analysis.complex.real_deriv ⟷ Mathlib.Analysis.Complex.RealDeriv

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

@@ -3,7 +3,7 @@ Copyright (c) Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yourong Zang
 -/
-import Analysis.Calculus.ContDiff
+import Analysis.Calculus.ContDiff.Basic
 import Analysis.Calculus.Deriv.Linear
 import Analysis.Complex.Conformal
 import Analysis.Calculus.Conformal.NormedSpace

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

@@ -205,7 +205,7 @@ theorem conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj {f : ℂ
   have h_diff := h.imp_symm fderiv_zero_of_not_differentiableAt
   apply or_congr
   · rw [differentiableAt_iff_restrictScalars ℝ h_diff]
-  rw [← conj_conj z] at h_diff 
+  rw [← conj_conj z] at h_diff
   rw [differentiableAt_iff_restrictScalars ℝ (h_diff.comp _ conj_cle.differentiable_at)]
   refine' exists_congr fun g => rfl.congr _
   have : fderiv ℝ conj (conj z) = _ := conj_cle.fderiv

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

@@ -104,7 +104,7 @@ variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E]
 #print HasStrictDerivAt.complexToReal_fderiv' /-
 theorem HasStrictDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E}
     (h : HasStrictDerivAt f f' x) :
-    HasStrictFDerivAt f (reClm.smul_right f' + I • imClm.smul_right f') x := by
+    HasStrictFDerivAt f (reCLM.smul_right f' + I • imCLM.smul_right f') x := by
   simpa only [Complex.restrictScalars_one_smulRight'] using
     h.has_strict_fderiv_at.restrict_scalars ℝ
 #align has_strict_deriv_at.complex_to_real_fderiv' HasStrictDerivAt.complexToReal_fderiv'
@@ -112,7 +112,7 @@ theorem HasStrictDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E
 
 #print HasDerivAt.complexToReal_fderiv' /-
 theorem HasDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E} (h : HasDerivAt f f' x) :
-    HasFDerivAt f (reClm.smul_right f' + I • imClm.smul_right f') x := by
+    HasFDerivAt f (reCLM.smul_right f' + I • imCLM.smul_right f') x := by
   simpa only [Complex.restrictScalars_one_smulRight'] using h.has_fderiv_at.restrict_scalars ℝ
 #align has_deriv_at.complex_to_real_fderiv' HasDerivAt.complexToReal_fderiv'
 -/
@@ -120,7 +120,7 @@ theorem HasDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E} (h :
 #print HasDerivWithinAt.complexToReal_fderiv' /-
 theorem HasDerivWithinAt.complexToReal_fderiv' {f : ℂ → E} {s : Set ℂ} {x : ℂ} {f' : E}
     (h : HasDerivWithinAt f f' s x) :
-    HasFDerivWithinAt f (reClm.smul_right f' + I • imClm.smul_right f') s x := by
+    HasFDerivWithinAt f (reCLM.smul_right f' + I • imCLM.smul_right f') s x := by
   simpa only [Complex.restrictScalars_one_smulRight'] using
     h.has_fderiv_within_at.restrict_scalars ℝ
 #align has_deriv_within_at.complex_to_real_fderiv' HasDerivWithinAt.complexToReal_fderiv'

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

@@ -3,10 +3,10 @@ Copyright (c) Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yourong Zang
 -/
-import Mathbin.Analysis.Calculus.ContDiff
-import Mathbin.Analysis.Calculus.Deriv.Linear
-import Mathbin.Analysis.Complex.Conformal
-import Mathbin.Analysis.Calculus.Conformal.NormedSpace
+import Analysis.Calculus.ContDiff
+import Analysis.Calculus.Deriv.Linear
+import Analysis.Complex.Conformal
+import Analysis.Calculus.Conformal.NormedSpace
 
 #align_import analysis.complex.real_deriv from "leanprover-community/mathlib"@"575b4ea3738b017e30fb205cb9b4a8742e5e82b6"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yourong Zang
-
-! This file was ported from Lean 3 source module analysis.complex.real_deriv
-! 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
 import Mathbin.Analysis.Calculus.Deriv.Linear
 import Mathbin.Analysis.Complex.Conformal
 import Mathbin.Analysis.Calculus.Conformal.NormedSpace
 
+#align_import analysis.complex.real_deriv from "leanprover-community/mathlib"@"575b4ea3738b017e30fb205cb9b4a8742e5e82b6"
+
 /-! # Real differentiability of complex-differentiable functions
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

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

@@ -51,6 +51,7 @@ open Complex
 
 variable {e : ℂ → ℂ} {e' : ℂ} {z : ℝ}
 
+#print HasStrictDerivAt.real_of_complex /-
 /-- If a complex function is differentiable at a real point, then the induced real function is also
 differentiable at this point, with a derivative equal to the real part of the complex derivative. -/
 theorem HasStrictDerivAt.real_of_complex (h : HasStrictDerivAt e e' z) :
@@ -64,7 +65,9 @@ theorem HasStrictDerivAt.real_of_complex (h : HasStrictDerivAt e e' z) :
   have C : HasStrictFDerivAt re re_clm (e (of_real_clm z)) := re_clm.has_strict_fderiv_at
   simpa using (C.comp z (B.comp z A)).HasStrictDerivAt
 #align has_strict_deriv_at.real_of_complex HasStrictDerivAt.real_of_complex
+-/
 
