analysis.calculus.fderiv_measurable ⟷ Mathlib.Analysis.Calculus.FDeriv.Measurable

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

@@ -114,7 +114,7 @@ variable {f : E → F} (K : Set (E →L[𝕜] F))
 
 namespace FderivMeasurableAux
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (y z «expr ∈ » ball[metric.ball] x r') -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (y z «expr ∈ » ball[metric.ball] x r') -/
 #print FDerivMeasurableAux.A /-
 /-- The set `A f L r ε` is the set of points `x` around which the function `f` is well approximated
 at scale `r` by the linear map `L`, up to an error `ε`. We tweak the definition to make sure that
@@ -226,10 +226,10 @@ theorem norm_sub_le_of_mem_A {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
       apply add_le_add
       · apply le_of_mem_A h₂
         · simp only [le_of_lt (half_pos hr), mem_closed_ball, dist_self]
-        · simp only [dist_eq_norm, add_sub_cancel', mem_closed_ball, ylt.le]
+        · simp only [dist_eq_norm, add_sub_cancel_left, mem_closed_ball, ylt.le]
       · apply le_of_mem_A h₁
         · simp only [le_of_lt (half_pos hr), mem_closed_ball, dist_self]
-        · simp only [dist_eq_norm, add_sub_cancel', mem_closed_ball, ylt.le]
+        · simp only [dist_eq_norm, add_sub_cancel_left, mem_closed_ball, ylt.le]
     _ = 2 * ε * r := by ring
     _ ≤ 2 * ε * (2 * ‖c‖ * ‖y‖) := (mul_le_mul_of_nonneg_left ley (mul_nonneg (by norm_num) hε.le))
     _ = 4 * ‖c‖ * ε * ‖y‖ := by ring
@@ -391,12 +391,12 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       · simp only [mem_closed_ball, dist_self]
         exact div_nonneg (le_of_lt P) zero_le_two
       ·
-        simpa only [dist_eq_norm, add_sub_cancel', mem_closed_ball, pow_succ', mul_one_div] using
+        simpa only [dist_eq_norm, add_sub_cancel_left, mem_closed_ball, pow_succ, mul_one_div] using
           h'k
     have J2 : ‖f (x + y) - f x - L e (n e) m y‖ ≤ 4 * (1 / 2) ^ e * ‖y‖ :=
       calc
         ‖f (x + y) - f x - L e (n e) m y‖ ≤ (1 / 2) ^ e * (1 / 2) ^ m := by
-          simpa only [add_sub_cancel'] using J1
+          simpa only [add_sub_cancel_left] using J1
         _ = 4 * (1 / 2) ^ e * (1 / 2) ^ (m + 2) := by field_simp; ring
         _ ≤ 4 * (1 / 2) ^ e * ‖y‖ :=
           mul_le_mul_of_nonneg_left (le_of_lt hk) (mul_nonneg (by norm_num) (le_of_lt P))
@@ -522,7 +522,7 @@ variable {f : ℝ → F} (K : Set F)
 
 namespace RightDerivMeasurableAux
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (y z «expr ∈ » Icc[set.Icc] x «expr + »(x, r')) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (y z «expr ∈ » Icc[set.Icc] x «expr + »(x, r')) -/
 #print RightDerivMeasurableAux.A /-
 /-- The set `A f L r ε` is the set of points `x` around which the function `f` is well approximated
 at scale `r` by the linear map `h ↦ h • L`, up to an error `ε`. We tweak the definition to

