analysis.calculus.uniform_limits_deriv ⟷ Mathlib.Analysis.Calculus.UniformLimitsDeriv

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin H. Wilson
 -/
 import Analysis.Calculus.MeanValue
-import Analysis.NormedSpace.IsROrC
+import Analysis.NormedSpace.RCLike
 import Order.Filter.Curry
 
 #align_import analysis.calculus.uniform_limits_deriv from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
@@ -104,7 +104,7 @@ open scoped uniformity Filter Topology
 
 section LimitsOfDerivatives
 
-variable {ι : Type _} {l : Filter ι} {E : Type _} [NormedAddCommGroup E] {𝕜 : Type _} [IsROrC 𝕜]
+variable {ι : Type _} {l : Filter ι} {E : Type _} [NormedAddCommGroup E] {𝕜 : Type _} [RCLike 𝕜]
   [NormedSpace 𝕜 E] {G : Type _} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {f : ι → E → G}
   {g : E → G} {f' : ι → E → E →L[𝕜] G} {g' : E → E →L[𝕜] G} {x : E}
 
@@ -303,7 +303,7 @@ theorem difference_quotients_converge_uniformly (hf' : TendstoUniformlyOnFilter
     ⟨_, b, fun e : E => Metric.ball x r e,
       eventually_mem_set.mpr (metric.nhds_basis_ball.mem_of_mem hr), fun n hn y hy => _⟩
   simp only [Pi.zero_apply, dist_zero_left]
-  rw [← smul_sub, norm_smul, norm_inv, IsROrC.norm_coe_norm]
+  rw [← smul_sub, norm_smul, norm_inv, RCLike.norm_coe_norm]
   refine' lt_of_le_of_lt _ hqε
   by_cases hyz' : x = y; · simp [hyz', hqpos.le]
   have hyz : 0 < ‖y - x‖ := by rw [norm_pos_iff]; intro hy'; exact hyz' (eq_of_sub_eq_zero hy').symm
@@ -357,7 +357,7 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
   conv =>
     congr
     ext
-    rw [← abs_norm, ← abs_inv, ← @IsROrC.norm_ofReal 𝕜 _ _, IsROrC.ofReal_inv, ← norm_smul]
+    rw [← abs_norm, ← abs_inv, ← @RCLike.norm_ofReal 𝕜 _ _, RCLike.ofReal_inv, ← norm_smul]
   rw [← tendsto_zero_iff_norm_tendsto_zero]
   have :
     (fun a : ι × E => (‖a.2 - x‖⁻¹ : 𝕜) • (g a.2 - g x - (g' x) (a.2 - x))) =
@@ -392,7 +392,7 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     refine' (this ε hε).mono fun y hy => _
     rw [dist_eq_norm] at hy ⊢
     simp only [sub_zero, map_sub, norm_mul, norm_inv, norm_norm] at hy ⊢
-    rw [norm_smul, norm_inv, IsROrC.norm_coe_norm]
+    rw [norm_smul, norm_inv, RCLike.norm_coe_norm]
     exact hy
   · -- hfg' after specializing to `x` and applying the definition of the operator norm
     refine' tendsto.mono_left _ curry_le_prod
@@ -407,7 +407,7 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     have := tendsto_fst.comp (h2.prod_map tendsto_id)
     refine' squeeze_zero_norm _ (tendsto_zero_iff_norm_tendsto_zero.mp this)
     intro n
-    simp_rw [norm_smul, norm_inv, IsROrC.norm_coe_norm]
+    simp_rw [norm_smul, norm_inv, RCLike.norm_coe_norm]
     by_cases hx : x = n.2; · simp [hx]
     have hnx : 0 < ‖n.2 - x‖ := by rw [norm_pos_iff]; intro hx';
       exact hx (eq_of_sub_eq_zero hx').symm
@@ -485,7 +485,7 @@ derivatives
 -/
 
 
-variable {ι : Type _} {l : Filter ι} {𝕜 : Type _} [IsROrC 𝕜] {G : Type _} [NormedAddCommGroup G]
+variable {ι : Type _} {l : Filter ι} {𝕜 : Type _} [RCLike 𝕜] {G : Type _} [NormedAddCommGroup G]
   [NormedSpace 𝕜 G] {f : ι → 𝕜 → G} {g : 𝕜 → G} {f' : ι → 𝕜 → G} {g' : 𝕜 → G} {x : 𝕜}
 
 #print UniformCauchySeqOnFilter.one_smulRight /-

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

@@ -125,7 +125,7 @@ theorem uniformCauchySeqOnFilter_of_fderiv (hf' : UniformCauchySeqOnFilter f' l
       TendstoUniformlyOnFilter (fun (n : ι × ι) (z : E) => f n.1 x - f n.2 x) 0 (l ×ᶠ l) (𝓝 x)
     by
     have := this.1.add this.2
-    rw [add_zero] at this 
+    rw [add_zero] at this
     exact this.congr (by simp)
   constructor
   · -- This inequality follows from the mean value theorem. To apply it, we will need to shrink our
@@ -142,7 +142,7 @@ theorem uniformCauchySeqOnFilter_of_fderiv (hf' : UniformCauchySeqOnFilter f' l
     have hxy : ∀ y : E, y ∈ Metric.ball x r → ‖y - x‖ < 1 :=
       by
       intro y hy
-      rw [Metric.mem_ball, dist_eq_norm] at hy 
+      rw [Metric.mem_ball, dist_eq_norm] at hy
       exact lt_of_lt_of_le hy (min_le_left _ _)
     have hxyε : ∀ y : E, y ∈ Metric.ball x r → ε * ‖y - x‖ < ε :=
       by
@@ -198,7 +198,7 @@ theorem uniformCauchySeqOn_ball_of_fderiv {r : ℝ} (hf' : UniformCauchySeqOn f'
       TendstoUniformlyOn (fun (n : ι × ι) (z : E) => f n.1 x - f n.2 x) 0 (l ×ᶠ l) (Metric.ball x r)
     by
     have := this.1.add this.2
-    rw [add_zero] at this 
+    rw [add_zero] at this
     refine' this.congr _
     apply eventually_of_forall
     intro n z hz
@@ -290,8 +290,8 @@ theorem difference_quotients_converge_uniformly (hf' : TendstoUniformlyOnFilter
   rw [SeminormedAddGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_zero]
   rw [Metric.tendstoUniformlyOnFilter_iff]
   have hfg' := hf'.uniform_cauchy_seq_on_filter
-  rw [SeminormedAddGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_zero] at hfg' 
-  rw [Metric.tendstoUniformlyOnFilter_iff] at hfg' 
+  rw [SeminormedAddGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_zero] at hfg'
+  rw [Metric.tendstoUniformlyOnFilter_iff] at hfg'
   intro ε hε
   obtain ⟨q, hqpos, hqε⟩ := exists_pos_rat_lt hε
   specialize hfg' (q : ℝ) (by simp [hqpos])
@@ -308,7 +308,7 @@ theorem difference_quotients_converge_uniformly (hf' : TendstoUniformlyOnFilter
   by_cases hyz' : x = y; · simp [hyz', hqpos.le]
   have hyz : 0 < ‖y - x‖ := by rw [norm_pos_iff]; intro hy'; exact hyz' (eq_of_sub_eq_zero hy').symm
   rw [inv_mul_le_iff hyz, mul_comm, sub_sub_sub_comm]
-  simp only [Pi.zero_apply, dist_zero_left] at e 
+  simp only [Pi.zero_apply, dist_zero_left] at e
   refine'
     Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le
       (fun y hy => ((e hn (hr' hy)).2.1.sub (e hn (hr' hy)).2.2).HasFDerivWithinAt)
@@ -345,8 +345,8 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     rw [Metric.tendsto_nhds] at this ⊢
     intro ε hε
     specialize this ε hε
-    rw [eventually_curry_iff] at this 
-    simp only at this 
+    rw [eventually_curry_iff] at this
+    simp only at this
     exact (eventually_const.mp this).mono (by simp only [imp_self, forall_const])
   -- With the new quantifier in hand, we can perform the famous `ε/3` proof. Specifically,
   -- we will break up the limit (the difference functions minus the derivative go to 0) into 3:
@@ -374,13 +374,13 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
   refine' tendsto.add (tendsto.add _ _) _
   simp only
   · have := difference_quotients_converge_uniformly hf' hf hfg
-    rw [Metric.tendstoUniformlyOnFilter_iff] at this 
+    rw [Metric.tendstoUniformlyOnFilter_iff] at this
     rw [Metric.tendsto_nhds]
     intro ε hε
     apply ((this ε hε).filter_mono curry_le_prod).mono
     intro n hn
     rw [dist_eq_norm] at hn ⊢
-    rw [← smul_sub] at hn 
+    rw [← smul_sub] at hn
     rwa [sub_zero]
   · -- (Almost) the definition of the derivatives
     rw [Metric.tendsto_nhds]
@@ -388,7 +388,7 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     rw [eventually_curry_iff]
     refine' hf.curry.mono fun n hn => _
     have := hn.self_of_nhds
-    rw [hasFDerivAt_iff_tendsto, Metric.tendsto_nhds] at this 
+    rw [hasFDerivAt_iff_tendsto, Metric.tendsto_nhds] at this
     refine' (this ε hε).mono fun y hy => _
     rw [dist_eq_norm] at hy ⊢
     simp only [sub_zero, map_sub, norm_mul, norm_inv, norm_norm] at hy ⊢
@@ -398,7 +398,7 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     refine' tendsto.mono_left _ curry_le_prod
     have h1 : tendsto (fun n : ι × E => g' n.2 - f' n.1 n.2) (l ×ᶠ 𝓝 x) (𝓝 0) :=
       by
-      rw [Metric.tendstoUniformlyOnFilter_iff] at hf' 
+      rw [Metric.tendstoUniformlyOnFilter_iff] at hf'
       exact metric.tendsto_nhds.mpr fun ε hε => by simpa using hf' ε hε
     have h2 : tendsto (fun n : ι => g' x - f' n x) l (𝓝 0) :=
       by
@@ -519,7 +519,7 @@ theorem uniformCauchySeqOnFilter_of_deriv (hf' : UniformCauchySeqOnFilter f' l (
     (hf : ∀ᶠ n : ι × 𝕜 in l ×ᶠ 𝓝 x, HasDerivAt (f n.1) (f' n.1 n.2) n.2)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOnFilter f l (𝓝 x) :=
   by
-  simp_rw [hasDerivAt_iff_hasFDerivAt] at hf 
+  simp_rw [hasDerivAt_iff_hasFDerivAt] at hf
   exact uniformCauchySeqOnFilter_of_fderiv hf'.one_smul_right hf hfg
 #align uniform_cauchy_seq_on_filter_of_deriv uniformCauchySeqOnFilter_of_deriv
 -/
@@ -529,8 +529,8 @@ theorem uniformCauchySeqOn_ball_of_deriv {r : ℝ} (hf' : UniformCauchySeqOn f'
     (hf : ∀ n : ι, ∀ y : 𝕜, y ∈ Metric.ball x r → HasDerivAt (f n) (f' n y) y)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOn f l (Metric.ball x r) :=
   by
-  simp_rw [hasDerivAt_iff_hasFDerivAt] at hf 
-  rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf' 
+  simp_rw [hasDerivAt_iff_hasFDerivAt] at hf
+  rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf'
   have hf' :
     UniformCauchySeqOn (fun n => fun z => (1 : 𝕜 →L[𝕜] 𝕜).smul_right (f' n z)) l
       (Metric.ball x r) :=

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

@@ -414,7 +414,7 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     rw [inv_mul_le_iff hnx, mul_comm]
     simp only [Function.comp_apply, Prod_map]
     rw [norm_sub_rev]
-    exact (f' n.1 x - g' x).le_op_norm (n.2 - x)
+    exact (f' n.1 x - g' x).le_opNorm (n.2 - x)
 #align has_fderiv_at_of_tendsto_uniformly_on_filter hasFDerivAt_of_tendstoUniformlyOnFilter
 -/
 
@@ -505,7 +505,7 @@ theorem UniformCauchySeqOnFilter.one_smulRight {l' : Filter 𝕜}
   intro n hn
   refine' lt_of_le_of_lt _ hq'
   simp only [dist_eq_norm, Pi.zero_apply, zero_sub, norm_neg] at hn ⊢
-  refine' ContinuousLinearMap.op_norm_le_bound _ hq.le _
+  refine' ContinuousLinearMap.opNorm_le_bound _ hq.le _
   intro z
   simp only [ContinuousLinearMap.coe_sub', Pi.sub_apply, ContinuousLinearMap.smulRight_apply,
     ContinuousLinearMap.one_apply]
@@ -564,7 +564,7 @@ theorem hasDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     intro n hn
     refine' lt_of_le_of_lt _ hq'
     simp only [F', G', dist_eq_norm] at hn ⊢
-    refine' ContinuousLinearMap.op_norm_le_bound _ hq.le _
+    refine' ContinuousLinearMap.opNorm_le_bound _ hq.le _
     intro z
     simp only [ContinuousLinearMap.coe_sub', Pi.sub_apply, ContinuousLinearMap.smulRight_apply,
       ContinuousLinearMap.one_apply]