+#print HasDerivAt.real_of_complex /-
 /-- If a complex function `e` is differentiable at a real point, then the function `ℝ → ℝ` given by
 the real part of `e` is also differentiable at this point, with a derivative equal to the real part
 of the complex derivative. -/
@@ -79,7 +82,9 @@ theorem HasDerivAt.real_of_complex (h : HasDerivAt e e' z) :
   have C : HasFDerivAt re re_clm (e (of_real_clm z)) := re_clm.has_fderiv_at
   simpa using (C.comp z (B.comp z A)).HasDerivAt
 #align has_deriv_at.real_of_complex HasDerivAt.real_of_complex
+-/
 
+#print ContDiffAt.real_of_complex /-
 theorem ContDiffAt.real_of_complex {n : ℕ∞} (h : ContDiffAt ℂ n e z) :
     ContDiffAt ℝ n (fun x : ℝ => (e x).re) z :=
   by
@@ -88,54 +93,72 @@ theorem ContDiffAt.real_of_complex {n : ℕ∞} (h : ContDiffAt ℂ n e z) :
   have C : ContDiffAt ℝ n re (e z) := re_clm.cont_diff.cont_diff_at
   exact C.comp z (B.comp z A)
 #align cont_diff_at.real_of_complex ContDiffAt.real_of_complex
+-/
 
+#print ContDiff.real_of_complex /-
 theorem ContDiff.real_of_complex {n : ℕ∞} (h : ContDiff ℂ n e) :
     ContDiff ℝ n fun x : ℝ => (e x).re :=
   contDiff_iff_contDiffAt.2 fun x => h.ContDiffAt.real_of_complex
 #align cont_diff.real_of_complex ContDiff.real_of_complex
+-/
 
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E]
 
+#print HasStrictDerivAt.complexToReal_fderiv' /-
 theorem HasStrictDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E}
     (h : HasStrictDerivAt f f' x) :
     HasStrictFDerivAt f (reClm.smul_right f' + I • imClm.smul_right f') x := by
   simpa only [Complex.restrictScalars_one_smulRight'] using
     h.has_strict_fderiv_at.restrict_scalars ℝ
 #align has_strict_deriv_at.complex_to_real_fderiv' HasStrictDerivAt.complexToReal_fderiv'
+-/
 
+#print HasDerivAt.complexToReal_fderiv' /-
 theorem HasDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E} (h : HasDerivAt f f' x) :
     HasFDerivAt f (reClm.smul_right f' + I • imClm.smul_right f') x := by
   simpa only [Complex.restrictScalars_one_smulRight'] using h.has_fderiv_at.restrict_scalars ℝ
 #align has_deriv_at.complex_to_real_fderiv' HasDerivAt.complexToReal_fderiv'
+-/
 
+#print HasDerivWithinAt.complexToReal_fderiv' /-
 theorem HasDerivWithinAt.complexToReal_fderiv' {f : ℂ → E} {s : Set ℂ} {x : ℂ} {f' : E}
     (h : HasDerivWithinAt f f' s x) :
     HasFDerivWithinAt f (reClm.smul_right f' + I • imClm.smul_right f') s x := by
   simpa only [Complex.restrictScalars_one_smulRight'] using
     h.has_fderiv_within_at.restrict_scalars ℝ
 #align has_deriv_within_at.complex_to_real_fderiv' HasDerivWithinAt.complexToReal_fderiv'
+-/
 
+#print HasStrictDerivAt.complexToReal_fderiv /-
 theorem HasStrictDerivAt.complexToReal_fderiv {f : ℂ → ℂ} {f' x : ℂ} (h : HasStrictDerivAt f f' x) :
     HasStrictFDerivAt f (f' • (1 : ℂ →L[ℝ] ℂ)) x := by
   simpa only [Complex.restrictScalars_one_smulRight] using h.has_strict_fderiv_at.restrict_scalars ℝ
 #align has_strict_deriv_at.complex_to_real_fderiv HasStrictDerivAt.complexToReal_fderiv
+-/
 
+#print HasDerivAt.complexToReal_fderiv /-
 theorem HasDerivAt.complexToReal_fderiv {f : ℂ → ℂ} {f' x : ℂ} (h : HasDerivAt f f' x) :
     HasFDerivAt f (f' • (1 : ℂ →L[ℝ] ℂ)) x := by
   simpa only [Complex.restrictScalars_one_smulRight] using h.has_fderiv_at.restrict_scalars ℝ
 #align has_deriv_at.complex_to_real_fderiv HasDerivAt.complexToReal_fderiv
+-/
 
+#print HasDerivWithinAt.complexToReal_fderiv /-
 theorem HasDerivWithinAt.complexToReal_fderiv {f : ℂ → ℂ} {s : Set ℂ} {f' x : ℂ}
     (h : HasDerivWithinAt f f' s x) : HasFDerivWithinAt f (f' • (1 : ℂ →L[ℝ] ℂ)) s x := by
   simpa only [Complex.restrictScalars_one_smulRight] using h.has_fderiv_within_at.restrict_scalars ℝ
 #align has_deriv_within_at.complex_to_real_fderiv HasDerivWithinAt.complexToReal_fderiv
+-/
 