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

@@ -188,7 +188,7 @@ theorem mem_A_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (fderiv 𝕜 f x) r ε :=
   by
   have := hx.has_fderiv_at
-  simp only [HasFDerivAt, HasFDerivAtFilter, is_o_iff] at this 
+  simp only [HasFDerivAt, HasFDerivAtFilter, is_o_iff] at this
   rcases eventually_nhds_iff_ball.1 (this (half_pos hε)) with ⟨R, R_pos, hR⟩
   refine' ⟨R, R_pos, fun r hr => _⟩
   have : r ∈ Ioc (r / 2) r := ⟨half_lt_self hr.1, le_rfl⟩
@@ -217,7 +217,7 @@ theorem norm_sub_le_of_mem_A {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
     mul_nonneg (mul_nonneg (by norm_num : (0 : ℝ) ≤ 4) (norm_nonneg _)) hε.le
   refine' op_norm_le_of_shell (half_pos hr) this hc _
   intro y ley ylt
-  rw [div_div, div_le_iff' (mul_pos (by norm_num : (0 : ℝ) < 2) (zero_lt_one.trans hc))] at ley 
+  rw [div_div, div_le_iff' (mul_pos (by norm_num : (0 : ℝ) < 2) (zero_lt_one.trans hc))] at ley
   calc
     ‖(L₁ - L₂) y‖ = ‖f (x + y) - f x - L₂ (x + y - x) - (f (x + y) - f x - L₁ (x + y - x))‖ := by
       simp
@@ -275,7 +275,7 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     have := mem_Inter.1 hx e
     rcases mem_Union.1 this with ⟨n, hn⟩
     refine' ⟨n, fun p q hp hq => _⟩
-    simp only [mem_Inter, ge_iff_le] at hn 
+    simp only [mem_Inter, ge_iff_le] at hn
     rcases mem_Union.1 (hn p hp q hq) with ⟨L, hL⟩
     exact ⟨L, mem_Union.1 hL⟩
   /- Recast the assumptions: for each `e`, there exist `n e` and linear maps `L e p q` in `K`
@@ -377,12 +377,12 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     have k_gt : n e < k :=
       by
       have : ((1 : ℝ) / 2) ^ (k + 1) < (1 / 2) ^ (n e + 1) := lt_trans hk y_lt
-      rw [pow_lt_pow_iff_right_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this 
+      rw [pow_lt_pow_iff_right_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this
       linarith
     set m := k - 1 with hl
     have m_ge : n e ≤ m := Nat.le_pred_of_lt k_gt
     have km : k = m + 1 := (Nat.succ_pred_eq_of_pos (lt_of_le_of_lt (zero_le _) k_gt)).symm
-    rw [km] at hk h'k 
+    rw [km] at hk h'k
     -- `f` is well approximated by `L e (n e) k` at the relevant scale
     -- (in fact, we use `m = k - 1` instead of `k` because of the precise definition of `A`).
     have J1 : ‖f (x + y) - f x - L e (n e) m (x + y - x)‖ ≤ (1 / 2) ^ e * (1 / 2) ^ m :=
@@ -413,7 +413,7 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
           (mul_nonneg (add_nonneg (by norm_num) (mul_nonneg (by norm_num) (norm_nonneg _)))
             (norm_nonneg _)))
       _ = ε * ‖y‖ := by field_simp [ne_of_gt Pos]; ring
-  rw [← this.fderiv] at f'K 
+  rw [← this.fderiv] at f'K
   exact ⟨this.differentiable_at, f'K⟩
 #align fderiv_measurable_aux.D_subset_differentiable_set FDerivMeasurableAux.D_subset_differentiable_set
 -/
@@ -613,7 +613,7 @@ theorem mem_A_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (derivWithin f (Ici x) x) r ε :=
   by
   have := hx.has_deriv_within_at
-  simp_rw [hasDerivWithinAt_iff_isLittleO, is_o_iff] at this 
+  simp_rw [hasDerivWithinAt_iff_isLittleO, is_o_iff] at this
   rcases mem_nhdsWithin_Ici_iff_exists_Ico_subset.1 (this (half_pos hε)) with ⟨m, xm, hm⟩
   refine' ⟨m - x, by linarith [show x < m from xm], fun r hr => _⟩
   have : r ∈ Ioc (r / 2) r := ⟨half_lt_self hr.1, le_rfl⟩
@@ -645,7 +645,7 @@ theorem norm_sub_le_of_mem_A {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F}
     (h₂ : x ∈ A f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ε :=
   by
   suffices H : ‖(r / 2) • (L₁ - L₂)‖ ≤ r / 2 * (4 * ε)
-  · rwa [norm_smul, Real.norm_of_nonneg (half_pos hr).le, mul_le_mul_left (half_pos hr)] at H 
+  · rwa [norm_smul, Real.norm_of_nonneg (half_pos hr).le, mul_le_mul_left (half_pos hr)] at H
   calc
     ‖(r / 2) • (L₁ - L₂)‖ =
         ‖f (x + r / 2) - f x - (x + r / 2 - x) • L₂ -
@@ -701,7 +701,7 @@ theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     have := mem_Inter.1 hx e
     rcases mem_Union.1 this with ⟨n, hn⟩
     refine' ⟨n, fun p q hp hq => _⟩
-    simp only [mem_Inter, ge_iff_le] at hn 
+    simp only [mem_Inter, ge_iff_le] at hn
     rcases mem_Union.1 (hn p hp q hq) with ⟨L, hL⟩
     exact ⟨L, mem_Union.1 hL⟩
   /- Recast the assumptions: for each `e`, there exist `n e` and linear maps `L e p q` in `K`
@@ -800,12 +800,12 @@ theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     have k_gt : n e < k :=
       by
       have : ((1 : ℝ) / 2) ^ (k + 1) < (1 / 2) ^ (n e + 1) := lt_of_lt_of_le hk y_le
-      rw [pow_lt_pow_iff_right_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this 
+      rw [pow_lt_pow_iff_right_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this
       linarith
     set m := k - 1 with hl
     have m_ge : n e ≤ m := Nat.le_pred_of_lt k_gt
     have km : k = m + 1 := (Nat.succ_pred_eq_of_pos (lt_of_le_of_lt (zero_le _) k_gt)).symm
-    rw [km] at hk h'k 
+    rw [km] at hk h'k
     -- `f` is well approximated by `L e (n e) k` at the relevant scale
     -- (in fact, we use `m = k - 1` instead of `k` because of the precise definition of `A`).
     have J : ‖f y - f x - (y - x) • L e (n e) m‖ ≤ 4 * (1 / 2) ^ e * ‖y - x‖ :=
@@ -815,7 +815,7 @@ theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
           apply le_of_mem_A (hn e (n e) m le_rfl m_ge).2.2
           · simp only [one_div, inv_pow, left_mem_Icc, le_add_iff_nonneg_right]
             exact div_nonneg (inv_nonneg.2 (pow_nonneg zero_le_two _)) zero_le_two
-          · simp only [pow_add, tsub_le_iff_left] at h'k 
+          · simp only [pow_add, tsub_le_iff_left] at h'k
             simpa only [hy.1, mem_Icc, true_and_iff, one_div, pow_one] using h'k
         _ = 4 * (1 / 2) ^ e * (1 / 2) ^ (m + 2) := by field_simp; ring
         _ ≤ 4 * (1 / 2) ^ e * (y - x) :=
@@ -832,7 +832,7 @@ theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
       _ ≤ 16 * ‖y - x‖ * (ε / 16) :=
         (mul_le_mul_of_nonneg_left he.le (mul_nonneg (by norm_num) (norm_nonneg _)))
       _ = ε * ‖y - x‖ := by ring
-  rw [← this.deriv_within (uniqueDiffOn_Ici x x le_rfl)] at f'K 
+  rw [← this.deriv_within (uniqueDiffOn_Ici x x le_rfl)] at f'K
   exact ⟨this.differentiable_within_at, f'K⟩
 #align right_deriv_measurable_aux.D_subset_differentiable_set RightDerivMeasurableAux.D_subset_differentiable_set
 -/