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

@@ -3,9 +3,9 @@ Copyright (c) 2022 Kevin H. Wilson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin H. Wilson
 -/
-import Mathbin.Analysis.Calculus.MeanValue
-import Mathbin.Analysis.NormedSpace.IsROrC
-import Mathbin.Order.Filter.Curry
+import Analysis.Calculus.MeanValue
+import Analysis.NormedSpace.IsROrC
+import Order.Filter.Curry
 
 #align_import analysis.calculus.uniform_limits_deriv from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Kevin H. Wilson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin H. Wilson
-
-! This file was ported from Lean 3 source module analysis.calculus.uniform_limits_deriv
-! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.MeanValue
 import Mathbin.Analysis.NormedSpace.IsROrC
 import Mathbin.Order.Filter.Curry
 
+#align_import analysis.calculus.uniform_limits_deriv from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
+
 /-!
 # Swapping limits and derivatives via uniform convergence
 

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

@@ -111,6 +111,7 @@ variable {ι : Type _} {l : Filter ι} {E : Type _} [NormedAddCommGroup E] {𝕜
   [NormedSpace 𝕜 E] {G : Type _} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {f : ι → E → G}
   {g : E → G} {f' : ι → E → E →L[𝕜] G} {g' : E → E →L[𝕜] G} {x : E}
 
+#print uniformCauchySeqOnFilter_of_fderiv /-
 /-- If a sequence of functions real or complex functions are eventually differentiable on a
 neighborhood of `x`, they are Cauchy _at_ `x`, and their derivatives
 are a uniform Cauchy sequence in a neighborhood of `x`, then the functions form a uniform Cauchy
@@ -170,7 +171,9 @@ theorem uniformCauchySeqOnFilter_of_fderiv (hf' : UniformCauchySeqOnFilter f' l
           eventually_prod_iff.mpr ⟨_, ht, _, ht, fun n hn n' hn' => ⟨hn, hn'⟩⟩, fun y => True, by
           simp, fun n hn y hy => by simpa [norm_sub_rev, dist_eq_norm] using ht' _ hn.1 _ hn.2⟩
 #align uniform_cauchy_seq_on_filter_of_fderiv uniformCauchySeqOnFilter_of_fderiv
+-/
 
+#print uniformCauchySeqOn_ball_of_fderiv /-
 /-- A variant of the second fundamental theorem of calculus (FTC-2): If a sequence of functions
 between real or complex normed spaces are differentiable on a ball centered at `x`, they
 form a Cauchy sequence _at_ `x`, and their derivatives are Cauchy uniformly on the ball, then the
@@ -232,7 +235,9 @@ theorem uniformCauchySeqOn_ball_of_fderiv {r : ℝ} (hf' : UniformCauchySeqOn f'
     rw [dist_eq_norm, Pi.zero_apply, zero_sub, norm_neg, ← dist_eq_norm]
     exact ht' _ hn _ hn'
 #align uniform_cauchy_seq_on_ball_of_fderiv uniformCauchySeqOn_ball_of_fderiv
+-/
 
+#print cauchy_map_of_uniformCauchySeqOn_fderiv /-
 /-- If a sequence of functions between real or complex normed spaces are differentiable on a
 preconnected open set, they form a Cauchy sequence _at_ `x`, and their derivatives are Cauchy
 uniformly on the set, then the functions form a Cauchy sequence at any point in the set. -/
@@ -265,7 +270,9 @@ theorem cauchy_map_of_uniformCauchySeqOn_fderiv {s : Set E} (hs : IsOpen s) (h's
     rw [dist_comm]; linarith
   exact A y (ε / 2) yt (B.trans hε) (Metric.mem_ball.2 hxy)
 #align cauchy_map_of_uniform_cauchy_seq_on_fderiv cauchy_map_of_uniformCauchySeqOn_fderiv
+-/
 
+#print difference_quotients_converge_uniformly /-
 /-- If `f_n → g` pointwise and the derivatives `(f_n)' → h` _uniformly_ converge, then
 in fact for a fixed `y`, the difference quotients `‖z - y‖⁻¹ • (f_n z - f_n y)` converge
 _uniformly_ to `‖z - y‖⁻¹ • (g z - g y)` -/
@@ -310,7 +317,9 @@ theorem difference_quotients_converge_uniformly (hf' : TendstoUniformlyOnFilter
       (fun y hy => ((e hn (hr' hy)).2.1.sub (e hn (hr' hy)).2.2).HasFDerivWithinAt)
       (fun y hy => (e hn (hr' hy)).1.le) (convex_ball x r) (Metric.mem_ball_self hr) hy
 #align difference_quotients_converge_uniformly difference_quotients_converge_uniformly
+-/
 
+#print hasFDerivAt_of_tendstoUniformlyOnFilter /-
 /-- `(d/dx) lim_{n → ∞} f n x = lim_{n → ∞} f' n x` when the `f' n` converge
 _uniformly_ to their limit at `x`.
 
@@ -410,8 +419,10 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     rw [norm_sub_rev]
     exact (f' n.1 x - g' x).le_op_norm (n.2 - x)
 #align has_fderiv_at_of_tendsto_uniformly_on_filter hasFDerivAt_of_tendstoUniformlyOnFilter
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print hasFDerivAt_of_tendstoLocallyUniformlyOn /-
 theorem hasFDerivAt_of_tendstoLocallyUniformlyOn [NeBot l] {s : Set E} (hs : IsOpen s)
     (hf' : TendstoLocallyUniformlyOn f' g' l s) (hf : ∀ n, ∀ x ∈ s, HasFDerivAt (f n) (f' n x) x)
     (hfg : ∀ x ∈ s, Tendsto (fun n => f n x) l (𝓝 (g x))) (hx : x ∈ s) : HasFDerivAt g (g' x) x :=
@@ -423,7 +434,9 @@ theorem hasFDerivAt_of_tendstoLocallyUniformlyOn [NeBot l] {s : Set E} (hs : IsO
   refine' hasFDerivAt_of_tendstoUniformlyOnFilter _ h4 (eventually_of_mem h1 hfg)
   simpa [IsOpen.nhdsWithin_eq hs hx] using tendsto_locally_uniformly_on_iff_filter.mp hf' x hx
 #align has_fderiv_at_of_tendsto_locally_uniformly_on hasFDerivAt_of_tendstoLocallyUniformlyOn
+-/
 
+#print hasFDerivAt_of_tendsto_locally_uniformly_on' /-
 /-- A slight variant of `has_fderiv_at_of_tendsto_locally_uniformly_on` with the assumption stated
 in terms of `differentiable_on` rather than `has_fderiv_at`. This makes a few proofs nicer in
 complex analysis where holomorphicity is assumed but the derivative is not known a priori. -/
@@ -434,7 +447,9 @@ theorem hasFDerivAt_of_tendsto_locally_uniformly_on' [NeBot l] {s : Set E} (hs :
   refine' hasFDerivAt_of_tendstoLocallyUniformlyOn hs hf' (fun n z hz => _) hfg hx
   exact ((hf n z hz).DifferentiableAt (hs.mem_nhds hz)).HasFDerivAt
 #align has_fderiv_at_of_tendsto_locally_uniformly_on' hasFDerivAt_of_tendsto_locally_uniformly_on'
+-/
 
+#print hasFDerivAt_of_tendstoUniformlyOn /-
 /-- `(d/dx) lim_{n → ∞} f n x = lim_{n → ∞} f' n x` when the `f' n` converge
 _uniformly_ to their limit on an open set containing `x`. -/
 theorem hasFDerivAt_of_tendstoUniformlyOn [NeBot l] {s : Set E} (hs : IsOpen s)
@@ -444,7 +459,9 @@ theorem hasFDerivAt_of_tendstoUniformlyOn [NeBot l] {s : Set E} (hs : IsOpen s)
     ∀ x : E, x ∈ s → HasFDerivAt g (g' x) x := fun x =>
   hasFDerivAt_of_tendstoLocallyUniformlyOn hs hf'.TendstoLocallyUniformlyOn hf hfg
 #align has_fderiv_at_of_tendsto_uniformly_on hasFDerivAt_of_tendstoUniformlyOn
+-/
 
+#print hasFDerivAt_of_tendstoUniformly /-
 /-- `(d/dx) lim_{n → ∞} f n x = lim_{n → ∞} f' n x` when the `f' n` converge
 _uniformly_ to their limit. -/
 theorem hasFDerivAt_of_tendstoUniformly [NeBot l] (hf' : TendstoUniformly f' g' l)
@@ -457,6 +474,7 @@ theorem hasFDerivAt_of_tendstoUniformly [NeBot l] (hf' : TendstoUniformly f' g'
   have hf' : TendstoUniformlyOn f' g' l Set.univ := by rwa [tendstoUniformlyOn_univ]
   refine' hasFDerivAt_of_tendstoUniformlyOn isOpen_univ hf' hf hfg x (Set.mem_univ x)
 #align has_fderiv_at_of_tendsto_uniformly hasFDerivAt_of_tendstoUniformly
+-/
 
 end LimitsOfDerivatives
 
@@ -473,6 +491,7 @@ derivatives
 variable {ι : Type _} {l : Filter ι} {𝕜 : Type _} [IsROrC 𝕜] {G : Type _} [NormedAddCommGroup G]
   [NormedSpace 𝕜 G] {f : ι → 𝕜 → G} {g : 𝕜 → G} {f' : ι → 𝕜 → G} {g' : 𝕜 → G} {x : 𝕜}
 
+#print UniformCauchySeqOnFilter.one_smulRight /-
 /-- If our derivatives converge uniformly, then the Fréchet derivatives converge uniformly -/
 theorem UniformCauchySeqOnFilter.one_smulRight {l' : Filter 𝕜}
     (hf' : UniformCauchySeqOnFilter f' l l') :
@@ -496,7 +515,9 @@ theorem UniformCauchySeqOnFilter.one_smulRight {l' : Filter 𝕜}
   rw [← smul_sub, norm_smul, mul_comm]
   exact mul_le_mul hn.le rfl.le (norm_nonneg _) hq.le
 #align uniform_cauchy_seq_on_filter.one_smul_right UniformCauchySeqOnFilter.one_smulRight
+-/
 
+#print uniformCauchySeqOnFilter_of_deriv /-
 theorem uniformCauchySeqOnFilter_of_deriv (hf' : UniformCauchySeqOnFilter f' l (𝓝 x))
     (hf : ∀ᶠ n : ι × 𝕜 in l ×ᶠ 𝓝 x, HasDerivAt (f n.1) (f' n.1 n.2) n.2)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOnFilter f l (𝓝 x) :=
@@ -504,7 +525,9 @@ theorem uniformCauchySeqOnFilter_of_deriv (hf' : UniformCauchySeqOnFilter f' l (
   simp_rw [hasDerivAt_iff_hasFDerivAt] at hf 
   exact uniformCauchySeqOnFilter_of_fderiv hf'.one_smul_right hf hfg
 #align uniform_cauchy_seq_on_filter_of_deriv uniformCauchySeqOnFilter_of_deriv
+-/
 
+#print uniformCauchySeqOn_ball_of_deriv /-
 theorem uniformCauchySeqOn_ball_of_deriv {r : ℝ} (hf' : UniformCauchySeqOn f' l (Metric.ball x r))
     (hf : ∀ n : ι, ∀ y : 𝕜, y ∈ Metric.ball x r → HasDerivAt (f n) (f' n y) y)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOn f l (Metric.ball x r) :=
@@ -519,7 +542,9 @@ theorem uniformCauchySeqOn_ball_of_deriv {r : ℝ} (hf' : UniformCauchySeqOn f'
     exact hf'.one_smul_right
   exact uniformCauchySeqOn_ball_of_fderiv hf' hf hfg
 #align uniform_cauchy_seq_on_ball_of_deriv uniformCauchySeqOn_ball_of_deriv
+-/
 
+#print hasDerivAt_of_tendstoUniformlyOnFilter /-
 theorem hasDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     (hf' : TendstoUniformlyOnFilter f' g' l (𝓝 x))
     (hf : ∀ᶠ n : ι × 𝕜 in l ×ᶠ 𝓝 x, HasDerivAt (f n.1) (f' n.1 n.2) n.2)
@@ -550,7 +575,9 @@ theorem hasDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     exact mul_le_mul hn.le rfl.le (norm_nonneg _) hq.le
   exact hasFDerivAt_of_tendstoUniformlyOnFilter hf' hf hfg
 #align has_deriv_at_of_tendsto_uniformly_on_filter hasDerivAt_of_tendstoUniformlyOnFilter
+-/
 
+#print hasDerivAt_of_tendstoLocallyUniformlyOn /-
 theorem hasDerivAt_of_tendstoLocallyUniformlyOn [NeBot l] {s : Set 𝕜} (hs : IsOpen s)
     (hf' : TendstoLocallyUniformlyOn f' g' l s)
     (hf : ∀ᶠ n in l, ∀ x ∈ s, HasDerivAt (f n) (f' n x) x)
@@ -562,7 +589,9 @@ theorem hasDerivAt_of_tendstoLocallyUniformlyOn [NeBot l] {s : Set 𝕜} (hs : I
   refine' hasDerivAt_of_tendstoUniformlyOnFilter _ h2 (eventually_of_mem h1 hfg)
   simpa [IsOpen.nhdsWithin_eq hs hx] using tendsto_locally_uniformly_on_iff_filter.mp hf' x hx
 #align has_deriv_at_of_tendsto_locally_uniformly_on hasDerivAt_of_tendstoLocallyUniformlyOn
+-/
 