+#print HasDerivAt.comp_ofReal /-
 /-- If a complex function `e` is differentiable at a real point, then its restriction to `ℝ` is
 differentiable there as a function `ℝ → ℂ`, with the same derivative. -/
 theorem HasDerivAt.comp_ofReal (hf : HasDerivAt e e' ↑z) : HasDerivAt (fun y : ℝ => e ↑y) e' z := by
   simpa only [of_real_clm_apply, of_real_one, mul_one] using hf.comp z of_real_clm.has_deriv_at
 #align has_deriv_at.comp_of_real HasDerivAt.comp_ofReal
+-/
 
+#print HasDerivAt.ofReal_comp /-
 /-- If a function `f : ℝ → ℝ` is differentiable at a (real) point `x`, then it is also
 differentiable as a function `ℝ → ℂ`. -/
 theorem HasDerivAt.ofReal_comp {f : ℝ → ℝ} {u : ℝ} (hf : HasDerivAt f u z) :
@@ -143,6 +166,7 @@ theorem HasDerivAt.ofReal_comp {f : ℝ → ℝ} {u : ℝ} (hf : HasDerivAt f u
   simpa only [of_real_clm_apply, of_real_one, real_smul, mul_one] using
     of_real_clm.has_deriv_at.scomp z hf
 #align has_deriv_at.of_real_comp HasDerivAt.ofReal_comp
+-/
 
 end RealDerivOfComplex
 
@@ -157,6 +181,7 @@ open scoped ComplexConjugate
 
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E] {z : ℂ} {f : ℂ → E}
 
+#print DifferentiableAt.conformalAt /-
 /-- A real differentiable function of the complex plane into some complex normed space `E` is
     conformal at a point `z` if it is holomorphic at that point with a nonvanishing differential.
     This is a version of the Cauchy-Riemann equations. -/
@@ -167,7 +192,9 @@ theorem DifferentiableAt.conformalAt (h : DifferentiableAt ℂ f z) (hf' : deriv
   apply isConformalMap_complex_linear
   simpa only [Ne.def, ext_ring_iff]
 #align differentiable_at.conformal_at DifferentiableAt.conformalAt
+-/
 
+#print conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj /-
 /-- A complex function is conformal if and only if the function is holomorphic or antiholomorphic
     with a nonvanishing differential. -/
 theorem conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj {f : ℂ → ℂ} {z : ℂ} :
@@ -187,6 +214,7 @@ theorem conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj {f : ℂ
   have : fderiv ℝ conj (conj z) = _ := conj_cle.fderiv
   simp [fderiv.comp _ h_diff conj_cle.differentiable_at, this, conj_conj]
 #align conformal_at_iff_differentiable_at_or_differentiable_at_comp_conj conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj
+-/
 
 end Conformality
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -132,17 +132,17 @@ theorem HasDerivWithinAt.complexToReal_fderiv {f : ℂ → ℂ} {s : Set ℂ} {f
 
 /-- If a complex function `e` is differentiable at a real point, then its restriction to `ℝ` is
 differentiable there as a function `ℝ → ℂ`, with the same derivative. -/
-theorem HasDerivAt.comp_of_real (hf : HasDerivAt e e' ↑z) : HasDerivAt (fun y : ℝ => e ↑y) e' z :=
-  by simpa only [of_real_clm_apply, of_real_one, mul_one] using hf.comp z of_real_clm.has_deriv_at
-#align has_deriv_at.comp_of_real HasDerivAt.comp_of_real
+theorem HasDerivAt.comp_ofReal (hf : HasDerivAt e e' ↑z) : HasDerivAt (fun y : ℝ => e ↑y) e' z := by
+  simpa only [of_real_clm_apply, of_real_one, mul_one] using hf.comp z of_real_clm.has_deriv_at
+#align has_deriv_at.comp_of_real HasDerivAt.comp_ofReal
 
 /-- If a function `f : ℝ → ℝ` is differentiable at a (real) point `x`, then it is also
 differentiable as a function `ℝ → ℂ`. -/
-theorem HasDerivAt.of_real_comp {f : ℝ → ℝ} {u : ℝ} (hf : HasDerivAt f u z) :
+theorem HasDerivAt.ofReal_comp {f : ℝ → ℝ} {u : ℝ} (hf : HasDerivAt f u z) :
     HasDerivAt (fun y : ℝ => ↑(f y) : ℝ → ℂ) u z := by
   simpa only [of_real_clm_apply, of_real_one, real_smul, mul_one] using
     of_real_clm.has_deriv_at.scomp z hf
-#align has_deriv_at.of_real_comp HasDerivAt.of_real_comp
+#align has_deriv_at.of_real_comp HasDerivAt.ofReal_comp
 
 end RealDerivOfComplex
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yourong Zang
 
 ! This file was ported from Lean 3 source module analysis.complex.real_deriv
-! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
+! leanprover-community/mathlib commit 575b4ea3738b017e30fb205cb9b4a8742e5e82b6
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.Calculus.Conformal.NormedSpace
 
 /-! # Real differentiability of complex-differentiable functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 `has_deriv_at.real_of_complex` expresses that, if a function on `ℂ` is differentiable (over `ℂ`),
 then its restriction to `ℝ` is differentiable over `ℝ`, with derivative the real part of the
 complex derivative.

