathbin.Analysis.Complex.RemovableSingularity
 
+#align_import analysis.complex.schwarz from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"
+
 /-!
 # Schwarz lemma
 

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

@@ -66,6 +66,7 @@ section Space
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E] {R R₁ R₂ : ℝ} {f : ℂ → E}
   {c z z₀ : ℂ}
 
+#print Complex.schwarz_aux /-
 /-- An auxiliary lemma for `complex.norm_dslope_le_div_of_maps_to_ball`. -/
 theorem schwarz_aux {f : ℂ → ℂ} (hd : DifferentiableOn ℂ f (ball c R₁))
     (h_maps : MapsTo f (ball c R₁) (ball (f c) R₂)) (hz : z ∈ ball c R₁) :
@@ -94,7 +95,9 @@ theorem schwarz_aux {f : ℂ → ℂ} (hd : DifferentiableOn ℂ f (ball c R₁)
   · rw [closure_ball c hr₀.ne', mem_closed_ball]
     exact hr.1.le
 #align complex.schwarz_aux Complex.schwarz_aux
+-/
 
+#print Complex.norm_dslope_le_div_of_mapsTo_ball /-
 /-- Two cases of the **Schwarz Lemma** (derivative and distance), merged together. -/
 theorem norm_dslope_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R₁))
     (h_maps : MapsTo f (ball c R₁) (ball (f c) R₂)) (hz : z ∈ ball c R₁) :
@@ -117,7 +120,9 @@ theorem norm_dslope_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R
       refine' schwarz_aux (g.differentiable.comp_differentiable_on hd) (maps_to.comp _ h_maps) hz
       simpa only [hg', NNReal.coe_one, one_mul] using g.lipschitz.maps_to_ball hg₀ (f c) R₂
 #align complex.norm_dslope_le_div_of_maps_to_ball Complex.norm_dslope_le_div_of_mapsTo_ball
+-/
 
+#print Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div /-
 /-- Equality case in the **Schwarz Lemma**: in the setup of `norm_dslope_le_div_of_maps_to_ball`, if
 `‖dslope f c z₀‖ = R₂ / R₁` holds at a point in the ball then the map `f` is affine. -/
 theorem affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div [CompleteSpace E] [StrictConvexSpace ℝ E]
@@ -140,7 +145,9 @@ theorem affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div [CompleteSpace E] [St
       h_z₀ g_max hz
   simp [← this]
 #align complex.affine_of_maps_to_ball_of_exists_norm_dslope_eq_div Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div
+-/
 
+#print Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div' /-
 theorem affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div' [CompleteSpace E]
     [StrictConvexSpace ℝ E] (hd : DifferentiableOn ℂ f (ball c R₁))
     (h_maps : Set.MapsTo f (ball c R₁) (ball (f c) R₂))
@@ -149,7 +156,9 @@ theorem affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div' [CompleteSpace E]
   let ⟨z₀, h_z₀, h_eq⟩ := h_z₀
   ⟨dslope f c z₀, h_eq, affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div hd h_maps h_z₀ h_eq⟩
 #align complex.affine_of_maps_to_ball_of_exists_norm_dslope_eq_div' Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div'
+-/
 
+#print Complex.norm_deriv_le_div_of_mapsTo_ball /-
 /-- The **Schwarz Lemma**: if `f : ℂ → E` sends an open disk with center `c` and a positive radius
 `R₁` to an open ball with center `f c` and radius `R₂`, then the absolute value of the derivative of
 `f` at `c` is at most the ratio `R₂ / R₁`. -/
@@ -157,7 +166,9 @@ theorem norm_deriv_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R
     (h_maps : MapsTo f (ball c R₁) (ball (f c) R₂)) (h₀ : 0 < R₁) : ‖deriv f c‖ ≤ R₂ / R₁ := by
   simpa only [dslope_same] using norm_dslope_le_div_of_maps_to_ball hd h_maps (mem_ball_self h₀)
 #align complex.norm_deriv_le_div_of_maps_to_ball Complex.norm_deriv_le_div_of_mapsTo_ball
+-/
 