+#print hasDerivAt_of_tendsto_locally_uniformly_on' /-
 /-- A slight variant of `has_deriv_at_of_tendsto_locally_uniformly_on` with the assumption stated in
 terms of `differentiable_on` rather than `has_deriv_at`. This makes a few proofs nicer in complex
 analysis where holomorphicity is assumed but the derivative is not known a priori. -/
@@ -574,7 +603,9 @@ theorem hasDerivAt_of_tendsto_locally_uniformly_on' [NeBot l] {s : Set 𝕜} (hs
   refine' hasDerivAt_of_tendstoLocallyUniformlyOn hs hf' _ hfg hx
   filter_upwards [hf] with n h z hz using ((h z hz).DifferentiableAt (hs.mem_nhds hz)).HasDerivAt
 #align has_deriv_at_of_tendsto_locally_uniformly_on' hasDerivAt_of_tendsto_locally_uniformly_on'
+-/
 
+#print hasDerivAt_of_tendstoUniformlyOn /-
 theorem hasDerivAt_of_tendstoUniformlyOn [NeBot l] {s : Set 𝕜} (hs : IsOpen s)
     (hf' : TendstoUniformlyOn f' g' l s)
     (hf : ∀ᶠ n in l, ∀ x : 𝕜, x ∈ s → HasDerivAt (f n) (f' n x) x)
@@ -582,7 +613,9 @@ theorem hasDerivAt_of_tendstoUniformlyOn [NeBot l] {s : Set 𝕜} (hs : IsOpen s
     ∀ x : 𝕜, x ∈ s → HasDerivAt g (g' x) x := fun x =>
   hasDerivAt_of_tendstoLocallyUniformlyOn hs hf'.TendstoLocallyUniformlyOn hf hfg
 #align has_deriv_at_of_tendsto_uniformly_on hasDerivAt_of_tendstoUniformlyOn
+-/
 
+#print hasDerivAt_of_tendstoUniformly /-
 theorem hasDerivAt_of_tendstoUniformly [NeBot l] (hf' : TendstoUniformly f' g' l)
     (hf : ∀ᶠ n in l, ∀ x : 𝕜, HasDerivAt (f n) (f' n x) x)
     (hfg : ∀ x : 𝕜, Tendsto (fun n => f n x) l (𝓝 (g x))) : ∀ x : 𝕜, HasDerivAt g (g' x) x :=
@@ -594,6 +627,7 @@ theorem hasDerivAt_of_tendstoUniformly [NeBot l] (hf' : TendstoUniformly f' g' l
   have hf' : TendstoUniformlyOn f' g' l Set.univ := by rwa [tendstoUniformlyOn_univ]
   exact hasDerivAt_of_tendstoUniformlyOn isOpen_univ hf' hf hfg x (Set.mem_univ x)
 #align has_deriv_at_of_tendsto_uniformly hasDerivAt_of_tendstoUniformly
+-/
 
 end deriv
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin H. Wilson
 
 ! This file was ported from Lean 3 source module analysis.calculus.uniform_limits_deriv
-! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
+! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Order.Filter.Curry
 /-!
 # Swapping limits and derivatives via uniform convergence
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The purpose of this file is to prove that the derivative of the pointwise limit of a sequence of
 functions is the pointwise limit of the functions' derivatives when the derivatives converge
 _uniformly_. The formal statement appears as `has_fderiv_at_of_tendsto_locally_uniformly_at`.
@@ -239,7 +242,7 @@ theorem cauchy_map_of_uniformCauchySeqOn_fderiv {s : Set E} (hs : IsOpen s) (h's
     Cauchy (map (fun n => f n x) l) :=
   by
   have : ne_bot l := (cauchy_map_iff.1 hfg).1
-  let t := { y | y ∈ s ∧ Cauchy (map (fun n => f n y) l) }
+  let t := {y | y ∈ s ∧ Cauchy (map (fun n => f n y) l)}
   suffices H : s ⊆ t; exact (H hx).2
   have A : ∀ x ε, x ∈ t → Metric.ball x ε ⊆ s → Metric.ball x ε ⊆ t := fun x ε xt hx y hy =>
     ⟨hx hy,
@@ -569,7 +572,7 @@ theorem hasDerivAt_of_tendsto_locally_uniformly_on' [NeBot l] {s : Set 𝕜} (hs
     (hfg : ∀ x ∈ s, Tendsto (fun n => f n x) l (𝓝 (g x))) (hx : x ∈ s) : HasDerivAt g (g' x) x :=
   by
   refine' hasDerivAt_of_tendstoLocallyUniformlyOn hs hf' _ hfg hx
-  filter_upwards [hf]with n h z hz using((h z hz).DifferentiableAt (hs.mem_nhds hz)).HasDerivAt
+  filter_upwards [hf] with n h z hz using ((h z hz).DifferentiableAt (hs.mem_nhds hz)).HasDerivAt
 #align has_deriv_at_of_tendsto_locally_uniformly_on' hasDerivAt_of_tendsto_locally_uniformly_on'
 
 theorem hasDerivAt_of_tendstoUniformlyOn [NeBot l] {s : Set 𝕜} (hs : IsOpen s)
@@ -586,7 +589,7 @@ theorem hasDerivAt_of_tendstoUniformly [NeBot l] (hf' : TendstoUniformly f' g' l
   by
   intro x
   have hf : ∀ᶠ n in l, ∀ x : 𝕜, x ∈ Set.univ → HasDerivAt (f n) (f' n x) x := by
-    filter_upwards [hf]with n h x hx using h x
+    filter_upwards [hf] with n h x hx using h x
   have hfg : ∀ x : 𝕜, x ∈ Set.univ → tendsto (fun n => f n x) l (𝓝 (g x)) := by simp [hfg]
   have hf' : TendstoUniformlyOn f' g' l Set.univ := by rwa [tendstoUniformlyOn_univ]
   exact hasDerivAt_of_tendstoUniformlyOn isOpen_univ hf' hf hfg x (Set.mem_univ x)

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

@@ -155,7 +155,7 @@ theorem uniformCauchySeqOnFilter_of_fderiv (hf' : UniformCauchySeqOnFilter f' l
     simp only [Pi.zero_apply, dist_zero_left] at e ⊢
     refine' lt_of_le_of_lt _ (hxyε y hy)
     exact
-      Convex.norm_image_sub_le_of_norm_has_fderiv_within_le
+      Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le
         (fun y hy => ((e hn (hr' hy)).2.1.sub (e hn (hr' hy)).2.2).HasFDerivWithinAt)
         (fun y hy => (e hn (hr' hy)).1.le) (convex_ball x r) (Metric.mem_ball_self hr) hy
   · -- This is just `hfg` run through `eventually_prod_iff`
@@ -212,7 +212,7 @@ theorem uniformCauchySeqOn_ball_of_fderiv {r : ℝ} (hf' : UniformCauchySeqOn f'
     intro n hn y hy
     simp_rw [dist_eq_norm, Pi.zero_apply, zero_sub, norm_neg] at hn ⊢
     have mvt :=
-      Convex.norm_image_sub_le_of_norm_has_fderiv_within_le
+      Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le
         (fun z hz => ((hf n.1 z hz).sub (hf n.2 z hz)).HasFDerivWithinAt) (fun z hz => (hn z hz).le)
         (convex_ball x r) (Metric.mem_ball_self hr) hy
     refine' lt_of_le_of_lt mvt _
@@ -303,7 +303,7 @@ theorem difference_quotients_converge_uniformly (hf' : TendstoUniformlyOnFilter
   rw [inv_mul_le_iff hyz, mul_comm, sub_sub_sub_comm]
   simp only [Pi.zero_apply, dist_zero_left] at e 
   refine'
-    Convex.norm_image_sub_le_of_norm_has_fderiv_within_le
+    Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le
       (fun y hy => ((e hn (hr' hy)).2.1.sub (e hn (hr' hy)).2.2).HasFDerivWithinAt)
       (fun y hy => (e hn (hr' hy)).1.le) (convex_ball x r) (Metric.mem_ball_self hr) hy
 #align difference_quotients_converge_uniformly difference_quotients_converge_uniformly