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

@@ -178,7 +178,7 @@ theorem conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj {f : ℂ
   have h_diff := h.imp_symm fderiv_zero_of_not_differentiableAt
   apply or_congr
   · rw [differentiableAt_iff_restrictScalars ℝ h_diff]
-  rw [← conj_conj z] at h_diff
+  rw [← conj_conj z] at h_diff 
   rw [differentiableAt_iff_restrictScalars ℝ (h_diff.comp _ conj_cle.differentiable_at)]
   refine' exists_congr fun g => rfl.congr _
   have : fderiv ℝ conj (conj z) = _ := conj_cle.fderiv

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

@@ -150,7 +150,7 @@ section Conformality
 
 open Complex ContinuousLinearMap
 
-open ComplexConjugate
+open scoped ComplexConjugate
 
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E] {z : ℂ} {f : ℂ → E}
 

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

@@ -4,11 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yourong Zang
 
 ! This file was ported from Lean 3 source module analysis.complex.real_deriv
-! leanprover-community/mathlib commit e9be2fa75faa22892937c275e27a91cd558cf8c0
+! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.ContDiff
+import Mathbin.Analysis.Calculus.Deriv.Linear
 import Mathbin.Analysis.Complex.Conformal
 import Mathbin.Analysis.Calculus.Conformal.NormedSpace
 
@@ -95,19 +96,19 @@ variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E]
 theorem HasStrictDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E}
     (h : HasStrictDerivAt f f' x) :
     HasStrictFDerivAt f (reClm.smul_right f' + I • imClm.smul_right f') x := by
-  simpa only [Complex.restrictScalars_one_smul_right'] using
+  simpa only [Complex.restrictScalars_one_smulRight'] using
     h.has_strict_fderiv_at.restrict_scalars ℝ
 #align has_strict_deriv_at.complex_to_real_fderiv' HasStrictDerivAt.complexToReal_fderiv'
 
 theorem HasDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E} (h : HasDerivAt f f' x) :
     HasFDerivAt f (reClm.smul_right f' + I • imClm.smul_right f') x := by
-  simpa only [Complex.restrictScalars_one_smul_right'] using h.has_fderiv_at.restrict_scalars ℝ
+  simpa only [Complex.restrictScalars_one_smulRight'] using h.has_fderiv_at.restrict_scalars ℝ
 #align has_deriv_at.complex_to_real_fderiv' HasDerivAt.complexToReal_fderiv'
 
 theorem HasDerivWithinAt.complexToReal_fderiv' {f : ℂ → E} {s : Set ℂ} {x : ℂ} {f' : E}
     (h : HasDerivWithinAt f f' s x) :
     HasFDerivWithinAt f (reClm.smul_right f' + I • imClm.smul_right f') s x := by
-  simpa only [Complex.restrictScalars_one_smul_right'] using
+  simpa only [Complex.restrictScalars_one_smulRight'] using
     h.has_fderiv_within_at.restrict_scalars ℝ
 #align has_deriv_within_at.complex_to_real_fderiv' HasDerivWithinAt.complexToReal_fderiv'
 

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

@@ -52,12 +52,12 @@ differentiable at this point, with a derivative equal to the real part of the co
 theorem HasStrictDerivAt.real_of_complex (h : HasStrictDerivAt e e' z) :
     HasStrictDerivAt (fun x : ℝ => (e x).re) e'.re z :=
   by
-  have A : HasStrictFderivAt (coe : ℝ → ℂ) of_real_clm z := of_real_clm.has_strict_fderiv_at
+  have A : HasStrictFDerivAt (coe : ℝ → ℂ) of_real_clm z := of_real_clm.has_strict_fderiv_at
   have B :
-    HasStrictFderivAt e ((ContinuousLinearMap.smulRight 1 e' : ℂ →L[ℂ] ℂ).restrictScalars ℝ)
+    HasStrictFDerivAt e ((ContinuousLinearMap.smulRight 1 e' : ℂ →L[ℂ] ℂ).restrictScalars ℝ)
       (of_real_clm z) :=
     h.has_strict_fderiv_at.restrict_scalars ℝ
-  have C : HasStrictFderivAt re re_clm (e (of_real_clm z)) := re_clm.has_strict_fderiv_at
+  have C : HasStrictFDerivAt re re_clm (e (of_real_clm z)) := re_clm.has_strict_fderiv_at
   simpa using (C.comp z (B.comp z A)).HasStrictDerivAt
 #align has_strict_deriv_at.real_of_complex HasStrictDerivAt.real_of_complex
 