+#print Complex.dist_le_div_mul_dist_of_mapsTo_ball /-
 /-- The **Schwarz Lemma**: if `f : ℂ → E` sends an open disk with center `c` and radius `R₁` to an
 open ball with center `f c` and radius `R₂`, then for any `z` in the former disk we have
 `dist (f z) (f c) ≤ (R₂ / R₁) * dist z c`. -/
@@ -169,11 +180,13 @@ theorem dist_le_div_mul_dist_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c
   simpa only [dslope_of_ne _ hne, slope_def_module, norm_smul, norm_inv, ← div_eq_inv_mul, ←
     dist_eq_norm, div_le_iff (dist_pos.2 hne)] using norm_dslope_le_div_of_maps_to_ball hd h_maps hz
 #align complex.dist_le_div_mul_dist_of_maps_to_ball Complex.dist_le_div_mul_dist_of_mapsTo_ball
+-/
 
 end Space
 
 variable {f : ℂ → ℂ} {c z : ℂ} {R R₁ R₂ : ℝ}
 
+#print Complex.abs_deriv_le_div_of_mapsTo_ball /-
 /-- The **Schwarz Lemma**: if `f : ℂ → ℂ` sends an open disk with center `c` and a positive radius
 `R₁` to an open disk with center `f c` and radius `R₂`, then the absolute value of the derivative of
 `f` at `c` is at most the ratio `R₂ / R₁`. -/
@@ -181,7 +194,9 @@ theorem abs_deriv_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R
     (h_maps : MapsTo f (ball c R₁) (ball (f c) R₂)) (h₀ : 0 < R₁) : abs (deriv f c) ≤ R₂ / R₁ :=
   norm_deriv_le_div_of_mapsTo_ball hd h_maps h₀
 #align complex.abs_deriv_le_div_of_maps_to_ball Complex.abs_deriv_le_div_of_mapsTo_ball
+-/
 
+#print Complex.abs_deriv_le_one_of_mapsTo_ball /-
 /-- The **Schwarz Lemma**: if `f : ℂ → ℂ` sends an open disk of positive radius to itself and the
 center of this disk to itself, then the absolute value of the derivative of `f` at the center of
 this disk is at most `1`. -/
@@ -189,7 +204,9 @@ theorem abs_deriv_le_one_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R))
     (h_maps : MapsTo f (ball c R) (ball c R)) (hc : f c = c) (h₀ : 0 < R) : abs (deriv f c) ≤ 1 :=
   (norm_deriv_le_div_of_mapsTo_ball hd (by rwa [hc]) h₀).trans_eq (div_self h₀.ne')
 #align complex.abs_deriv_le_one_of_maps_to_ball Complex.abs_deriv_le_one_of_mapsTo_ball
+-/
 
+#print Complex.dist_le_dist_of_mapsTo_ball_self /-
 /-- The **Schwarz Lemma**: if `f : ℂ → ℂ` sends an open disk to itself and the center `c` of this
 disk to itself, then for any point `z` of this disk we have `dist (f z) c ≤ dist z c`. -/
 theorem dist_le_dist_of_mapsTo_ball_self (hd : DifferentiableOn ℂ f (ball c R))
@@ -200,7 +217,9 @@ theorem dist_le_dist_of_mapsTo_ball_self (hd : DifferentiableOn ℂ f (ball c R)
   simpa only [hc, div_self hR.ne', one_mul] using
     dist_le_div_mul_dist_of_maps_to_ball hd (by rwa [hc]) hz
 #align complex.dist_le_dist_of_maps_to_ball_self Complex.dist_le_dist_of_mapsTo_ball_self
+-/
 
+#print Complex.abs_le_abs_of_mapsTo_ball_self /-
 /-- The **Schwarz Lemma**: if `f : ℂ → ℂ` sends an open disk with center `0` to itself, the for any
 point `z` of this disk we have `abs (f z) ≤ abs z`. -/
 theorem abs_le_abs_of_mapsTo_ball_self (hd : DifferentiableOn ℂ f (ball 0 R))
@@ -209,6 +228,7 @@ theorem abs_le_abs_of_mapsTo_ball_self (hd : DifferentiableOn ℂ f (ball 0 R))
   replace hz : z ∈ ball (0 : ℂ) R; exact mem_ball_zero_iff.2 hz
   simpa only [dist_zero_right] using dist_le_dist_of_maps_to_ball_self hd h_maps h₀ hz
 #align complex.abs_le_abs_of_maps_to_ball_self Complex.abs_le_abs_of_mapsTo_ball_self
+-/
 
 end Complex
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/c471da714c044131b90c133701e51b877c246677