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

@@ -117,19 +117,19 @@ theorem uniformCauchySeqOnFilter_of_fderiv (hf' : UniformCauchySeqOnFilter f' l
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOnFilter f l (𝓝 x) :=
   by
   let : NormedSpace ℝ E; exact NormedSpace.restrictScalars ℝ 𝕜 _
-  rw [SeminormedAddGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_zero] at hf'⊢
+  rw [SeminormedAddGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_zero] at hf' ⊢
   suffices
     TendstoUniformlyOnFilter (fun (n : ι × ι) (z : E) => f n.1 z - f n.2 z - (f n.1 x - f n.2 x)) 0
         (l ×ᶠ l) (𝓝 x) ∧
       TendstoUniformlyOnFilter (fun (n : ι × ι) (z : E) => f n.1 x - f n.2 x) 0 (l ×ᶠ l) (𝓝 x)
     by
     have := this.1.add this.2
-    rw [add_zero] at this
+    rw [add_zero] at this 
     exact this.congr (by simp)
   constructor
   · -- This inequality follows from the mean value theorem. To apply it, we will need to shrink our
     -- neighborhood to small enough ball
-    rw [Metric.tendstoUniformlyOnFilter_iff] at hf'⊢
+    rw [Metric.tendstoUniformlyOnFilter_iff] at hf' ⊢
     intro ε hε
     have := (tendsto_swap4_prod.eventually (hf.prod_mk hf)).diag_of_prod_right
     obtain ⟨a, b, c, d, e⟩ := eventually_prod_iff.1 ((hf' ε hε).And this)
@@ -141,7 +141,7 @@ theorem uniformCauchySeqOnFilter_of_fderiv (hf' : UniformCauchySeqOnFilter f' l
     have hxy : ∀ y : E, y ∈ Metric.ball x r → ‖y - x‖ < 1 :=
       by
       intro y hy
-      rw [Metric.mem_ball, dist_eq_norm] at hy
+      rw [Metric.mem_ball, dist_eq_norm] at hy 
       exact lt_of_lt_of_le hy (min_le_left _ _)
     have hxyε : ∀ y : E, y ∈ Metric.ball x r → ε * ‖y - x‖ < ε :=
       by
@@ -152,7 +152,7 @@ theorem uniformCauchySeqOnFilter_of_fderiv (hf' : UniformCauchySeqOnFilter f' l
       eventually_prod_iff.mpr
         ⟨_, b, fun e : E => Metric.ball x r e,
           eventually_mem_set.mpr (metric.nhds_basis_ball.mem_of_mem hr), fun n hn y hy => _⟩
-    simp only [Pi.zero_apply, dist_zero_left] at e⊢
+    simp only [Pi.zero_apply, dist_zero_left] at e ⊢
     refine' lt_of_le_of_lt _ (hxyε y hy)
     exact
       Convex.norm_image_sub_le_of_norm_has_fderiv_within_le
@@ -188,21 +188,21 @@ theorem uniformCauchySeqOn_ball_of_fderiv {r : ℝ} (hf' : UniformCauchySeqOn f'
   ·
     simp only [Metric.ball_eq_empty.2 hr, UniformCauchySeqOn, Set.mem_empty_iff_false,
       IsEmpty.forall_iff, eventually_const, imp_true_iff]
-  rw [SeminormedAddGroup.uniformCauchySeqOn_iff_tendstoUniformlyOn_zero] at hf'⊢
+  rw [SeminormedAddGroup.uniformCauchySeqOn_iff_tendstoUniformlyOn_zero] at hf' ⊢
   suffices
     TendstoUniformlyOn (fun (n : ι × ι) (z : E) => f n.1 z - f n.2 z - (f n.1 x - f n.2 x)) 0
         (l ×ᶠ l) (Metric.ball x r) ∧
       TendstoUniformlyOn (fun (n : ι × ι) (z : E) => f n.1 x - f n.2 x) 0 (l ×ᶠ l) (Metric.ball x r)
     by
     have := this.1.add this.2
-    rw [add_zero] at this
+    rw [add_zero] at this 
     refine' this.congr _
     apply eventually_of_forall
     intro n z hz
     simp
   constructor
   · -- This inequality follows from the mean value theorem
-    rw [Metric.tendstoUniformlyOn_iff] at hf'⊢
+    rw [Metric.tendstoUniformlyOn_iff] at hf' ⊢
     intro ε hε
     obtain ⟨q, hqpos, hq⟩ : ∃ q : ℝ, 0 < q ∧ q * r < ε :=
       by
@@ -210,7 +210,7 @@ theorem uniformCauchySeqOn_ball_of_fderiv {r : ℝ} (hf' : UniformCauchySeqOn f'
       exact exists_pos_mul_lt hε.lt r
     apply (hf' q hqpos.gt).mono
     intro n hn y hy
-    simp_rw [dist_eq_norm, Pi.zero_apply, zero_sub, norm_neg] at hn⊢
+    simp_rw [dist_eq_norm, Pi.zero_apply, zero_sub, norm_neg] at hn ⊢
     have mvt :=
       Convex.norm_image_sub_le_of_norm_has_fderiv_within_le
         (fun z hz => ((hf n.1 z hz).sub (hf n.2 z hz)).HasFDerivWithinAt) (fun z hz => (hn z hz).le)
@@ -254,9 +254,9 @@ theorem cauchy_map_of_uniformCauchySeqOn_fderiv {s : Set E} (hs : IsOpen s) (h's
   have st_nonempty : (s ∩ t).Nonempty := ⟨x₀, hx₀, ⟨hx₀, hfg⟩⟩
   suffices H : closure t ∩ s ⊆ t; exact h's.subset_of_closure_inter_subset open_t st_nonempty H
   rintro x ⟨xt, xs⟩
-  obtain ⟨ε, εpos, hε⟩ : ∃ (ε : ℝ)(H : ε > 0), Metric.ball x ε ⊆ s
+  obtain ⟨ε, εpos, hε⟩ : ∃ (ε : ℝ) (H : ε > 0), Metric.ball x ε ⊆ s
   exact Metric.isOpen_iff.1 hs x xs
-  obtain ⟨y, yt, hxy⟩ : ∃ (y : E)(yt : y ∈ t), dist x y < ε / 2
+  obtain ⟨y, yt, hxy⟩ : ∃ (y : E) (yt : y ∈ t), dist x y < ε / 2
   exact Metric.mem_closure_iff.1 xt _ (half_pos εpos)
   have B : Metric.ball y (ε / 2) ⊆ Metric.ball x ε := by apply Metric.ball_subset_ball';
     rw [dist_comm]; linarith
@@ -283,8 +283,8 @@ theorem difference_quotients_converge_uniformly (hf' : TendstoUniformlyOnFilter
   rw [SeminormedAddGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_zero]
   rw [Metric.tendstoUniformlyOnFilter_iff]
   have hfg' := hf'.uniform_cauchy_seq_on_filter
-  rw [SeminormedAddGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_zero] at hfg'
-  rw [Metric.tendstoUniformlyOnFilter_iff] at hfg'
+  rw [SeminormedAddGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_zero] at hfg' 
+  rw [Metric.tendstoUniformlyOnFilter_iff] at hfg' 
   intro ε hε
   obtain ⟨q, hqpos, hqε⟩ := exists_pos_rat_lt hε
   specialize hfg' (q : ℝ) (by simp [hqpos])
@@ -301,7 +301,7 @@ theorem difference_quotients_converge_uniformly (hf' : TendstoUniformlyOnFilter
   by_cases hyz' : x = y; · simp [hyz', hqpos.le]
   have hyz : 0 < ‖y - x‖ := by rw [norm_pos_iff]; intro hy'; exact hyz' (eq_of_sub_eq_zero hy').symm
   rw [inv_mul_le_iff hyz, mul_comm, sub_sub_sub_comm]
-  simp only [Pi.zero_apply, dist_zero_left] at e
+  simp only [Pi.zero_apply, dist_zero_left] at e 
   refine'
     Convex.norm_image_sub_le_of_norm_has_fderiv_within_le
       (fun y hy => ((e hn (hr' hy)).2.1.sub (e hn (hr' hy)).2.2).HasFDerivWithinAt)
@@ -333,11 +333,11 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
   suffices
     tendsto (fun y : ι × E => ‖y.2 - x‖⁻¹ * ‖g y.2 - g x - (g' x) (y.2 - x)‖) (l.curry (𝓝 x)) (𝓝 0)
     by
-    rw [Metric.tendsto_nhds] at this⊢
+    rw [Metric.tendsto_nhds] at this ⊢
     intro ε hε
     specialize this ε hε
-    rw [eventually_curry_iff] at this
-    simp only at this
+    rw [eventually_curry_iff] at this 
+    simp only at this 
     exact (eventually_const.mp this).mono (by simp only [imp_self, forall_const])
   -- With the new quantifier in hand, we can perform the famous `ε/3` proof. Specifically,
   -- we will break up the limit (the difference functions minus the derivative go to 0) into 3:
@@ -365,13 +365,13 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
   refine' tendsto.add (tendsto.add _ _) _
   simp only
   · have := difference_quotients_converge_uniformly hf' hf hfg
-    rw [Metric.tendstoUniformlyOnFilter_iff] at this
+    rw [Metric.tendstoUniformlyOnFilter_iff] at this 
     rw [Metric.tendsto_nhds]
     intro ε hε
     apply ((this ε hε).filter_mono curry_le_prod).mono
     intro n hn
-    rw [dist_eq_norm] at hn⊢
-    rw [← smul_sub] at hn
+    rw [dist_eq_norm] at hn ⊢
+    rw [← smul_sub] at hn 
     rwa [sub_zero]
   · -- (Almost) the definition of the derivatives
     rw [Metric.tendsto_nhds]
@@ -379,21 +379,21 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     rw [eventually_curry_iff]
     refine' hf.curry.mono fun n hn => _
     have := hn.self_of_nhds
-    rw [hasFDerivAt_iff_tendsto, Metric.tendsto_nhds] at this
+    rw [hasFDerivAt_iff_tendsto, Metric.tendsto_nhds] at this 
     refine' (this ε hε).mono fun y hy => _
-    rw [dist_eq_norm] at hy⊢
-    simp only [sub_zero, map_sub, norm_mul, norm_inv, norm_norm] at hy⊢
+    rw [dist_eq_norm] at hy ⊢
+    simp only [sub_zero, map_sub, norm_mul, norm_inv, norm_norm] at hy ⊢
     rw [norm_smul, norm_inv, IsROrC.norm_coe_norm]
     exact hy
   · -- hfg' after specializing to `x` and applying the definition of the operator norm
     refine' tendsto.mono_left _ curry_le_prod
     have h1 : tendsto (fun n : ι × E => g' n.2 - f' n.1 n.2) (l ×ᶠ 𝓝 x) (𝓝 0) :=
       by
-      rw [Metric.tendstoUniformlyOnFilter_iff] at hf'
+      rw [Metric.tendstoUniformlyOnFilter_iff] at hf' 
       exact metric.tendsto_nhds.mpr fun ε hε => by simpa using hf' ε hε
     have h2 : tendsto (fun n : ι => g' x - f' n x) l (𝓝 0) :=
       by
-      rw [Metric.tendsto_nhds] at h1⊢
+      rw [Metric.tendsto_nhds] at h1 ⊢
       exact fun ε hε => (h1 ε hε).curry.mono fun n hn => hn.self_of_nhds
     have := tendsto_fst.comp (h2.prod_map tendsto_id)
     refine' squeeze_zero_norm _ (tendsto_zero_iff_norm_tendsto_zero.mp this)
@@ -479,13 +479,13 @@ theorem UniformCauchySeqOnFilter.one_smulRight {l' : Filter 𝕜}
   -- metrics are written in terms of `<`. So we need to shrink `ε` utilizing the archimedean
   -- property of `ℝ`
   rw [SeminormedAddGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_zero,
-    Metric.tendstoUniformlyOnFilter_iff] at hf'⊢
+    Metric.tendstoUniformlyOnFilter_iff] at hf' ⊢
   intro ε hε
   obtain ⟨q, hq, hq'⟩ := exists_between hε.lt
   apply (hf' q hq).mono
   intro n hn
   refine' lt_of_le_of_lt _ hq'
-  simp only [dist_eq_norm, Pi.zero_apply, zero_sub, norm_neg] at hn⊢
+  simp only [dist_eq_norm, Pi.zero_apply, zero_sub, norm_neg] at hn ⊢
   refine' ContinuousLinearMap.op_norm_le_bound _ hq.le _
   intro z
   simp only [ContinuousLinearMap.coe_sub', Pi.sub_apply, ContinuousLinearMap.smulRight_apply,
@@ -498,7 +498,7 @@ theorem uniformCauchySeqOnFilter_of_deriv (hf' : UniformCauchySeqOnFilter f' l (
     (hf : ∀ᶠ n : ι × 𝕜 in l ×ᶠ 𝓝 x, HasDerivAt (f n.1) (f' n.1 n.2) n.2)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOnFilter f l (𝓝 x) :=
   by
-  simp_rw [hasDerivAt_iff_hasFDerivAt] at hf
+  simp_rw [hasDerivAt_iff_hasFDerivAt] at hf 
   exact uniformCauchySeqOnFilter_of_fderiv hf'.one_smul_right hf hfg
 #align uniform_cauchy_seq_on_filter_of_deriv uniformCauchySeqOnFilter_of_deriv
 
@@ -506,8 +506,8 @@ theorem uniformCauchySeqOn_ball_of_deriv {r : ℝ} (hf' : UniformCauchySeqOn f'
     (hf : ∀ n : ι, ∀ y : 𝕜, y ∈ Metric.ball x r → HasDerivAt (f n) (f' n y) y)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOn f l (Metric.ball x r) :=
   by
-  simp_rw [hasDerivAt_iff_hasFDerivAt] at hf
-  rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf'
+  simp_rw [hasDerivAt_iff_hasFDerivAt] at hf 
+  rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf' 
   have hf' :
     UniformCauchySeqOn (fun n => fun z => (1 : 𝕜 →L[𝕜] 𝕜).smul_right (f' n z)) l
       (Metric.ball x r) :=
@@ -526,19 +526,19 @@ theorem hasDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
   -- can recognize them when we apply `has_fderiv_at_of_tendsto_uniformly_on_filter`
   let F' n z := (1 : 𝕜 →L[𝕜] 𝕜).smul_right (f' n z)
   let G' z := (1 : 𝕜 →L[𝕜] 𝕜).smul_right (g' z)
-  simp_rw [hasDerivAt_iff_hasFDerivAt] at hf⊢
+  simp_rw [hasDerivAt_iff_hasFDerivAt] at hf ⊢
   -- Now we need to rewrite hf' in terms of continuous_linear_maps. The tricky part is that
   -- operator norms are written in terms of `≤` whereas metrics are written in terms of `<`. So we
   -- need to shrink `ε` utilizing the archimedean property of `ℝ`
   have hf' : TendstoUniformlyOnFilter F' G' l (𝓝 x) :=
     by
-    rw [Metric.tendstoUniformlyOnFilter_iff] at hf'⊢
+    rw [Metric.tendstoUniformlyOnFilter_iff] at hf' ⊢
     intro ε hε
     obtain ⟨q, hq, hq'⟩ := exists_between hε.lt
     apply (hf' q hq).mono
     intro n hn
     refine' lt_of_le_of_lt _ hq'
-    simp only [F', G', dist_eq_norm] at hn⊢
+    simp only [F', G', dist_eq_norm] at hn ⊢
     refine' ContinuousLinearMap.op_norm_le_bound _ hq.le _
     intro z
     simp only [ContinuousLinearMap.coe_sub', Pi.sub_apply, ContinuousLinearMap.smulRight_apply,

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

@@ -100,7 +100,7 @@ uniform convergence, limits of derivatives
 
 open Filter
 
-open uniformity Filter Topology
+open scoped uniformity Filter Topology
 
 section LimitsOfDerivatives
 

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

@@ -116,8 +116,7 @@ theorem uniformCauchySeqOnFilter_of_fderiv (hf' : UniformCauchySeqOnFilter f' l
     (hf : ∀ᶠ n : ι × E in l ×ᶠ 𝓝 x, HasFDerivAt (f n.1) (f' n.1 n.2) n.2)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOnFilter f l (𝓝 x) :=
   by
-  let : NormedSpace ℝ E
-  exact NormedSpace.restrictScalars ℝ 𝕜 _
+  let : NormedSpace ℝ E; exact NormedSpace.restrictScalars ℝ 𝕜 _
   rw [SeminormedAddGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_zero] at hf'⊢
   suffices
     TendstoUniformlyOnFilter (fun (n : ι × ι) (z : E) => f n.1 z - f n.2 z - (f n.1 x - f n.2 x)) 0
@@ -183,8 +182,7 @@ theorem uniformCauchySeqOn_ball_of_fderiv {r : ℝ} (hf' : UniformCauchySeqOn f'
     (hf : ∀ n : ι, ∀ y : E, y ∈ Metric.ball x r → HasFDerivAt (f n) (f' n y) y)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOn f l (Metric.ball x r) :=
   by
-  let : NormedSpace ℝ E
-  exact NormedSpace.restrictScalars ℝ 𝕜 _
+  let : NormedSpace ℝ E; exact NormedSpace.restrictScalars ℝ 𝕜 _
   have : ne_bot l := (cauchy_map_iff.1 hfg).1
   rcases le_or_lt r 0 with (hr | hr)
   ·
@@ -242,8 +240,7 @@ theorem cauchy_map_of_uniformCauchySeqOn_fderiv {s : Set E} (hs : IsOpen s) (h's
   by
   have : ne_bot l := (cauchy_map_iff.1 hfg).1
   let t := { y | y ∈ s ∧ Cauchy (map (fun n => f n y) l) }
-  suffices H : s ⊆ t
-  exact (H hx).2
+  suffices H : s ⊆ t; exact (H hx).2
   have A : ∀ x ε, x ∈ t → Metric.ball x ε ⊆ s → Metric.ball x ε ⊆ t := fun x ε xt hx y hy =>
     ⟨hx hy,
       (uniformCauchySeqOn_ball_of_fderiv (hf'.mono hx) (fun n y hy => hf n y (hx hy))
@@ -255,18 +252,14 @@ theorem cauchy_map_of_uniformCauchySeqOn_fderiv {s : Set E} (hs : IsOpen s) (h's
     rcases Metric.isOpen_iff.1 hs x hx.1 with ⟨ε, εpos, hε⟩
     exact ⟨ε, εpos, A x ε hx hε⟩
   have st_nonempty : (s ∩ t).Nonempty := ⟨x₀, hx₀, ⟨hx₀, hfg⟩⟩
-  suffices H : closure t ∩ s ⊆ t
-  exact h's.subset_of_closure_inter_subset open_t st_nonempty H
+  suffices H : closure t ∩ s ⊆ t; exact h's.subset_of_closure_inter_subset open_t st_nonempty H
   rintro x ⟨xt, xs⟩
   obtain ⟨ε, εpos, hε⟩ : ∃ (ε : ℝ)(H : ε > 0), Metric.ball x ε ⊆ s
   exact Metric.isOpen_iff.1 hs x xs
   obtain ⟨y, yt, hxy⟩ : ∃ (y : E)(yt : y ∈ t), dist x y < ε / 2
   exact Metric.mem_closure_iff.1 xt _ (half_pos εpos)
-  have B : Metric.ball y (ε / 2) ⊆ Metric.ball x ε :=
-    by
-    apply Metric.ball_subset_ball'
-    rw [dist_comm]
-    linarith
+  have B : Metric.ball y (ε / 2) ⊆ Metric.ball x ε := by apply Metric.ball_subset_ball';
+    rw [dist_comm]; linarith
   exact A y (ε / 2) yt (B.trans hε) (Metric.mem_ball.2 hxy)
 #align cauchy_map_of_uniform_cauchy_seq_on_fderiv cauchy_map_of_uniformCauchySeqOn_fderiv
 