@@ -67,12 +67,12 @@ of the complex derivative. -/
 theorem HasDerivAt.real_of_complex (h : HasDerivAt e e' z) :
     HasDerivAt (fun x : ℝ => (e x).re) e'.re z :=
   by
-  have A : HasFderivAt (coe : ℝ → ℂ) of_real_clm z := of_real_clm.has_fderiv_at
+  have A : HasFDerivAt (coe : ℝ → ℂ) of_real_clm z := of_real_clm.has_fderiv_at
   have B :
-    HasFderivAt e ((ContinuousLinearMap.smulRight 1 e' : ℂ →L[ℂ] ℂ).restrictScalars ℝ)
+    HasFDerivAt e ((ContinuousLinearMap.smulRight 1 e' : ℂ →L[ℂ] ℂ).restrictScalars ℝ)
       (of_real_clm z) :=
     h.has_fderiv_at.restrict_scalars ℝ
-  have C : HasFderivAt re re_clm (e (of_real_clm z)) := re_clm.has_fderiv_at
+  have C : HasFDerivAt re re_clm (e (of_real_clm z)) := re_clm.has_fderiv_at
   simpa using (C.comp z (B.comp z A)).HasDerivAt
 #align has_deriv_at.real_of_complex HasDerivAt.real_of_complex
 
@@ -94,35 +94,35 @@ variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E]
 
 theorem HasStrictDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E}
     (h : HasStrictDerivAt f f' x) :
-    HasStrictFderivAt f (reClm.smul_right f' + I • imClm.smul_right f') x := by
+    HasStrictFDerivAt f (reClm.smul_right f' + I • imClm.smul_right f') x := by
   simpa only [Complex.restrictScalars_one_smul_right'] using
     h.has_strict_fderiv_at.restrict_scalars ℝ
 #align has_strict_deriv_at.complex_to_real_fderiv' HasStrictDerivAt.complexToReal_fderiv'
 
 theorem HasDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E} (h : HasDerivAt f f' x) :
-    HasFderivAt f (reClm.smul_right f' + I • imClm.smul_right f') x := by
+    HasFDerivAt f (reClm.smul_right f' + I • imClm.smul_right f') x := by
   simpa only [Complex.restrictScalars_one_smul_right'] using h.has_fderiv_at.restrict_scalars ℝ
 #align has_deriv_at.complex_to_real_fderiv' HasDerivAt.complexToReal_fderiv'
 
 theorem HasDerivWithinAt.complexToReal_fderiv' {f : ℂ → E} {s : Set ℂ} {x : ℂ} {f' : E}
     (h : HasDerivWithinAt f f' s x) :
-    HasFderivWithinAt f (reClm.smul_right f' + I • imClm.smul_right f') s x := by
+    HasFDerivWithinAt f (reClm.smul_right f' + I • imClm.smul_right f') s x := by
   simpa only [Complex.restrictScalars_one_smul_right'] using
     h.has_fderiv_within_at.restrict_scalars ℝ
 #align has_deriv_within_at.complex_to_real_fderiv' HasDerivWithinAt.complexToReal_fderiv'
 
 theorem HasStrictDerivAt.complexToReal_fderiv {f : ℂ → ℂ} {f' x : ℂ} (h : HasStrictDerivAt f f' x) :
-    HasStrictFderivAt f (f' • (1 : ℂ →L[ℝ] ℂ)) x := by
+    HasStrictFDerivAt f (f' • (1 : ℂ →L[ℝ] ℂ)) x := by
   simpa only [Complex.restrictScalars_one_smulRight] using h.has_strict_fderiv_at.restrict_scalars ℝ
 #align has_strict_deriv_at.complex_to_real_fderiv HasStrictDerivAt.complexToReal_fderiv
 
 theorem HasDerivAt.complexToReal_fderiv {f : ℂ → ℂ} {f' x : ℂ} (h : HasDerivAt f f' x) :
-    HasFderivAt f (f' • (1 : ℂ →L[ℝ] ℂ)) x := by
+    HasFDerivAt f (f' • (1 : ℂ →L[ℝ] ℂ)) x := by
   simpa only [Complex.restrictScalars_one_smulRight] using h.has_fderiv_at.restrict_scalars ℝ
 #align has_deriv_at.complex_to_real_fderiv HasDerivAt.complexToReal_fderiv
 
 theorem HasDerivWithinAt.complexToReal_fderiv {f : ℂ → ℂ} {s : Set ℂ} {f' x : ℂ}
-    (h : HasDerivWithinAt f f' s x) : HasFderivWithinAt f (f' • (1 : ℂ →L[ℝ] ℂ)) s x := by
+    (h : HasDerivWithinAt f f' s x) : HasFDerivWithinAt f (f' • (1 : ℂ →L[ℝ] ℂ)) s x := by
   simpa only [Complex.restrictScalars_one_smulRight] using h.has_fderiv_within_at.restrict_scalars ℝ
 #align has_deriv_within_at.complex_to_real_fderiv HasDerivWithinAt.complexToReal_fderiv
 