@@ -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.complex.schwarz
-! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
+! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
 ! 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.Complex.RemovableSingularity
 /-!
 # Schwarz lemma
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove several versions of the Schwarz lemma.
 
 * `complex.norm_deriv_le_div_of_maps_to_ball`, `complex.abs_deriv_le_div_of_maps_to_ball`: if

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

@@ -113,7 +113,6 @@ theorem norm_dslope_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R
       by
       refine' schwarz_aux (g.differentiable.comp_differentiable_on hd) (maps_to.comp _ h_maps) hz
       simpa only [hg', NNReal.coe_one, one_mul] using g.lipschitz.maps_to_ball hg₀ (f c) R₂
-    
 #align complex.norm_dslope_le_div_of_maps_to_ball Complex.norm_dslope_le_div_of_mapsTo_ball
 
 /-- Equality case in the **Schwarz Lemma**: in the setup of `norm_dslope_le_div_of_maps_to_ball`, if

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

@@ -74,7 +74,7 @@ theorem schwarz_aux {f : ℂ → ℂ} (hd : DifferentiableOn ℂ f (ball c R₁)
     refine' ge_of_tendsto _ this
     exact (tendsto_const_nhds.div tendsto_id hR₁.ne').mono_left nhdsWithin_le_nhds
   rw [mem_ball] at hz 
-  filter_upwards [Ioo_mem_nhdsWithin_Iio ⟨hz, le_rfl⟩]with r hr
+  filter_upwards [Ioo_mem_nhdsWithin_Iio ⟨hz, le_rfl⟩] with r hr
   have hr₀ : 0 < r := dist_nonneg.trans_lt hr.1
   replace hd : DiffContOnCl ℂ (dslope f c) (ball c r)
   · refine' DifferentiableOn.diffContOnCl _

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

@@ -73,7 +73,7 @@ theorem schwarz_aux {f : ℂ → ℂ} (hd : DifferentiableOn ℂ f (ball c R₁)
     by
     refine' ge_of_tendsto _ this
     exact (tendsto_const_nhds.div tendsto_id hR₁.ne').mono_left nhdsWithin_le_nhds
-  rw [mem_ball] at hz
+  rw [mem_ball] at hz 
   filter_upwards [Ioo_mem_nhdsWithin_Iio ⟨hz, le_rfl⟩]with r hr
   have hr₀ : 0 < r := dist_nonneg.trans_lt hr.1
   replace hd : DiffContOnCl ℂ (dslope f c) (ball c r)