@@ -279,8 +272,7 @@ theorem difference_quotients_converge_uniformly (hf' : TendstoUniformlyOnFilter
     TendstoUniformlyOnFilter (fun n : ι => fun y : E => (‖y - x‖⁻¹ : 𝕜) • (f n y - f n x))
       (fun y : E => (‖y - x‖⁻¹ : 𝕜) • (g y - g x)) l (𝓝 x) :=
   by
-  let : NormedSpace ℝ E
-  exact NormedSpace.restrictScalars ℝ 𝕜 _
+  let : NormedSpace ℝ E; exact NormedSpace.restrictScalars ℝ 𝕜 _
   rcases eq_or_ne l ⊥ with (hl | hl)
   · simp only [hl, TendstoUniformlyOnFilter, bot_prod, eventually_bot, imp_true_iff]
   haveI : ne_bot l := ⟨hl⟩
@@ -306,12 +298,8 @@ theorem difference_quotients_converge_uniformly (hf' : TendstoUniformlyOnFilter
   simp only [Pi.zero_apply, dist_zero_left]
   rw [← smul_sub, norm_smul, norm_inv, IsROrC.norm_coe_norm]
   refine' lt_of_le_of_lt _ hqε
-  by_cases hyz' : x = y
-  · simp [hyz', hqpos.le]
-  have hyz : 0 < ‖y - x‖ := by
-    rw [norm_pos_iff]
-    intro hy'
-    exact hyz' (eq_of_sub_eq_zero hy').symm
+  by_cases hyz' : x = y; · simp [hyz', hqpos.le]
+  have hyz : 0 < ‖y - x‖ := by rw [norm_pos_iff]; intro hy'; exact hyz' (eq_of_sub_eq_zero hy').symm
   rw [inv_mul_le_iff hyz, mul_comm, sub_sub_sub_comm]
   simp only [Pi.zero_apply, dist_zero_left] at e
   refine'
@@ -369,14 +357,10 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
           (‖a.2 - x‖⁻¹ : 𝕜) • (f a.1 a.2 - f a.1 x - ((f' a.1 x) a.2 - (f' a.1 x) x))) +
         fun a : ι × E => (‖a.2 - x‖⁻¹ : 𝕜) • (f' a.1 x - g' x) (a.2 - x) :=
     by
-    ext
-    simp only [Pi.add_apply]
-    rw [← smul_add, ← smul_add]
-    congr
+    ext; simp only [Pi.add_apply]; rw [← smul_add, ← smul_add]; congr
     simp only [map_sub, sub_add_sub_cancel, ContinuousLinearMap.coe_sub', Pi.sub_apply]
   simp_rw [this]
-  have : 𝓝 (0 : G) = 𝓝 (0 + 0 + 0)
-  simp only [add_zero]
+  have : 𝓝 (0 : G) = 𝓝 (0 + 0 + 0); simp only [add_zero]
   rw [this]
   refine' tendsto.add (tendsto.add _ _) _
   simp only
@@ -415,11 +399,8 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     refine' squeeze_zero_norm _ (tendsto_zero_iff_norm_tendsto_zero.mp this)
     intro n
     simp_rw [norm_smul, norm_inv, IsROrC.norm_coe_norm]
-    by_cases hx : x = n.2
-    · simp [hx]
-    have hnx : 0 < ‖n.2 - x‖ := by
-      rw [norm_pos_iff]
-      intro hx'
+    by_cases hx : x = n.2; · simp [hx]
+    have hnx : 0 < ‖n.2 - x‖ := by rw [norm_pos_iff]; intro hx';
       exact hx (eq_of_sub_eq_zero hx').symm
     rw [inv_mul_le_iff hnx, mul_comm]
     simp only [Function.comp_apply, Prod_map]

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

@@ -113,7 +113,7 @@ neighborhood of `x`, they are Cauchy _at_ `x`, and their derivatives
 are a uniform Cauchy sequence in a neighborhood of `x`, then the functions form a uniform Cauchy
 sequence in a neighborhood of `x`. -/
 theorem uniformCauchySeqOnFilter_of_fderiv (hf' : UniformCauchySeqOnFilter f' l (𝓝 x))
-    (hf : ∀ᶠ n : ι × E in l ×ᶠ 𝓝 x, HasFderivAt (f n.1) (f' n.1 n.2) n.2)
+    (hf : ∀ᶠ n : ι × E in l ×ᶠ 𝓝 x, HasFDerivAt (f n.1) (f' n.1 n.2) n.2)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOnFilter f l (𝓝 x) :=
   by
   let : NormedSpace ℝ E
@@ -157,7 +157,7 @@ theorem uniformCauchySeqOnFilter_of_fderiv (hf' : UniformCauchySeqOnFilter f' l
     refine' lt_of_le_of_lt _ (hxyε y hy)
     exact
       Convex.norm_image_sub_le_of_norm_has_fderiv_within_le
-        (fun y hy => ((e hn (hr' hy)).2.1.sub (e hn (hr' hy)).2.2).HasFderivWithinAt)
+        (fun y hy => ((e hn (hr' hy)).2.1.sub (e hn (hr' hy)).2.2).HasFDerivWithinAt)
         (fun y hy => (e hn (hr' hy)).1.le) (convex_ball x r) (Metric.mem_ball_self hr) hy
   · -- This is just `hfg` run through `eventually_prod_iff`
     refine' metric.tendsto_uniformly_on_filter_iff.mpr fun ε hε => _
@@ -180,7 +180,7 @@ with any connected, bounded, open set and replacing uniform convergence with loc
 convergence. See `cauchy_map_of_uniform_cauchy_seq_on_fderiv`.
 -/
 theorem uniformCauchySeqOn_ball_of_fderiv {r : ℝ} (hf' : UniformCauchySeqOn f' l (Metric.ball x r))
-    (hf : ∀ n : ι, ∀ y : E, y ∈ Metric.ball x r → HasFderivAt (f n) (f' n y) y)
+    (hf : ∀ n : ι, ∀ y : E, y ∈ Metric.ball x r → HasFDerivAt (f n) (f' n y) y)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOn f l (Metric.ball x r) :=
   by
   let : NormedSpace ℝ E
@@ -215,7 +215,7 @@ theorem uniformCauchySeqOn_ball_of_fderiv {r : ℝ} (hf' : UniformCauchySeqOn f'
     simp_rw [dist_eq_norm, Pi.zero_apply, zero_sub, norm_neg] at hn⊢
     have mvt :=
       Convex.norm_image_sub_le_of_norm_has_fderiv_within_le
-        (fun z hz => ((hf n.1 z hz).sub (hf n.2 z hz)).HasFderivWithinAt) (fun z hz => (hn z hz).le)
+        (fun z hz => ((hf n.1 z hz).sub (hf n.2 z hz)).HasFDerivWithinAt) (fun z hz => (hn z hz).le)
         (convex_ball x r) (Metric.mem_ball_self hr) hy
     refine' lt_of_le_of_lt mvt _
     have : q * ‖y - x‖ < q * r :=
@@ -236,7 +236,7 @@ theorem uniformCauchySeqOn_ball_of_fderiv {r : ℝ} (hf' : UniformCauchySeqOn f'
 preconnected open set, they form a Cauchy sequence _at_ `x`, and their derivatives are Cauchy
 uniformly on the set, then the functions form a Cauchy sequence at any point in the set. -/
 theorem cauchy_map_of_uniformCauchySeqOn_fderiv {s : Set E} (hs : IsOpen s) (h's : IsPreconnected s)
-    (hf' : UniformCauchySeqOn f' l s) (hf : ∀ n : ι, ∀ y : E, y ∈ s → HasFderivAt (f n) (f' n y) y)
+    (hf' : UniformCauchySeqOn f' l s) (hf : ∀ n : ι, ∀ y : E, y ∈ s → HasFDerivAt (f n) (f' n y) y)
     {x₀ x : E} (hx₀ : x₀ ∈ s) (hx : x ∈ s) (hfg : Cauchy (map (fun n => f n x₀) l)) :
     Cauchy (map (fun n => f n x) l) :=
   by
@@ -274,7 +274,7 @@ theorem cauchy_map_of_uniformCauchySeqOn_fderiv {s : Set E} (hs : IsOpen s) (h's
 in fact for a fixed `y`, the difference quotients `‖z - y‖⁻¹ • (f_n z - f_n y)` converge
 _uniformly_ to `‖z - y‖⁻¹ • (g z - g y)` -/
 theorem difference_quotients_converge_uniformly (hf' : TendstoUniformlyOnFilter f' g' l (𝓝 x))
-    (hf : ∀ᶠ n : ι × E in l ×ᶠ 𝓝 x, HasFderivAt (f n.1) (f' n.1 n.2) n.2)
+    (hf : ∀ᶠ n : ι × E in l ×ᶠ 𝓝 x, HasFDerivAt (f n.1) (f' n.1 n.2) n.2)
     (hfg : ∀ᶠ y : E in 𝓝 x, Tendsto (fun n => f n y) l (𝓝 (g y))) :
     TendstoUniformlyOnFilter (fun n : ι => fun y : E => (‖y - x‖⁻¹ : 𝕜) • (f n y - f n x))
       (fun y : E => (‖y - x‖⁻¹ : 𝕜) • (g y - g x)) l (𝓝 x) :=
@@ -316,7 +316,7 @@ theorem difference_quotients_converge_uniformly (hf' : TendstoUniformlyOnFilter
   simp only [Pi.zero_apply, dist_zero_left] at e
   refine'
     Convex.norm_image_sub_le_of_norm_has_fderiv_within_le
-      (fun y hy => ((e hn (hr' hy)).2.1.sub (e hn (hr' hy)).2.2).HasFderivWithinAt)
+      (fun y hy => ((e hn (hr' hy)).2.1.sub (e hn (hr' hy)).2.2).HasFDerivWithinAt)
       (fun y hy => (e hn (hr' hy)).1.le) (convex_ball x r) (Metric.mem_ball_self hr) hy
 #align difference_quotients_converge_uniformly difference_quotients_converge_uniformly
 