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

@@ -94,19 +94,19 @@ variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E]
 
 theorem HasStrictDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E}
     (h : HasStrictDerivAt f f' x) :
-    HasStrictFderivAt f (reClm.smul_right f' + i • imClm.smul_right f') x := by
+    HasStrictFderivAt f (reClm.smul_right f' + I • imClm.smul_right f') x := by
   simpa only [Complex.restrictScalars_one_smul_right'] using
     h.has_strict_fderiv_at.restrict_scalars ℝ
 #align has_strict_deriv_at.complex_to_real_fderiv' HasStrictDerivAt.complexToReal_fderiv'
 
 theorem HasDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E} (h : HasDerivAt f f' x) :
-    HasFderivAt f (reClm.smul_right f' + i • imClm.smul_right f') x := by
+    HasFderivAt f (reClm.smul_right f' + I • imClm.smul_right f') x := by
   simpa only [Complex.restrictScalars_one_smul_right'] using h.has_fderiv_at.restrict_scalars ℝ
 #align has_deriv_at.complex_to_real_fderiv' HasDerivAt.complexToReal_fderiv'
 
 theorem HasDerivWithinAt.complexToReal_fderiv' {f : ℂ → E} {s : Set ℂ} {x : ℂ} {f' : E}
     (h : HasDerivWithinAt f f' s x) :
-    HasFderivWithinAt f (reClm.smul_right f' + i • imClm.smul_right f') s x := by
+    HasFderivWithinAt f (reClm.smul_right f' + I • imClm.smul_right f') s x := by
   simpa only [Complex.restrictScalars_one_smul_right'] using
     h.has_fderiv_within_at.restrict_scalars ℝ
 #align has_deriv_within_at.complex_to_real_fderiv' HasDerivWithinAt.complexToReal_fderiv'

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

@@ -163,7 +163,7 @@ theorem DifferentiableAt.conformalAt (h : DifferentiableAt ℂ f z) (hf' : deriv
     ConformalAt f z := by
   rw [conformalAt_iff_isConformalMap_fderiv, (h.hasFDerivAt.restrictScalars ℝ).fderiv]
   apply isConformalMap_complex_linear
-  simpa only [Ne.def, ext_ring_iff]
+  simpa only [Ne, ext_ring_iff]
 #align differentiable_at.conformal_at DifferentiableAt.conformalAt
 
 /-- A complex function is conformal if and only if the function is holomorphic or antiholomorphic

Rename

• Complex.equivRealProdClm → Complex.equivRealProdCLM;
  • TODO: should this one use CLE?
• Complex.reClm → Complex.reCLM;
• Complex.imClm → Complex.imCLM;
• Complex.conjLie → Complex.conjLIE;
• Complex.conjCle → Complex.conjCLE;
• Complex.ofRealLi → Complex.ofRealLI;
• Complex.ofRealClm → Complex.ofRealCLM;
• fderivInnerClm → fderivInnerCLM;
• LinearPMap.adjointDomainMkClm → LinearPMap.adjointDomainMkCLM;
• LinearPMap.adjointDomainMkClmExtend → LinearPMap.adjointDomainMkCLMExtend;
• IsROrC.reClm → IsROrC.reCLM;
• IsROrC.imClm → IsROrC.imCLM;
• IsROrC.conjLie → IsROrC.conjLIE;
• IsROrC.conjCle → IsROrC.conjCLE;
• IsROrC.ofRealLi → IsROrC.ofRealLI;
• IsROrC.ofRealClm → IsROrC.ofRealCLM;
• MeasureTheory.condexpL1Clm → MeasureTheory.condexpL1CLM;
• algebraMapClm → algebraMapCLM;
• WeakDual.CharacterSpace.toClm → WeakDual.CharacterSpace.toCLM;
• BoundedContinuousFunction.evalClm → BoundedContinuousFunction.evalCLM;
• ContinuousMap.evalClm → ContinuousMap.evalCLM;
• TrivSqZeroExt.fstClm → TrivSqZeroExt.fstClm;
• TrivSqZeroExt.sndClm → TrivSqZeroExt.sndCLM;
• TrivSqZeroExt.inlClm → TrivSqZeroExt.inlCLM;
• TrivSqZeroExt.inrClm → TrivSqZeroExt.inrCLM

and related theorems.

@@ -48,12 +48,12 @@ variable {e : ℂ → ℂ} {e' : ℂ} {z : ℝ}
 differentiable at this point, with a derivative equal to the real part of the complex derivative. -/
 theorem HasStrictDerivAt.real_of_complex (h : HasStrictDerivAt e e' z) :
     HasStrictDerivAt (fun x : ℝ => (e x).re) e'.re z := by
-  have A : HasStrictFDerivAt ((↑) : ℝ → ℂ) ofRealClm z := ofRealClm.hasStrictFDerivAt
+  have A : HasStrictFDerivAt ((↑) : ℝ → ℂ) ofRealCLM z := ofRealCLM.hasStrictFDerivAt
   have B :
     HasStrictFDerivAt e ((ContinuousLinearMap.smulRight 1 e' : ℂ →L[ℂ] ℂ).restrictScalars ℝ)
-      (ofRealClm z) :=
+      (ofRealCLM z) :=
     h.hasStrictFDerivAt.restrictScalars ℝ
-  have C : HasStrictFDerivAt re reClm (e (ofRealClm z)) := reClm.hasStrictFDerivAt
+  have C : HasStrictFDerivAt re reCLM (e (ofRealCLM z)) := reCLM.hasStrictFDerivAt
   -- Porting note: this should be by:
   -- simpa using (C.comp z (B.comp z A)).hasStrictDerivAt
   -- but for some reason simp can not use `ContinuousLinearMap.comp_apply`
@@ -67,12 +67,12 @@ the real part of `e` is also differentiable at this point, with a derivative equ
 of the complex derivative. -/
 theorem HasDerivAt.real_of_complex (h : HasDerivAt e e' z) :
     HasDerivAt (fun x : ℝ => (e x).re) e'.re z := by
-  have A : HasFDerivAt ((↑) : ℝ → ℂ) ofRealClm z := ofRealClm.hasFDerivAt
+  have A : HasFDerivAt ((↑) : ℝ → ℂ) ofRealCLM z := ofRealCLM.hasFDerivAt
   have B :
     HasFDerivAt e ((ContinuousLinearMap.smulRight 1 e' : ℂ →L[ℂ] ℂ).restrictScalars ℝ)
-      (ofRealClm z) :=
+      (ofRealCLM z) :=
     h.hasFDerivAt.restrictScalars ℝ
-  have C : HasFDerivAt re reClm (e (ofRealClm z)) := reClm.hasFDerivAt
+  have C : HasFDerivAt re reCLM (e (ofRealCLM z)) := reCLM.hasFDerivAt
   -- Porting note: this should be by:
   -- simpa using (C.comp z (B.comp z A)).hasStrictDerivAt
   -- but for some reason simp can not use `ContinuousLinearMap.comp_apply`
@@ -83,9 +83,9 @@ theorem HasDerivAt.real_of_complex (h : HasDerivAt e e' z) :
 