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

@@ -54,7 +54,7 @@ Schwarz lemma
 
 open Metric Set Function Filter TopologicalSpace
 
-open Topology
+open scoped Topology
 
 namespace Complex
 

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

@@ -87,13 +87,7 @@ theorem schwarz_aux {f : ℂ → ℂ} (hd : DifferentiableOn ℂ f (ball c R₁)
     have hz' : z ≠ c := ne_of_mem_sphere hz hr₀.ne'
     rw [dslope_of_ne _ hz', slope_def_module, norm_smul, norm_inv, mem_sphere_iff_norm.1 hz, ←
       div_eq_inv_mul, div_le_div_right hr₀, ← dist_eq_norm]
-    exact
-      le_of_lt
-        (h_maps
-          (mem_ball.2
-            (by
-              rw [mem_sphere.1 hz]
-              exact hr.2)))
+    exact le_of_lt (h_maps (mem_ball.2 (by rw [mem_sphere.1 hz]; exact hr.2)))
   · rw [closure_ball c hr₀.ne', mem_closed_ball]
     exact hr.1.le
 #align complex.schwarz_aux Complex.schwarz_aux
@@ -106,8 +100,7 @@ theorem norm_dslope_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R
   have hR₁ : 0 < R₁ := nonempty_ball.1 ⟨z, hz⟩
   have hR₂ : 0 < R₂ := nonempty_ball.1 ⟨f z, h_maps hz⟩
   cases' eq_or_ne (dslope f c z) 0 with hc hc
-  · rw [hc, norm_zero]
-    exact div_nonneg hR₂.le hR₁.le
+  · rw [hc, norm_zero]; exact div_nonneg hR₂.le hR₁.le
   rcases exists_dual_vector ℂ _ hc with ⟨g, hg, hgf⟩
   have hg' : ‖g‖₊ = 1 := NNReal.eq hg
   have hg₀ : ‖g‖₊ ≠ 0 := by simpa only [hg'] using one_ne_zero
@@ -132,8 +125,7 @@ theorem affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div [CompleteSpace E] [St
   by
   set g := dslope f c
   rintro z hz
-  by_cases z = c
-  · simp [h]
+  by_cases z = c; · simp [h]
   have h_R₁ : 0 < R₁ := nonempty_ball.mp ⟨_, h_z₀⟩
   have g_le_div : ∀ z ∈ ball c R₁, ‖g z‖ ≤ R₂ / R₁ := fun z hz =>
     norm_dslope_le_div_of_maps_to_ball hd h_maps hz

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -114,7 +114,7 @@ theorem norm_dslope_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R
   calc
     ‖dslope f c z‖ = ‖dslope (g ∘ f) c z‖ :=
       by
-      rw [g.dslope_comp, hgf, IsROrC.norm_of_real, abs_norm]
+      rw [g.dslope_comp, hgf, IsROrC.norm_ofReal, abs_norm]
       exact fun _ => hd.differentiable_at (ball_mem_nhds _ hR₁)
     _ ≤ R₂ / R₁ :=
       by

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

@@ -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.complex.schwarz
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -114,7 +114,7 @@ theorem norm_dslope_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R
   calc
     ‖dslope f c z‖ = ‖dslope (g ∘ f) c z‖ :=
       by
-      rw [g.dslope_comp, hgf, IsROrC.norm_of_real, norm_norm]
+      rw [g.dslope_comp, hgf, IsROrC.norm_of_real, abs_norm]
       exact fun _ => hd.differentiable_at (ball_mem_nhds _ hR₁)
     _ ≤ R₂ / R₁ :=
       by

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

@@ -184,8 +184,7 @@ variable {f : ℂ → ℂ} {c z : ℂ} {R R₁ R₂ : ℝ}
 `R₁` to an open disk with center `f c` and radius `R₂`, then the absolute value of the derivative of
 `f` at `c` is at most the ratio `R₂ / R₁`. -/
 theorem abs_deriv_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R₁))
-    (h_maps : MapsTo f (ball c R₁) (ball (f c) R₂)) (h₀ : 0 < R₁) :
-    Complex.AbsTheory.Complex.abs (deriv f c) ≤ R₂ / R₁ :=
+    (h_maps : MapsTo f (ball c R₁) (ball (f c) R₂)) (h₀ : 0 < R₁) : abs (deriv f c) ≤ R₂ / R₁ :=
   norm_deriv_le_div_of_mapsTo_ball hd h_maps h₀
 #align complex.abs_deriv_le_div_of_maps_to_ball Complex.abs_deriv_le_div_of_mapsTo_ball
 
@@ -193,8 +192,7 @@ theorem abs_deriv_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R
 center of this disk to itself, then the absolute value of the derivative of `f` at the center of
 this disk is at most `1`. -/
 theorem abs_deriv_le_one_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R))
-    (h_maps : MapsTo f (ball c R) (ball c R)) (hc : f c = c) (h₀ : 0 < R) :
-    Complex.AbsTheory.Complex.abs (deriv f c) ≤ 1 :=
+    (h_maps : MapsTo f (ball c R) (ball c R)) (hc : f c = c) (h₀ : 0 < R) : abs (deriv f c) ≤ 1 :=
   (norm_deriv_le_div_of_mapsTo_ball hd (by rwa [hc]) h₀).trans_eq (div_self h₀.ne')
 #align complex.abs_deriv_le_one_of_maps_to_ball Complex.abs_deriv_le_one_of_mapsTo_ball
 