@@ -329,10 +329,10 @@ In words the assumptions mean the following:
   * `hf`: For all `(y, n)` with `y` sufficiently close to `x` and `n` sufficiently large, `f' n` is
     the derivative of `f n`
   * `hfg`: The `f n` converge pointwise to `g` on a neighborhood of `x` -/
-theorem hasFderivAt_of_tendstoUniformlyOnFilter [NeBot l]
+theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     (hf' : TendstoUniformlyOnFilter f' g' l (𝓝 x))
-    (hf : ∀ᶠ n : ι × E in l ×ᶠ 𝓝 x, HasFderivAt (f n.1) (f' n.1 n.2) n.2)
-    (hfg : ∀ᶠ y in 𝓝 x, Tendsto (fun n => f n y) l (𝓝 (g y))) : HasFderivAt g (g' x) x :=
+    (hf : ∀ᶠ n : ι × E in l ×ᶠ 𝓝 x, HasFDerivAt (f n.1) (f' n.1 n.2) n.2)
+    (hfg : ∀ᶠ y in 𝓝 x, Tendsto (fun n => f n y) l (𝓝 (g y))) : HasFDerivAt g (g' x) x :=
   by
   -- The proof strategy follows several steps:
   --   1. The quantifiers in the definition of the derivative are
@@ -340,7 +340,7 @@ theorem hasFderivAt_of_tendstoUniformlyOnFilter [NeBot l]
   --      `∀ ε > 0, ∃N, ∀n ≥ N, ∃δ > 0, ∀y ∈ B_δ(x)` which will allow us to introduce the `f(') n`
   --   2. The order of the quantifiers `hfg` are opposite to what we need. We will be able to swap
   --      the quantifiers using the uniform convergence assumption
-  rw [hasFderivAt_iff_tendsto]
+  rw [hasFDerivAt_iff_tendsto]
   -- Introduce extra quantifier via curried filters
   suffices
     tendsto (fun y : ι × E => ‖y.2 - x‖⁻¹ * ‖g y.2 - g x - (g' x) (y.2 - x)‖) (l.curry (𝓝 x)) (𝓝 0)
@@ -395,7 +395,7 @@ theorem hasFderivAt_of_tendstoUniformlyOnFilter [NeBot l]
     rw [eventually_curry_iff]
     refine' hf.curry.mono fun n hn => _
     have := hn.self_of_nhds
-    rw [hasFderivAt_iff_tendsto, Metric.tendsto_nhds] at this
+    rw [hasFDerivAt_iff_tendsto, Metric.tendsto_nhds] at this
     refine' (this ε hε).mono fun y hy => _
     rw [dist_eq_norm] at hy⊢
     simp only [sub_zero, map_sub, norm_mul, norm_inv, norm_norm] at hy⊢
@@ -425,54 +425,54 @@ theorem hasFderivAt_of_tendstoUniformlyOnFilter [NeBot l]
     simp only [Function.comp_apply, Prod_map]
     rw [norm_sub_rev]
     exact (f' n.1 x - g' x).le_op_norm (n.2 - x)
-#align has_fderiv_at_of_tendsto_uniformly_on_filter hasFderivAt_of_tendstoUniformlyOnFilter
+#align has_fderiv_at_of_tendsto_uniformly_on_filter hasFDerivAt_of_tendstoUniformlyOnFilter
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-theorem hasFderivAt_of_tendstoLocallyUniformlyOn [NeBot l] {s : Set E} (hs : IsOpen s)
-    (hf' : TendstoLocallyUniformlyOn f' g' l s) (hf : ∀ n, ∀ x ∈ s, HasFderivAt (f n) (f' n x) x)
-    (hfg : ∀ x ∈ s, Tendsto (fun n => f n x) l (𝓝 (g x))) (hx : x ∈ s) : HasFderivAt g (g' x) x :=
+theorem hasFDerivAt_of_tendstoLocallyUniformlyOn [NeBot l] {s : Set E} (hs : IsOpen s)
+    (hf' : TendstoLocallyUniformlyOn f' g' l s) (hf : ∀ n, ∀ x ∈ s, HasFDerivAt (f n) (f' n x) x)
+    (hfg : ∀ x ∈ s, Tendsto (fun n => f n x) l (𝓝 (g x))) (hx : x ∈ s) : HasFDerivAt g (g' x) x :=
   by
   have h1 : s ∈ 𝓝 x := hs.mem_nhds hx
   have h3 : Set.univ ×ˢ s ∈ l ×ᶠ 𝓝 x := by simp only [h1, prod_mem_prod_iff, univ_mem, and_self_iff]
-  have h4 : ∀ᶠ n : ι × E in l ×ᶠ 𝓝 x, HasFderivAt (f n.1) (f' n.1 n.2) n.2 :=
+  have h4 : ∀ᶠ n : ι × E in l ×ᶠ 𝓝 x, HasFDerivAt (f n.1) (f' n.1 n.2) n.2 :=
     eventually_of_mem h3 fun ⟨n, z⟩ ⟨hn, hz⟩ => hf n z hz
-  refine' hasFderivAt_of_tendstoUniformlyOnFilter _ h4 (eventually_of_mem h1 hfg)
+  refine' hasFDerivAt_of_tendstoUniformlyOnFilter _ h4 (eventually_of_mem h1 hfg)
   simpa [IsOpen.nhdsWithin_eq hs hx] using tendsto_locally_uniformly_on_iff_filter.mp hf' x hx
-#align has_fderiv_at_of_tendsto_locally_uniformly_on hasFderivAt_of_tendstoLocallyUniformlyOn
+#align has_fderiv_at_of_tendsto_locally_uniformly_on hasFDerivAt_of_tendstoLocallyUniformlyOn
 
 /-- A slight variant of `has_fderiv_at_of_tendsto_locally_uniformly_on` with the assumption stated
 in terms of `differentiable_on` rather than `has_fderiv_at`. This makes a few proofs nicer in
 complex analysis where holomorphicity is assumed but the derivative is not known a priori. -/
-theorem hasFderivAt_of_tendsto_locally_uniformly_on' [NeBot l] {s : Set E} (hs : IsOpen s)
+theorem hasFDerivAt_of_tendsto_locally_uniformly_on' [NeBot l] {s : Set E} (hs : IsOpen s)
     (hf' : TendstoLocallyUniformlyOn (fderiv 𝕜 ∘ f) g' l s) (hf : ∀ n, DifferentiableOn 𝕜 (f n) s)
-    (hfg : ∀ x ∈ s, Tendsto (fun n => f n x) l (𝓝 (g x))) (hx : x ∈ s) : HasFderivAt g (g' x) x :=
+    (hfg : ∀ x ∈ s, Tendsto (fun n => f n x) l (𝓝 (g x))) (hx : x ∈ s) : HasFDerivAt g (g' x) x :=
   by
-  refine' hasFderivAt_of_tendstoLocallyUniformlyOn hs hf' (fun n z hz => _) hfg hx
-  exact ((hf n z hz).DifferentiableAt (hs.mem_nhds hz)).HasFderivAt
-#align has_fderiv_at_of_tendsto_locally_uniformly_on' hasFderivAt_of_tendsto_locally_uniformly_on'
+  refine' hasFDerivAt_of_tendstoLocallyUniformlyOn hs hf' (fun n z hz => _) hfg hx
+  exact ((hf n z hz).DifferentiableAt (hs.mem_nhds hz)).HasFDerivAt
+#align has_fderiv_at_of_tendsto_locally_uniformly_on' hasFDerivAt_of_tendsto_locally_uniformly_on'
 
 /-- `(d/dx) lim_{n → ∞} f n x = lim_{n → ∞} f' n x` when the `f' n` converge
 _uniformly_ to their limit on an open set containing `x`. -/
-theorem hasFderivAt_of_tendstoUniformlyOn [NeBot l] {s : Set E} (hs : IsOpen s)
+theorem hasFDerivAt_of_tendstoUniformlyOn [NeBot l] {s : Set E} (hs : IsOpen s)
     (hf' : TendstoUniformlyOn f' g' l s)
-    (hf : ∀ n : ι, ∀ x : E, x ∈ s → HasFderivAt (f n) (f' n x) x)
+    (hf : ∀ n : ι, ∀ x : E, x ∈ s → HasFDerivAt (f n) (f' n x) x)
     (hfg : ∀ x : E, x ∈ s → Tendsto (fun n => f n x) l (𝓝 (g x))) :
-    ∀ x : E, x ∈ s → HasFderivAt g (g' x) x := fun x =>
-  hasFderivAt_of_tendstoLocallyUniformlyOn hs hf'.TendstoLocallyUniformlyOn hf hfg
-#align has_fderiv_at_of_tendsto_uniformly_on hasFderivAt_of_tendstoUniformlyOn
+    ∀ x : E, x ∈ s → HasFDerivAt g (g' x) x := fun x =>
+  hasFDerivAt_of_tendstoLocallyUniformlyOn hs hf'.TendstoLocallyUniformlyOn hf hfg
+#align has_fderiv_at_of_tendsto_uniformly_on hasFDerivAt_of_tendstoUniformlyOn
 
 /-- `(d/dx) lim_{n → ∞} f n x = lim_{n → ∞} f' n x` when the `f' n` converge
 _uniformly_ to their limit. -/
-theorem hasFderivAt_of_tendstoUniformly [NeBot l] (hf' : TendstoUniformly f' g' l)
-    (hf : ∀ n : ι, ∀ x : E, HasFderivAt (f n) (f' n x) x)
-    (hfg : ∀ x : E, Tendsto (fun n => f n x) l (𝓝 (g x))) : ∀ x : E, HasFderivAt g (g' x) x :=
+theorem hasFDerivAt_of_tendstoUniformly [NeBot l] (hf' : TendstoUniformly f' g' l)
+    (hf : ∀ n : ι, ∀ x : E, HasFDerivAt (f n) (f' n x) x)
+    (hfg : ∀ x : E, Tendsto (fun n => f n x) l (𝓝 (g x))) : ∀ x : E, HasFDerivAt g (g' x) x :=
   by
   intro x
-  have hf : ∀ n : ι, ∀ x : E, x ∈ Set.univ → HasFderivAt (f n) (f' n x) x := by simp [hf]
+  have hf : ∀ n : ι, ∀ x : E, x ∈ Set.univ → HasFDerivAt (f n) (f' n x) x := by simp [hf]
   have hfg : ∀ x : E, x ∈ Set.univ → tendsto (fun n => f n x) l (𝓝 (g x)) := by simp [hfg]
   have hf' : TendstoUniformlyOn f' g' l Set.univ := by rwa [tendstoUniformlyOn_univ]
-  refine' hasFderivAt_of_tendstoUniformlyOn isOpen_univ hf' hf hfg x (Set.mem_univ x)
-#align has_fderiv_at_of_tendsto_uniformly hasFderivAt_of_tendstoUniformly
+  refine' hasFDerivAt_of_tendstoUniformlyOn isOpen_univ hf' hf hfg x (Set.mem_univ x)
+#align has_fderiv_at_of_tendsto_uniformly hasFDerivAt_of_tendstoUniformly
 
 end LimitsOfDerivatives
 
@@ -517,7 +517,7 @@ theorem uniformCauchySeqOnFilter_of_deriv (hf' : UniformCauchySeqOnFilter f' l (
     (hf : ∀ᶠ n : ι × 𝕜 in l ×ᶠ 𝓝 x, HasDerivAt (f n.1) (f' n.1 n.2) n.2)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOnFilter f l (𝓝 x) :=
   by
-  simp_rw [hasDerivAt_iff_hasFderivAt] at hf
+  simp_rw [hasDerivAt_iff_hasFDerivAt] at hf
   exact uniformCauchySeqOnFilter_of_fderiv hf'.one_smul_right hf hfg
 #align uniform_cauchy_seq_on_filter_of_deriv uniformCauchySeqOnFilter_of_deriv
 
@@ -525,7 +525,7 @@ theorem uniformCauchySeqOn_ball_of_deriv {r : ℝ} (hf' : UniformCauchySeqOn f'
     (hf : ∀ n : ι, ∀ y : 𝕜, y ∈ Metric.ball x r → HasDerivAt (f n) (f' n y) y)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOn f l (Metric.ball x r) :=
   by
-  simp_rw [hasDerivAt_iff_hasFderivAt] at hf
+  simp_rw [hasDerivAt_iff_hasFDerivAt] at hf
   rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf'
   have hf' :
     UniformCauchySeqOn (fun n => fun z => (1 : 𝕜 →L[𝕜] 𝕜).smul_right (f' n z)) l
@@ -545,7 +545,7 @@ theorem hasDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
   -- can recognize them when we apply `has_fderiv_at_of_tendsto_uniformly_on_filter`
   let F' n z := (1 : 𝕜 →L[𝕜] 𝕜).smul_right (f' n z)
   let G' z := (1 : 𝕜 →L[𝕜] 𝕜).smul_right (g' z)
-  simp_rw [hasDerivAt_iff_hasFderivAt] at hf⊢
+  simp_rw [hasDerivAt_iff_hasFDerivAt] at hf⊢
   -- Now we need to rewrite hf' in terms of continuous_linear_maps. The tricky part is that
   -- operator norms are written in terms of `≤` whereas metrics are written in terms of `<`. So we
   -- need to shrink `ε` utilizing the archimedean property of `ℝ`
@@ -564,7 +564,7 @@ theorem hasDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
       ContinuousLinearMap.one_apply]
     rw [← smul_sub, norm_smul, mul_comm]
     exact mul_le_mul hn.le rfl.le (norm_nonneg _) hq.le
-  exact hasFderivAt_of_tendstoUniformlyOnFilter hf' hf hfg
+  exact hasFDerivAt_of_tendstoUniformlyOnFilter hf' hf hfg
 #align has_deriv_at_of_tendsto_uniformly_on_filter hasDerivAt_of_tendstoUniformlyOnFilter
 
 theorem hasDerivAt_of_tendstoLocallyUniformlyOn [NeBot l] {s : Set 𝕜} (hs : IsOpen s)

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

@@ -360,7 +360,7 @@ theorem hasFderivAt_of_tendstoUniformlyOnFilter [NeBot l]
   conv =>
     congr
     ext
-    rw [← abs_norm, ← abs_inv, ← @IsROrC.norm_of_real 𝕜 _ _, IsROrC.of_real_inv, ← norm_smul]
+    rw [← abs_norm, ← abs_inv, ← @IsROrC.norm_ofReal 𝕜 _ _, IsROrC.ofReal_inv, ← norm_smul]
   rw [← tendsto_zero_iff_norm_tendsto_zero]
   have :
     (fun a : ι × E => (‖a.2 - x‖⁻¹ : 𝕜) • (g a.2 - g x - (g' x) (a.2 - x))) =

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: Kevin H. Wilson
 
 ! This file was ported from Lean 3 source module analysis.calculus.uniform_limits_deriv
-! 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.
 -/
@@ -360,7 +360,7 @@ theorem hasFderivAt_of_tendstoUniformlyOnFilter [NeBot l]
   conv =>
     congr
     ext
-    rw [← norm_norm, ← norm_inv, ← @IsROrC.norm_of_real 𝕜 _ _, IsROrC.of_real_inv, ← norm_smul]
+    rw [← abs_norm, ← abs_inv, ← @IsROrC.norm_of_real 𝕜 _ _, IsROrC.of_real_inv, ← norm_smul]
   rw [← tendsto_zero_iff_norm_tendsto_zero]
   have :
     (fun a : ι × E => (‖a.2 - x‖⁻¹ : 𝕜) • (g a.2 - g x - (g' x) (a.2 - x))) =

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

A PR accompanying #12339.