 theorem ContDiffAt.real_of_complex {n : ℕ∞} (h : ContDiffAt ℂ n e z) :
     ContDiffAt ℝ n (fun x : ℝ => (e x).re) z := by
-  have A : ContDiffAt ℝ n ((↑) : ℝ → ℂ) z := ofRealClm.contDiff.contDiffAt
+  have A : ContDiffAt ℝ n ((↑) : ℝ → ℂ) z := ofRealCLM.contDiff.contDiffAt
   have B : ContDiffAt ℝ n e z := h.restrict_scalars ℝ
-  have C : ContDiffAt ℝ n re (e z) := reClm.contDiff.contDiffAt
+  have C : ContDiffAt ℝ n re (e z) := reCLM.contDiff.contDiffAt
   exact C.comp z (B.comp z A)
 #align cont_diff_at.real_of_complex ContDiffAt.real_of_complex
 
@@ -98,19 +98,19 @@ variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E]
 
 theorem HasStrictDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E}
     (h : HasStrictDerivAt f f' x) :
-    HasStrictFDerivAt f (reClm.smulRight f' + I • imClm.smulRight f') x := by
+    HasStrictFDerivAt f (reCLM.smulRight f' + I • imCLM.smulRight f') x := by
   simpa only [Complex.restrictScalars_one_smulRight'] using
     h.hasStrictFDerivAt.restrictScalars ℝ
 #align has_strict_deriv_at.complex_to_real_fderiv' HasStrictDerivAt.complexToReal_fderiv'
 
 theorem HasDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E} (h : HasDerivAt f f' x) :
-    HasFDerivAt f (reClm.smulRight f' + I • imClm.smulRight f') x := by
+    HasFDerivAt f (reCLM.smulRight f' + I • imCLM.smulRight f') x := by
   simpa only [Complex.restrictScalars_one_smulRight'] using h.hasFDerivAt.restrictScalars ℝ
 #align has_deriv_at.complex_to_real_fderiv' HasDerivAt.complexToReal_fderiv'
 
 theorem HasDerivWithinAt.complexToReal_fderiv' {f : ℂ → E} {s : Set ℂ} {x : ℂ} {f' : E}
     (h : HasDerivWithinAt f f' s x) :
-    HasFDerivWithinAt f (reClm.smulRight f' + I • imClm.smulRight f') s x := by
+    HasFDerivWithinAt f (reCLM.smulRight f' + I • imCLM.smulRight f') s x := by
   simpa only [Complex.restrictScalars_one_smulRight'] using
     h.hasFDerivWithinAt.restrictScalars ℝ
 #align has_deriv_within_at.complex_to_real_fderiv' HasDerivWithinAt.complexToReal_fderiv'
@@ -133,15 +133,15 @@ theorem HasDerivWithinAt.complexToReal_fderiv {f : ℂ → ℂ} {s : Set ℂ} {f
 /-- If a complex function `e` is differentiable at a real point, then its restriction to `ℝ` is
 differentiable there as a function `ℝ → ℂ`, with the same derivative. -/
 theorem HasDerivAt.comp_ofReal (hf : HasDerivAt e e' ↑z) : HasDerivAt (fun y : ℝ => e ↑y) e' z :=
-  by simpa only [ofRealClm_apply, ofReal_one, mul_one] using hf.comp z ofRealClm.hasDerivAt
+  by simpa only [ofRealCLM_apply, ofReal_one, mul_one] using hf.comp z ofRealCLM.hasDerivAt
 #align has_deriv_at.comp_of_real HasDerivAt.comp_ofReal
 