@@ -212,9 +210,7 @@ theorem dist_le_dist_of_mapsTo_ball_self (hd : DifferentiableOn ℂ f (ball c R)
 /-- The **Schwarz Lemma**: if `f : ℂ → ℂ` sends an open disk with center `0` to itself, the for any
 point `z` of this disk we have `abs (f z) ≤ abs z`. -/
 theorem abs_le_abs_of_mapsTo_ball_self (hd : DifferentiableOn ℂ f (ball 0 R))
-    (h_maps : MapsTo f (ball 0 R) (ball 0 R)) (h₀ : f 0 = 0)
-    (hz : Complex.AbsTheory.Complex.abs z < R) :
-    Complex.AbsTheory.Complex.abs (f z) ≤ Complex.AbsTheory.Complex.abs z :=
+    (h_maps : MapsTo f (ball 0 R) (ball 0 R)) (h₀ : f 0 = 0) (hz : abs z < R) : abs (f z) ≤ abs z :=
   by
   replace hz : z ∈ ball (0 : ℂ) R; exact mem_ball_zero_iff.2 hz
   simpa only [dist_zero_right] using dist_le_dist_of_maps_to_ball_self hd h_maps h₀ hz

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

@@ -171,7 +171,7 @@ theorem dist_le_div_mul_dist_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c
     (h_maps : MapsTo f (ball c R₁) (ball (f c) R₂)) (hz : z ∈ ball c R₁) :
     dist (f z) (f c) ≤ R₂ / R₁ * dist z c :=
   by
-  rcases eq_or_ne z c with (rfl | hne); · simp only [dist_self, mul_zero]
+  rcases eq_or_ne z c with (rfl | hne); · simp only [dist_self, MulZeroClass.mul_zero]
   simpa only [dslope_of_ne _ hne, slope_def_module, norm_smul, norm_inv, ← div_eq_inv_mul, ←
     dist_eq_norm, div_le_iff (dist_pos.2 hne)] using norm_dslope_le_div_of_maps_to_ball hd h_maps hz
 #align complex.dist_le_div_mul_dist_of_maps_to_ball Complex.dist_le_div_mul_dist_of_mapsTo_ball

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

@@ -184,7 +184,8 @@ variable {f : ℂ → ℂ} {c z : ℂ} {R R₁ R₂ : ℝ}
 `R₁` to an open disk with center `f c` and radius `R₂`, then the absolute value of the derivative of
 `f` at `c` is at most the ratio `R₂ / R₁`. -/
 theorem abs_deriv_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R₁))
-    (h_maps : MapsTo f (ball c R₁) (ball (f c) R₂)) (h₀ : 0 < R₁) : abs (deriv f c) ≤ R₂ / R₁ :=
+    (h_maps : MapsTo f (ball c R₁) (ball (f c) R₂)) (h₀ : 0 < R₁) :
+    Complex.AbsTheory.Complex.abs (deriv f c) ≤ R₂ / R₁ :=
   norm_deriv_le_div_of_mapsTo_ball hd h_maps h₀
 #align complex.abs_deriv_le_div_of_maps_to_ball Complex.abs_deriv_le_div_of_mapsTo_ball
 
@@ -192,7 +193,8 @@ theorem abs_deriv_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R
 center of this disk to itself, then the absolute value of the derivative of `f` at the center of
 this disk is at most `1`. -/
 theorem abs_deriv_le_one_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R))
-    (h_maps : MapsTo f (ball c R) (ball c R)) (hc : f c = c) (h₀ : 0 < R) : abs (deriv f c) ≤ 1 :=
+    (h_maps : MapsTo f (ball c R) (ball c R)) (hc : f c = c) (h₀ : 0 < R) :
+    Complex.AbsTheory.Complex.abs (deriv f c) ≤ 1 :=
   (norm_deriv_le_div_of_mapsTo_ball hd (by rwa [hc]) h₀).trans_eq (div_self h₀.ne')
 #align complex.abs_deriv_le_one_of_maps_to_ball Complex.abs_deriv_le_one_of_mapsTo_ball
 