Zulip discussion

@@ -350,8 +350,8 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
   have : 𝓝 (0 : G) = 𝓝 (0 + 0 + 0) := by simp only [add_zero]
   rw [this]
   refine' Tendsto.add (Tendsto.add _ _) _
-  simp only
-  · have := difference_quotients_converge_uniformly hf' hf hfg
+  · simp only
+    have := difference_quotients_converge_uniformly hf' hf hfg
     rw [Metric.tendstoUniformlyOnFilter_iff] at this
     rw [Metric.tendsto_nhds]
     intro ε hε

@@ -503,7 +503,7 @@ theorem hasDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
   let F' n z := (1 : 𝕜 →L[𝕜] 𝕜).smulRight (f' n z)
   let G' z := (1 : 𝕜 →L[𝕜] 𝕜).smulRight (g' z)
   simp_rw [hasDerivAt_iff_hasFDerivAt] at hf ⊢
-  -- Now we need to rewrite hf' in terms of continuous_linear_maps. The tricky part is that
+  -- Now we need to rewrite hf' in terms of `ContinuousLinearMap`s. The tricky part is that
   -- operator norms are written in terms of `≤` whereas metrics are written in terms of `<`. So we
   -- need to shrink `ε` utilizing the archimedean property of `ℝ`
   have hf' : TendstoUniformlyOnFilter F' G' l (𝓝 x) := by

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.

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin H. Wilson
 -/
 import Mathlib.Analysis.Calculus.MeanValue
-import Mathlib.Analysis.NormedSpace.IsROrC
+import Mathlib.Analysis.NormedSpace.RCLike
 import Mathlib.Order.Filter.Curry
 
 #align_import analysis.calculus.uniform_limits_deriv from "leanprover-community/mathlib"@"3f655f5297b030a87d641ad4e825af8d9679eb0b"
@@ -101,7 +101,7 @@ open scoped uniformity Filter Topology
 
 section LimitsOfDerivatives
 
-variable {ι : Type*} {l : Filter ι} {E : Type*} [NormedAddCommGroup E] {𝕜 : Type*} [IsROrC 𝕜]
+variable {ι : Type*} {l : Filter ι} {E : Type*} [NormedAddCommGroup E] {𝕜 : Type*} [RCLike 𝕜]
   [NormedSpace 𝕜 E] {G : Type*} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {f : ι → E → G}
   {g : E → G} {f' : ι → E → E →L[𝕜] G} {g' : E → E →L[𝕜] G} {x : E}
 
@@ -283,7 +283,7 @@ theorem difference_quotients_converge_uniformly (hf' : TendstoUniformlyOnFilter
     ⟨_, b, fun e : E => Metric.ball x r e,
       eventually_mem_set.mpr (Metric.nhds_basis_ball.mem_of_mem hr), fun {n} hn {y} hy => _⟩
   simp only [Pi.zero_apply, dist_zero_left]
-  rw [← smul_sub, norm_smul, norm_inv, IsROrC.norm_coe_norm]
+  rw [← smul_sub, norm_smul, norm_inv, RCLike.norm_coe_norm]
   refine' lt_of_le_of_lt _ hqε
   by_cases hyz' : x = y; · simp [hyz', hqpos.le]
   have hyz : 0 < ‖y - x‖ := by rw [norm_pos_iff]; intro hy'; exact hyz' (eq_of_sub_eq_zero hy').symm
@@ -334,7 +334,7 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
   conv =>
     congr
     ext
-    rw [← abs_norm, ← abs_inv, ← @IsROrC.norm_ofReal 𝕜 _ _, IsROrC.ofReal_inv, ← norm_smul]
+    rw [← abs_norm, ← abs_inv, ← @RCLike.norm_ofReal 𝕜 _ _, RCLike.ofReal_inv, ← norm_smul]
   rw [← tendsto_zero_iff_norm_tendsto_zero]
   have :
     (fun a : ι × E => (‖a.2 - x‖⁻¹ : 𝕜) • (g a.2 - g x - (g' x) (a.2 - x))) =
@@ -370,7 +370,7 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     refine' (this ε hε).mono fun y hy => _
     rw [dist_eq_norm] at hy ⊢
     simp only [sub_zero, map_sub, norm_mul, norm_inv, norm_norm] at hy ⊢
-    rw [norm_smul, norm_inv, IsROrC.norm_coe_norm]
+    rw [norm_smul, norm_inv, RCLike.norm_coe_norm]
     exact hy
   · -- hfg' after specializing to `x` and applying the definition of the operator norm
     refine' Tendsto.mono_left _ curry_le_prod
@@ -383,7 +383,7 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     refine' squeeze_zero_norm _
       (tendsto_zero_iff_norm_tendsto_zero.mp (tendsto_fst.comp (h2.prod_map tendsto_id)))
     intro n
-    simp_rw [norm_smul, norm_inv, IsROrC.norm_coe_norm]
+    simp_rw [norm_smul, norm_inv, RCLike.norm_coe_norm]
     by_cases hx : x = n.2; · simp [hx]
     have hnx : 0 < ‖n.2 - x‖ := by
       rw [norm_pos_iff]; intro hx'; exact hx (eq_of_sub_eq_zero hx').symm
@@ -448,7 +448,7 @@ In this section, we provide `deriv` equivalents of the `fderiv` lemmas in the pr
 -/
 
 
-variable {ι : Type*} {l : Filter ι} {𝕜 : Type*} [IsROrC 𝕜] {G : Type*} [NormedAddCommGroup G]
+variable {ι : Type*} {l : Filter ι} {𝕜 : Type*} [RCLike 𝕜] {G : Type*} [NormedAddCommGroup G]
   [NormedSpace 𝕜 G] {f : ι → 𝕜 → G} {g : 𝕜 → G} {f' : ι → 𝕜 → G} {g' : 𝕜 → G} {x : 𝕜}
 
 /-- If our derivatives converge uniformly, then the Fréchet derivatives converge uniformly -/

This is presumably not exhaustive, but covers about a hundred instances.

Style opinions (e.g., why a particular change is great/not a good idea) are very welcome; I'm still forming my own.

@@ -189,10 +189,8 @@ theorem uniformCauchySeqOn_ball_of_fderiv {r : ℝ} (hf' : UniformCauchySeqOn f'
         (l ×ˢ l) (Metric.ball x r) by
     have := this.1.add this.2
     rw [add_zero] at this
-    refine' this.congr _
-    apply eventually_of_forall
-    intro n z _
-    simp
+    refine this.congr ?_
+    filter_upwards with n z _ using (by simp)
   constructor
   · -- This inequality follows from the mean value theorem
     rw [Metric.tendstoUniformlyOn_iff] at hf' ⊢

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

@@ -130,7 +130,7 @@ theorem uniformCauchySeqOnFilter_of_fderiv (hf' : UniformCauchySeqOnFilter f' l
     obtain ⟨a, b, c, d, e⟩ := eventually_prod_iff.1 ((hf' ε hε).and this)
     obtain ⟨R, hR, hR'⟩ := Metric.nhds_basis_ball.eventually_iff.mp d
     let r := min 1 R
-    have hr : 0 < r := by simp [hR]
+    have hr : 0 < r := by simp [r, hR]
     have hr' : ∀ ⦃y : E⦄, y ∈ Metric.ball x r → c y := fun y hy =>
       hR' (lt_of_lt_of_le (Metric.mem_ball.mp hy) (min_le_right _ _))
     have hxy : ∀ y : E, y ∈ Metric.ball x r → ‖y - x‖ < 1 := by
@@ -518,8 +518,8 @@ theorem hasDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     simp only [dist_eq_norm] at hn ⊢
     refine' ContinuousLinearMap.opNorm_le_bound _ hq.le _
     intro z
-    simp only [ContinuousLinearMap.coe_sub', Pi.sub_apply, ContinuousLinearMap.smulRight_apply,
-      ContinuousLinearMap.one_apply]
+    simp only [F', G', ContinuousLinearMap.coe_sub', Pi.sub_apply,
+      ContinuousLinearMap.smulRight_apply, ContinuousLinearMap.one_apply]
     rw [← smul_sub, norm_smul, mul_comm]
     gcongr
   exact hasFDerivAt_of_tendstoUniformlyOnFilter hf' hf hfg

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -437,7 +437,7 @@ theorem hasFDerivAt_of_tendstoUniformly [NeBot l] (hf' : TendstoUniformly f' g'
   have hf : ∀ n : ι, ∀ x : E, x ∈ Set.univ → HasFDerivAt (f n) (f' n x) x := by simp [hf]
   have hfg : ∀ x : E, x ∈ Set.univ → Tendsto (fun n => f n x) l (𝓝 (g x)) := by simp [hfg]
   have hf' : TendstoUniformlyOn f' g' l Set.univ := by rwa [tendstoUniformlyOn_univ]
-  refine' hasFDerivAt_of_tendstoUniformlyOn isOpen_univ hf' hf hfg x (Set.mem_univ x)
+  exact hasFDerivAt_of_tendstoUniformlyOn isOpen_univ hf' hf hfg x (Set.mem_univ x)
 #align has_fderiv_at_of_tendsto_uniformly hasFDerivAt_of_tendstoUniformly
 
 end LimitsOfDerivatives

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>

@@ -231,7 +231,7 @@ theorem cauchy_map_of_uniformCauchySeqOn_fderiv {s : Set E} (hs : IsOpen s) (h's
     Cauchy (map (fun n => f n x) l) := by
   have : NeBot l := (cauchy_map_iff.1 hfg).1
   let t := { y | y ∈ s ∧ Cauchy (map (fun n => f n y) l) }
-  suffices H : s ⊆ t; exact (H hx).2
+  suffices H : s ⊆ t from (H hx).2
   have A : ∀ x ε, x ∈ t → Metric.ball x ε ⊆ s → Metric.ball x ε ⊆ t := fun x ε xt hx y hy =>
     ⟨hx hy,
       (uniformCauchySeqOn_ball_of_fderiv (hf'.mono hx) (fun n y hy => hf n y (hx hy))
@@ -243,7 +243,7 @@ theorem cauchy_map_of_uniformCauchySeqOn_fderiv {s : Set E} (hs : IsOpen s) (h's
     rcases Metric.isOpen_iff.1 hs x hx.1 with ⟨ε, εpos, hε⟩
     exact ⟨ε, εpos, A x ε hx hε⟩
   have st_nonempty : (s ∩ t).Nonempty := ⟨x₀, hx₀, ⟨hx₀, hfg⟩⟩
-  suffices H : closure t ∩ s ⊆ t; exact h's.subset_of_closure_inter_subset open_t st_nonempty H
+  suffices H : closure t ∩ s ⊆ t from h's.subset_of_closure_inter_subset open_t st_nonempty H
   rintro x ⟨xt, xs⟩
   obtain ⟨ε, εpos, hε⟩ : ∃ (ε : ℝ), ε > 0 ∧ Metric.ball x ε ⊆ s := Metric.isOpen_iff.1 hs x xs
   obtain ⟨y, yt, hxy⟩ : ∃ (y : E), y ∈ t ∧ dist x y < ε / 2 :=
@@ -261,7 +261,7 @@ theorem difference_quotients_converge_uniformly (hf' : TendstoUniformlyOnFilter
     (hfg : ∀ᶠ y : E in 𝓝 x, Tendsto (fun n => f n y) l (𝓝 (g y))) :
     TendstoUniformlyOnFilter (fun n : ι => fun y : E => (‖y - x‖⁻¹ : 𝕜) • (f n y - f n x))
       (fun y : E => (‖y - x‖⁻¹ : 𝕜) • (g y - g x)) l (𝓝 x) := by
-  let : NormedSpace ℝ E; exact NormedSpace.restrictScalars ℝ 𝕜 _
+  let A : NormedSpace ℝ E := NormedSpace.restrictScalars ℝ 𝕜 _
   rcases eq_or_ne l ⊥ with (hl | hl)
   · simp only [hl, TendstoUniformlyOnFilter, bot_prod, eventually_bot, imp_true_iff]
   haveI : NeBot l := ⟨hl⟩
@@ -349,7 +349,7 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     -- Porting note: added
     abel
   simp_rw [this]
-  have : 𝓝 (0 : G) = 𝓝 (0 + 0 + 0); simp only [add_zero]
+  have : 𝓝 (0 : G) = 𝓝 (0 + 0 + 0) := by simp only [add_zero]
   rw [this]
   refine' Tendsto.add (Tendsto.add _ _) _
   simp only

Co-authored-by: adomani <adomani@gmail.com>

@@ -392,7 +392,7 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     rw [inv_mul_le_iff hnx, mul_comm]
     simp only [Function.comp_apply, Prod_map]
     rw [norm_sub_rev]
-    exact (f' n.1 x - g' x).le_op_norm (n.2 - x)
+    exact (f' n.1 x - g' x).le_opNorm (n.2 - x)
 #align has_fderiv_at_of_tendsto_uniformly_on_filter hasFDerivAt_of_tendstoUniformlyOnFilter
 
 theorem hasFDerivAt_of_tendstoLocallyUniformlyOn [NeBot l] {s : Set E} (hs : IsOpen s)
@@ -468,7 +468,7 @@ theorem UniformCauchySeqOnFilter.one_smulRight {l' : Filter 𝕜}
   intro n hn
   refine' lt_of_le_of_lt _ hq'
   simp only [dist_eq_norm, Pi.zero_apply, zero_sub, norm_neg] at hn ⊢
-  refine' ContinuousLinearMap.op_norm_le_bound _ hq.le _
+  refine' ContinuousLinearMap.opNorm_le_bound _ hq.le _
   intro z
   simp only [ContinuousLinearMap.coe_sub', Pi.sub_apply, ContinuousLinearMap.smulRight_apply,
     ContinuousLinearMap.one_apply]
@@ -516,7 +516,7 @@ theorem hasDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     intro n hn
     refine' lt_of_le_of_lt _ hq'
     simp only [dist_eq_norm] at hn ⊢
-    refine' ContinuousLinearMap.op_norm_le_bound _ hq.le _
+    refine' ContinuousLinearMap.opNorm_le_bound _ hq.le _
     intro z
     simp only [ContinuousLinearMap.coe_sub', Pi.sub_apply, ContinuousLinearMap.smulRight_apply,
       ContinuousLinearMap.one_apply]

mathport was forgetting a space in filter_upwards [...]with instead of filter_upwards [...] with.