 /-- If a function `f : ℝ → ℝ` is differentiable at a (real) point `x`, then it is also
 differentiable as a function `ℝ → ℂ`. -/
 theorem HasDerivAt.ofReal_comp {f : ℝ → ℝ} {u : ℝ} (hf : HasDerivAt f u z) :
     HasDerivAt (fun y : ℝ => ↑(f y) : ℝ → ℂ) u z := by
-  simpa only [ofRealClm_apply, ofReal_one, real_smul, mul_one] using
-    ofRealClm.hasDerivAt.scomp z hf
+  simpa only [ofRealCLM_apply, ofReal_one, real_smul, mul_one] using
+    ofRealCLM.hasDerivAt.scomp z hf
 #align has_deriv_at.of_real_comp HasDerivAt.ofReal_comp
 
 end RealDerivOfComplex
@@ -179,10 +179,10 @@ theorem conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj {f : ℂ
   apply or_congr
   · rw [differentiableAt_iff_restrictScalars ℝ h_diff]
   rw [← conj_conj z] at h_diff
-  rw [differentiableAt_iff_restrictScalars ℝ (h_diff.comp _ conjCle.differentiableAt)]
+  rw [differentiableAt_iff_restrictScalars ℝ (h_diff.comp _ conjCLE.differentiableAt)]
   refine' exists_congr fun g => rfl.congr _
-  have : fderiv ℝ conj (conj z) = _ := conjCle.fderiv
-  simp [fderiv.comp _ h_diff conjCle.differentiableAt, this, conj_conj]
+  have : fderiv ℝ conj (conj z) = _ := conjCLE.fderiv
+  simp [fderiv.comp _ h_diff conjCLE.differentiableAt, this, conj_conj]
 #align conformal_at_iff_differentiable_at_or_differentiable_at_comp_conj conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj
 
 end Conformality

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>

@@ -3,7 +3,7 @@ Copyright (c) Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yourong Zang
 -/
-import Mathlib.Analysis.Calculus.ContDiff
+import Mathlib.Analysis.Calculus.ContDiff.Basic
 import Mathlib.Analysis.Calculus.Deriv.Linear
 import Mathlib.Analysis.Complex.Conformal
 import Mathlib.Analysis.Calculus.Conformal.NormedSpace

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

This has nice performance benefits.

@@ -94,7 +94,7 @@ theorem ContDiff.real_of_complex {n : ℕ∞} (h : ContDiff ℂ n e) :
   contDiff_iff_contDiffAt.2 fun _ => h.contDiffAt.real_of_complex
 #align cont_diff.real_of_complex ContDiff.real_of_complex
 
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E]
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E]
 
 theorem HasStrictDerivAt.complexToReal_fderiv' {f : ℂ → E} {x : ℂ} {f' : E}
     (h : HasStrictDerivAt f f' x) :
@@ -154,7 +154,7 @@ open Complex ContinuousLinearMap
 
 open scoped ComplexConjugate
 
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E] {z : ℂ} {f : ℂ → E}
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] {z : ℂ} {f : ℂ → E}
 
 /-- A real differentiable function of the complex plane into some complex normed space `E` is
     conformal at a point `z` if it is holomorphic at that point with a nonvanishing differential.

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yourong Zang
-
-! This file was ported from Lean 3 source module analysis.complex.real_deriv
-! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Calculus.ContDiff
 import Mathlib.Analysis.Calculus.Deriv.Linear
 import Mathlib.Analysis.Complex.Conformal
 import Mathlib.Analysis.Calculus.Conformal.NormedSpace
 
+#align_import analysis.complex.real_deriv from "leanprover-community/mathlib"@"3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe"
+
 /-! # Real differentiability of complex-differentiable functions
 
 `HasDerivAt.real_of_complex` expresses that, if a function on `ℂ` is differentiable (over `ℂ`),

@@ -135,17 +135,17 @@ theorem HasDerivWithinAt.complexToReal_fderiv {f : ℂ → ℂ} {s : Set ℂ} {f
 
 /-- If a complex function `e` is differentiable at a real point, then its restriction to `ℝ` is
 differentiable there as a function `ℝ → ℂ`, with the same derivative. -/
-theorem HasDerivAt.comp_of_real (hf : HasDerivAt e e' ↑z) : HasDerivAt (fun y : ℝ => e ↑y) e' z :=
+theorem HasDerivAt.comp_ofReal (hf : HasDerivAt e e' ↑z) : HasDerivAt (fun y : ℝ => e ↑y) e' z :=
   by simpa only [ofRealClm_apply, ofReal_one, mul_one] using hf.comp z ofRealClm.hasDerivAt
-#align has_deriv_at.comp_of_real HasDerivAt.comp_of_real
+#align has_deriv_at.comp_of_real HasDerivAt.comp_ofReal
 
 /-- If a function `f : ℝ → ℝ` is differentiable at a (real) point `x`, then it is also
 differentiable as a function `ℝ → ℂ`. -/
-theorem HasDerivAt.of_real_comp {f : ℝ → ℝ} {u : ℝ} (hf : HasDerivAt f u z) :
+theorem HasDerivAt.ofReal_comp {f : ℝ → ℝ} {u : ℝ} (hf : HasDerivAt f u z) :
     HasDerivAt (fun y : ℝ => ↑(f y) : ℝ → ℂ) u z := by
   simpa only [ofRealClm_apply, ofReal_one, real_smul, mul_one] using
     ofRealClm.hasDerivAt.scomp z hf
-#align has_deriv_at.of_real_comp HasDerivAt.of_real_comp
+#align has_deriv_at.of_real_comp HasDerivAt.ofReal_comp
 
 end RealDerivOfComplex
 

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