@@ -210,7 +212,9 @@ theorem dist_le_dist_of_mapsTo_ball_self (hd : DifferentiableOn ℂ f (ball c R)
 /-- The **Schwarz Lemma**: if `f : ℂ → ℂ` sends an open disk with center `0` to itself, the for any
 point `z` of this disk we have `abs (f z) ≤ abs z`. -/
 theorem abs_le_abs_of_mapsTo_ball_self (hd : DifferentiableOn ℂ f (ball 0 R))
-    (h_maps : MapsTo f (ball 0 R) (ball 0 R)) (h₀ : f 0 = 0) (hz : abs z < R) : abs (f z) ≤ abs z :=
+    (h_maps : MapsTo f (ball 0 R) (ball 0 R)) (h₀ : f 0 = 0)
+    (hz : Complex.AbsTheory.Complex.abs z < R) :
+    Complex.AbsTheory.Complex.abs (f z) ≤ Complex.AbsTheory.Complex.abs z :=
   by
   replace hz : z ∈ ball (0 : ℂ) R; exact mem_ball_zero_iff.2 hz
   simpa only [dist_zero_right] using dist_le_dist_of_maps_to_ball_self hd h_maps h₀ hz

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

IsROrC contains data, which goes against the expectation that classes prefixed with Is are prop-valued. People have been complaining about this on and off, so this PR renames IsROrC to RCLike.

@@ -101,7 +101,7 @@ theorem norm_dslope_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R
   have hg₀ : ‖g‖₊ ≠ 0 := by simpa only [hg'] using one_ne_zero
   calc
     ‖dslope f c z‖ = ‖dslope (g ∘ f) c z‖ := by
-      rw [g.dslope_comp, hgf, IsROrC.norm_ofReal, abs_norm]
+      rw [g.dslope_comp, hgf, RCLike.norm_ofReal, abs_norm]
       exact fun _ => hd.differentiableAt (ball_mem_nhds _ hR₁)
     _ ≤ R₂ / R₁ := by
       refine' schwarz_aux (g.differentiable.comp_differentiableOn hd) (MapsTo.comp _ h_maps) hz

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -185,7 +185,7 @@ disk to itself, then for any point `z` of this disk we have `dist (f z) c ≤ di
 theorem dist_le_dist_of_mapsTo_ball_self (hd : DifferentiableOn ℂ f (ball c R))
     (h_maps : MapsTo f (ball c R) (ball c R)) (hc : f c = c) (hz : z ∈ ball c R) :
     dist (f z) c ≤ dist z c := by
-  -- porting note: `simp` was failing to use `div_self`
+  -- Porting note: `simp` was failing to use `div_self`
   have := dist_le_div_mul_dist_of_mapsTo_ball hd (by rwa [hc]) hz
   rwa [hc, div_self, one_mul] at this
   exact (nonempty_ball.1 ⟨z, hz⟩).ne'

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

@@ -126,7 +126,9 @@ theorem affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div [CompleteSpace E] [St
     (differentiableOn_dslope (isOpen_ball.mem_nhds (mem_ball_self h_R₁))).mpr hd
   have : g z = g z₀ := eqOn_of_isPreconnected_of_isMaxOn_norm (convex_ball c R₁).isPreconnected
     isOpen_ball g_diff h_z₀ g_max hz
-  simp [← this]
+  simp [g] at this
+  simp [g, ← this]
+
 #align complex.affine_of_maps_to_ball_of_exists_norm_dslope_eq_div Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div
 
 theorem affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div' [CompleteSpace E]