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

@@ -377,7 +377,7 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     have k_gt : n e < k :=
       by
       have : ((1 : ℝ) / 2) ^ (k + 1) < (1 / 2) ^ (n e + 1) := lt_trans hk y_lt
-      rw [pow_lt_pow_iff_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this 
+      rw [pow_lt_pow_iff_right_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this 
       linarith
     set m := k - 1 with hl
     have m_ge : n e ≤ m := Nat.le_pred_of_lt k_gt
@@ -800,7 +800,7 @@ theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     have k_gt : n e < k :=
       by
       have : ((1 : ℝ) / 2) ^ (k + 1) < (1 / 2) ^ (n e + 1) := lt_of_lt_of_le hk y_le
-      rw [pow_lt_pow_iff_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this 
+      rw [pow_lt_pow_iff_right_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this 
       linarith
     set m := k - 1 with hl
     have m_ge : n e ≤ m := Nat.le_pred_of_lt k_gt

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yury Kudryashov
 -/
-import Mathbin.Analysis.Calculus.Deriv.Basic
-import Mathbin.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap
-import Mathbin.MeasureTheory.Function.StronglyMeasurable.Basic
+import Analysis.Calculus.Deriv.Basic
+import MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap
+import MeasureTheory.Function.StronglyMeasurable.Basic
 
 #align_import analysis.calculus.fderiv_measurable from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
 
@@ -114,7 +114,7 @@ variable {f : E → F} (K : Set (E →L[𝕜] F))
 
 namespace FderivMeasurableAux
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » ball[metric.ball] x r') -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (y z «expr ∈ » ball[metric.ball] x r') -/
 #print FDerivMeasurableAux.A /-
 /-- The set `A f L r ε` is the set of points `x` around which the function `f` is well approximated
 at scale `r` by the linear map `L`, up to an error `ε`. We tweak the definition to make sure that
@@ -522,7 +522,7 @@ variable {f : ℝ → F} (K : Set F)
 
 namespace RightDerivMeasurableAux
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » Icc[set.Icc] x «expr + »(x, r')) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (y z «expr ∈ » Icc[set.Icc] x «expr + »(x, r')) -/
 #print RightDerivMeasurableAux.A /-
 /-- The set `A f L r ε` is the set of points `x` around which the function `f` is well approximated
 at scale `r` by the linear map `h ↦ h • L`, up to an error `ε`. We tweak the definition to