@@ -544,7 +544,7 @@ theorem hasDerivAt_of_tendsto_locally_uniformly_on' [NeBot l] {s : Set 𝕜} (hs
     (hf : ∀ᶠ n in l, DifferentiableOn 𝕜 (f n) s)
     (hfg : ∀ x ∈ s, Tendsto (fun n => f n x) l (𝓝 (g x))) (hx : x ∈ s) : HasDerivAt g (g' x) x := by
   refine' hasDerivAt_of_tendstoLocallyUniformlyOn hs hf' _ hfg hx
-  filter_upwards [hf]with n h z hz using((h z hz).differentiableAt (hs.mem_nhds hz)).hasDerivAt
+  filter_upwards [hf] with n h z hz using ((h z hz).differentiableAt (hs.mem_nhds hz)).hasDerivAt
 #align has_deriv_at_of_tendsto_locally_uniformly_on' hasDerivAt_of_tendsto_locally_uniformly_on'
 
 theorem hasDerivAt_of_tendstoUniformlyOn [NeBot l] {s : Set 𝕜} (hs : IsOpen s)
@@ -560,7 +560,7 @@ theorem hasDerivAt_of_tendstoUniformly [NeBot l] (hf' : TendstoUniformly f' g' l
     (hfg : ∀ x : 𝕜, Tendsto (fun n => f n x) l (𝓝 (g x))) : ∀ x : 𝕜, HasDerivAt g (g' x) x := by
   intro x
   have hf : ∀ᶠ n in l, ∀ x : 𝕜, x ∈ Set.univ → HasDerivAt (f n) (f' n x) x := by
-    filter_upwards [hf]with n h x _ using h x
+    filter_upwards [hf] with n h x _ using h x
   have hfg : ∀ x : 𝕜, x ∈ Set.univ → Tendsto (fun n => f n x) l (𝓝 (g x)) := by simp [hfg]
   have hf' : TendstoUniformlyOn f' g' l Set.univ := by rwa [tendstoUniformlyOn_univ]
   exact hasDerivAt_of_tendstoUniformlyOn isOpen_univ hf' hf hfg x (Set.mem_univ x)

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

This has nice performance benefits.

@@ -101,8 +101,8 @@ open scoped uniformity Filter Topology
 
 section LimitsOfDerivatives
 
-variable {ι : Type _} {l : Filter ι} {E : Type _} [NormedAddCommGroup E] {𝕜 : Type _} [IsROrC 𝕜]
-  [NormedSpace 𝕜 E] {G : Type _} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {f : ι → E → G}
+variable {ι : Type*} {l : Filter ι} {E : Type*} [NormedAddCommGroup E] {𝕜 : Type*} [IsROrC 𝕜]
+  [NormedSpace 𝕜 E] {G : Type*} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {f : ι → E → G}
   {g : E → G} {f' : ι → E → E →L[𝕜] G} {g' : E → E →L[𝕜] G} {x : E}
 
 /-- If a sequence of functions real or complex functions are eventually differentiable on a
@@ -450,7 +450,7 @@ In this section, we provide `deriv` equivalents of the `fderiv` lemmas in the pr
 -/
 
 
-variable {ι : Type _} {l : Filter ι} {𝕜 : Type _} [IsROrC 𝕜] {G : Type _} [NormedAddCommGroup G]
+variable {ι : Type*} {l : Filter ι} {𝕜 : Type*} [IsROrC 𝕜] {G : Type*} [NormedAddCommGroup G]
   [NormedSpace 𝕜 G] {f : ι → 𝕜 → G} {g : 𝕜 → G} {f' : ι → 𝕜 → G} {g' : 𝕜 → G} {x : 𝕜}
 
 /-- If our derivatives converge uniformly, then the Fréchet derivatives converge uniformly -/

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Kevin H. Wilson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin H. Wilson
-
-! This file was ported from Lean 3 source module analysis.calculus.uniform_limits_deriv
-! 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.Calculus.MeanValue
 import Mathlib.Analysis.NormedSpace.IsROrC
 import Mathlib.Order.Filter.Curry
 
+#align_import analysis.calculus.uniform_limits_deriv from "leanprover-community/mathlib"@"3f655f5297b030a87d641ad4e825af8d9679eb0b"
+
 /-!
 # Swapping limits and derivatives via uniform convergence
 

@@ -17,7 +17,7 @@ import Mathlib.Order.Filter.Curry
 
 The purpose of this file is to prove that the derivative of the pointwise limit of a sequence of
 functions is the pointwise limit of the functions' derivatives when the derivatives converge
-_uniformly_. The formal statement appears as `has_fderiv_at_of_tendsto_locally_uniformly_at`.
+_uniformly_. The formal statement appears as `hasFDerivAt_of_tendstoLocallyUniformlyOn`.
 
 ## Main statements
 
@@ -62,7 +62,7 @@ tendsto (|y - x|⁻¹ * |(g y - g x) - g' x (y - x)|) (𝓝 x) (𝓝 0)
 There are two ways we might introduce `n`. We could do:
 
 ```lean
-∀ᶠ (n : ℕ) in at_top, tendsto (|y - x|⁻¹ * |(g y - g x) - g' x (y - x)|) (𝓝 x) (𝓝 0)
+∀ᶠ (n : ℕ) in atTop, Tendsto (|y - x|⁻¹ * |(g y - g x) - g' x (y - x)|) (𝓝 x) (𝓝 0)
 ```
 
 but this is equivalent to the quantifier order `∃ N, ∀ n ≥ N, ∀ ε > 0, ∃ δ > 0, ∀ y ∈ B_δ(x)`,
@@ -70,7 +70,7 @@ which _implies_ our desired `∀ ∃ ∀ ∃ ∀` but is _not_ equivalent to it.
 try
 
 ```lean
-tendsto (|y - x|⁻¹ * |(g y - g x) - g' x (y - x)|) (at_top ×ˢ 𝓝 x) (𝓝 0)
+Tendsto (|y - x|⁻¹ * |(g y - g x) - g' x (y - x)|) (atTop ×ˢ 𝓝 x) (𝓝 0)
 ```
 
 but this is equivalent to the quantifier order `∀ ε > 0, ∃ N, ∃ δ > 0, ∀ n ≥ N, ∀ y ∈ B_δ(x)`, which
@@ -80,7 +80,7 @@ So to get the quantifier order we want, we need to introduce a new filter constr
 call a "curried filter"
 
 ```lean
-tendsto (|y - x|⁻¹ * |(g y - g x) - g' x (y - x)|) (at_top.curry (𝓝 x)) (𝓝 0)
+Tendsto (|y - x|⁻¹ * |(g y - g x) - g' x (y - x)|) (atTop.curry (𝓝 x)) (𝓝 0)
 ```
 
 Then the above implications are `Filter.Tendsto.curry` and
@@ -450,8 +450,6 @@ section deriv
 /-! ### `deriv` versions of above theorems
 
 In this section, we provide `deriv` equivalents of the `fderiv` lemmas in the previous section.
-The protected function `promote_deriv` provides the translation between derivatives and Fréchet
-derivatives
 -/
 
 

These are all doc fixes

@@ -47,7 +47,7 @@ That is, we want to prove something like:
 ∀ ε > 0, ∃ δ > 0, ∀ y ∈ B_δ(x), |y - x|⁻¹ * |(g y - g x) - g' x (y - x)| < ε.
 ```
 
-To do so, we will need to introduce a pair of quantifers
+To do so, we will need to introduce a pair of quantifiers
 
 ```lean
 ∀ ε > 0, ∃ N, ∀ n ≥ N, ∃ δ > 0, ∀ y ∈ B_δ(x), |y - x|⁻¹ * |(g y - g x) - g' x (y - x)| < ε.
@@ -73,7 +73,7 @@ try
 tendsto (|y - x|⁻¹ * |(g y - g x) - g' x (y - x)|) (at_top ×ˢ 𝓝 x) (𝓝 0)
 ```
 
-but this is equivalent to the quantifer order `∀ ε > 0, ∃ N, ∃ δ > 0, ∀ n ≥ N, ∀ y ∈ B_δ(x)`, which
+but this is equivalent to the quantifier order `∀ ε > 0, ∃ N, ∃ δ > 0, ∀ n ≥ N, ∀ y ∈ B_δ(x)`, which
 again _implies_ our desired `∀ ∃ ∀ ∃ ∀` but is not equivalent to it.
 
 So to get the quantifier order we want, we need to introduce a new filter construction, which we

@@ -115,7 +115,7 @@ sequence in a neighborhood of `x`. -/
 theorem uniformCauchySeqOnFilter_of_fderiv (hf' : UniformCauchySeqOnFilter f' l (𝓝 x))
     (hf : ∀ᶠ n : ι × E in l ×ˢ 𝓝 x, HasFDerivAt (f n.1) (f' n.1 n.2) n.2)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOnFilter f l (𝓝 x) := by
-  let : NormedSpace ℝ E; exact NormedSpace.restrictScalars ℝ 𝕜 _
+  letI : NormedSpace ℝ E := NormedSpace.restrictScalars ℝ 𝕜 _
   rw [SeminormedAddGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_zero] at hf' ⊢
   suffices
     TendstoUniformlyOnFilter (fun (n : ι × ι) (z : E) => f n.1 z - f n.2 z - (f n.1 x - f n.2 x)) 0
@@ -179,7 +179,7 @@ convergence. See `cauchy_map_of_uniformCauchySeqOn_fderiv`.
 theorem uniformCauchySeqOn_ball_of_fderiv {r : ℝ} (hf' : UniformCauchySeqOn f' l (Metric.ball x r))
     (hf : ∀ n : ι, ∀ y : E, y ∈ Metric.ball x r → HasFDerivAt (f n) (f' n y) y)
     (hfg : Cauchy (map (fun n => f n x) l)) : UniformCauchySeqOn f l (Metric.ball x r) := by
-  let : NormedSpace ℝ E; exact NormedSpace.restrictScalars ℝ 𝕜 _
+  letI : NormedSpace ℝ E := NormedSpace.restrictScalars ℝ 𝕜 _
   have : NeBot l := (cauchy_map_iff.1 hfg).1
   rcases le_or_lt r 0 with (hr | hr)
   · simp only [Metric.ball_eq_empty.2 hr, UniformCauchySeqOn, Set.mem_empty_iff_false,

Following on from #4702, another hundred sample uses of the gcongr tactic.

@@ -478,7 +478,7 @@ theorem UniformCauchySeqOnFilter.one_smulRight {l' : Filter 𝕜}
   simp only [ContinuousLinearMap.coe_sub', Pi.sub_apply, ContinuousLinearMap.smulRight_apply,
     ContinuousLinearMap.one_apply]
   rw [← smul_sub, norm_smul, mul_comm]
-  exact mul_le_mul hn.le rfl.le (norm_nonneg _) hq.le
+  gcongr
 #align uniform_cauchy_seq_on_filter.one_smul_right UniformCauchySeqOnFilter.one_smulRight
 
 theorem uniformCauchySeqOnFilter_of_deriv (hf' : UniformCauchySeqOnFilter f' l (𝓝 x))
@@ -526,7 +526,7 @@ theorem hasDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     simp only [ContinuousLinearMap.coe_sub', Pi.sub_apply, ContinuousLinearMap.smulRight_apply,
       ContinuousLinearMap.one_apply]
     rw [← smul_sub, norm_smul, mul_comm]
-    exact mul_le_mul hn.le rfl.le (norm_nonneg _) hq.le
+    gcongr
   exact hasFDerivAt_of_tendstoUniformlyOnFilter hf' hf hfg
 #align has_deriv_at_of_tendsto_uniformly_on_filter hasDerivAt_of_tendstoUniformlyOnFilter