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -72,8 +72,8 @@ theorem schwarz_aux {f : ℂ → ℂ} (hd : DifferentiableOn ℂ f (ball c R₁)
   rw [mem_ball] at hz
   filter_upwards [Ioo_mem_nhdsWithin_Iio ⟨hz, le_rfl⟩] with r hr
   have hr₀ : 0 < r := dist_nonneg.trans_lt hr.1
-  replace hd : DiffContOnCl ℂ (dslope f c) (ball c r)
-  · refine' DifferentiableOn.diffContOnCl _
+  replace hd : DiffContOnCl ℂ (dslope f c) (ball c r) := by
+    refine DifferentiableOn.diffContOnCl ?_
     rw [closure_ball c hr₀.ne']
     exact ((differentiableOn_dslope <| ball_mem_nhds _ hR₁).mpr hd).mono
       (closedBall_subset_ball hr.2)
@@ -194,7 +194,7 @@ point `z` of this disk we have `abs (f z) ≤ abs z`. -/
 theorem abs_le_abs_of_mapsTo_ball_self (hd : DifferentiableOn ℂ f (ball 0 R))
     (h_maps : MapsTo f (ball 0 R) (ball 0 R)) (h₀ : f 0 = 0) (hz : abs z < R) :
     abs (f z) ≤ abs z := by
-  replace hz : z ∈ ball (0 : ℂ) R; exact mem_ball_zero_iff.2 hz
+  replace hz : z ∈ ball (0 : ℂ) R := mem_ball_zero_iff.2 hz
   simpa only [dist_zero_right] using dist_le_dist_of_mapsTo_ball_self hd h_maps h₀ hz
 #align complex.abs_le_abs_of_maps_to_ball_self Complex.abs_le_abs_of_mapsTo_ball_self
 

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.

@@ -94,7 +94,7 @@ theorem norm_dslope_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R
     ‖dslope f c z‖ ≤ R₂ / R₁ := by
   have hR₁ : 0 < R₁ := nonempty_ball.1 ⟨z, hz⟩
   have hR₂ : 0 < R₂ := nonempty_ball.1 ⟨f z, h_maps hz⟩
-  cases' eq_or_ne (dslope f c z) 0 with hc hc
+  rcases eq_or_ne (dslope f c z) 0 with hc | hc
   · rw [hc, norm_zero]; exact div_nonneg hR₂.le hR₁.le
   rcases exists_dual_vector ℂ _ hc with ⟨g, hg, hgf⟩
   have hg' : ‖g‖₊ = 1 := NNReal.eq hg

I've also got a change to make this required, but I'd like to land this first.

@@ -116,7 +116,7 @@ theorem affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div [CompleteSpace E] [St
     Set.EqOn f (fun z => f c + (z - c) • dslope f c z₀) (ball c R₁) := by
   set g := dslope f c
   rintro z hz
-  by_cases z = c; · simp [h]
+  by_cases h : z = c; · simp [h]
   have h_R₁ : 0 < R₁ := nonempty_ball.mp ⟨_, h_z₀⟩
   have g_le_div : ∀ z ∈ ball c R₁, ‖g z‖ ≤ R₂ / R₁ := fun z hz =>
     norm_dslope_le_div_of_mapsTo_ball hd h_maps hz

Use Bornology.IsBounded instead.

@@ -77,7 +77,7 @@ theorem schwarz_aux {f : ℂ → ℂ} (hd : DifferentiableOn ℂ f (ball c R₁)
     rw [closure_ball c hr₀.ne']
     exact ((differentiableOn_dslope <| ball_mem_nhds _ hR₁).mpr hd).mono
       (closedBall_subset_ball hr.2)
-  refine' norm_le_of_forall_mem_frontier_norm_le bounded_ball hd _ _
+  refine' norm_le_of_forall_mem_frontier_norm_le isBounded_ball hd _ _
   · rw [frontier_ball c hr₀.ne']
     intro z hz
     have hz' : z ≠ c := ne_of_mem_sphere hz hr₀.ne'

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

This has nice performance benefits.

@@ -58,7 +58,7 @@ namespace Complex
 
 section Space
 
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E] {R R₁ R₂ : ℝ} {f : ℂ → E}
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] {R R₁ R₂ : ℝ} {f : ℂ → E}
   {c z z₀ : ℂ}
 
 /-- An auxiliary lemma for `Complex.norm_dslope_le_div_of_mapsTo_ball`. -/

@@ -189,7 +189,7 @@ theorem dist_le_dist_of_mapsTo_ball_self (hd : DifferentiableOn ℂ f (ball c R)
   exact (nonempty_ball.1 ⟨z, hz⟩).ne'
 #align complex.dist_le_dist_of_maps_to_ball_self Complex.dist_le_dist_of_mapsTo_ball_self
 
-/-- The **Schwarz Lemma**: if `f : ℂ → ℂ` sends an open disk with center `0` to itself, the for any
+/-- The **Schwarz Lemma**: if `f : ℂ → ℂ` sends an open disk with center `0` to itself, then for any
 point `z` of this disk we have `abs (f z) ≤ abs z`. -/
 theorem abs_le_abs_of_mapsTo_ball_self (hd : DifferentiableOn ℂ f (ball 0 R))
     (h_maps : MapsTo f (ball 0 R) (ball 0 R)) (h₀ : f 0 = 0) (hz : abs z < R) :

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 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.complex.schwarz
-! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Complex.AbsMax
 import Mathlib.Analysis.Complex.RemovableSingularity
 
+#align_import analysis.complex.schwarz from "leanprover-community/mathlib"@"3f655f5297b030a87d641ad4e825af8d9679eb0b"
+
 /-!
 # Schwarz lemma
 

@@ -29,11 +29,12 @@ In this file we prove several versions of the Schwarz lemma.
   to itself and the center of this disk to itself, then the absolute value of the derivative of `f`
   at the center of this disk is at most `1`;
 
-* `complex.dist_le_dist_of_maps_to_ball`: if `f : ℂ → ℂ` sends an open disk to itself and the center
-  `c` of this disk to itself, then for any point `z` of this disk we have `dist (f z) c ≤ dist z c`;
+* `Complex.dist_le_dist_of_mapsTo_ball_self`: if `f : ℂ → ℂ` sends an open disk to itself and the
+  center `c` of this disk to itself, then for any point `z` of this disk we have
+  `dist (f z) c ≤ dist z c`;
 
-* `complex.abs_le_abs_of_maps_to_ball`: if `f : ℂ → ℂ` sends an open disk with center `0` to itself,
-  then for any point `z` of this disk we have `abs (f z) ≤ abs z`.
+* `Complex.abs_le_abs_of_mapsTo_ball_self`: if `f : ℂ → ℂ` sends an open disk with center `0` to
+  itself, then for any point `z` of this disk we have `abs (f z) ≤ abs z`.
 
 ## Implementation notes
 
@@ -71,7 +72,7 @@ theorem schwarz_aux {f : ℂ → ℂ} (hd : DifferentiableOn ℂ f (ball c R₁)
   suffices ∀ᶠ r in 𝓝[<] R₁, ‖dslope f c z‖ ≤ R₂ / r by
     refine' ge_of_tendsto _ this
     exact (tendsto_const_nhds.div tendsto_id hR₁.ne').mono_left nhdsWithin_le_nhds
-  rw [mem_ball] at hz 
+  rw [mem_ball] at hz
   filter_upwards [Ioo_mem_nhdsWithin_Iio ⟨hz, le_rfl⟩] with r hr
   have hr₀ : 0 < r := dist_nonneg.trans_lt hr.1
   replace hd : DiffContOnCl ℂ (dslope f c) (ball c r)
@@ -110,7 +111,7 @@ theorem norm_dslope_le_div_of_mapsTo_ball (hd : DifferentiableOn ℂ f (ball c R
       simpa only [hg', NNReal.coe_one, one_mul] using g.lipschitz.mapsTo_ball hg₀ (f c) R₂
 #align complex.norm_dslope_le_div_of_maps_to_ball Complex.norm_dslope_le_div_of_mapsTo_ball
 
-/-- Equality case in the **Schwarz Lemma**: in the setup of `norm_dslope_le_div_of_maps_to_ball`, if
+/-- Equality case in the **Schwarz Lemma**: in the setup of `norm_dslope_le_div_of_mapsTo_ball`, if
 `‖dslope f c z₀‖ = R₂ / R₁` holds at a point in the ball then the map `f` is affine. -/
 theorem affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div [CompleteSpace E] [StrictConvexSpace ℝ E]
     (hd : DifferentiableOn ℂ f (ball c R₁)) (h_maps : Set.MapsTo f (ball c R₁) (ball (f c) R₂))