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

@@ -144,8 +144,8 @@ def D (f : E → F) (K : Set (E →L[𝕜] F)) : Set E :=
 #align fderiv_measurable_aux.D FDerivMeasurableAux.D
 -/
 
-#print FDerivMeasurableAux.isOpen_a /-
-theorem isOpen_a (L : E →L[𝕜] F) (r ε : ℝ) : IsOpen (A f L r ε) :=
+#print FDerivMeasurableAux.isOpen_A /-
+theorem isOpen_A (L : E →L[𝕜] F) (r ε : ℝ) : IsOpen (A f L r ε) :=
   by
   rw [Metric.isOpen_iff]
   rintro x ⟨r', r'_mem, hr'⟩
@@ -155,36 +155,36 @@ theorem isOpen_a (L : E →L[𝕜] F) (r ε : ℝ) : IsOpen (A f L r ε) :=
   have B : ball x' s ⊆ ball x r' := ball_subset (le_of_lt hx')
   intro y hy z hz
   exact hr' y (B hy) z (B hz)
-#align fderiv_measurable_aux.is_open_A FDerivMeasurableAux.isOpen_a
+#align fderiv_measurable_aux.is_open_A FDerivMeasurableAux.isOpen_A
 -/
 
-#print FDerivMeasurableAux.isOpen_b /-
-theorem isOpen_b {K : Set (E →L[𝕜] F)} {r s ε : ℝ} : IsOpen (B f K r s ε) := by
+#print FDerivMeasurableAux.isOpen_B /-
+theorem isOpen_B {K : Set (E →L[𝕜] F)} {r s ε : ℝ} : IsOpen (B f K r s ε) := by
   simp [B, isOpen_iUnion, IsOpen.inter, is_open_A]
-#align fderiv_measurable_aux.is_open_B FDerivMeasurableAux.isOpen_b
+#align fderiv_measurable_aux.is_open_B FDerivMeasurableAux.isOpen_B
 -/
 
-#print FDerivMeasurableAux.a_mono /-
-theorem a_mono (L : E →L[𝕜] F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : A f L r ε ⊆ A f L r δ :=
+#print FDerivMeasurableAux.A_mono /-
+theorem A_mono (L : E →L[𝕜] F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : A f L r ε ⊆ A f L r δ :=
   by
   rintro x ⟨r', r'r, hr'⟩
   refine' ⟨r', r'r, fun y hy z hz => (hr' y hy z hz).trans (mul_le_mul_of_nonneg_right h _)⟩
   linarith [mem_ball.1 hy, r'r.2, @dist_nonneg _ _ y x]
-#align fderiv_measurable_aux.A_mono FDerivMeasurableAux.a_mono
+#align fderiv_measurable_aux.A_mono FDerivMeasurableAux.A_mono
 -/
 
-#print FDerivMeasurableAux.le_of_mem_a /-
-theorem le_of_mem_a {r ε : ℝ} {L : E →L[𝕜] F} {x : E} (hx : x ∈ A f L r ε) {y z : E}
+#print FDerivMeasurableAux.le_of_mem_A /-
+theorem le_of_mem_A {r ε : ℝ} {L : E →L[𝕜] F} {x : E} (hx : x ∈ A f L r ε) {y z : E}
     (hy : y ∈ closedBall x (r / 2)) (hz : z ∈ closedBall x (r / 2)) :
     ‖f z - f y - L (z - y)‖ ≤ ε * r :=
   by
   rcases hx with ⟨r', r'mem, hr'⟩
   exact hr' _ ((mem_closed_ball.1 hy).trans_lt r'mem.1) _ ((mem_closed_ball.1 hz).trans_lt r'mem.1)
-#align fderiv_measurable_aux.le_of_mem_A FDerivMeasurableAux.le_of_mem_a
+#align fderiv_measurable_aux.le_of_mem_A FDerivMeasurableAux.le_of_mem_A
 -/
 
-#print FDerivMeasurableAux.mem_a_of_differentiable /-
-theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : DifferentiableAt 𝕜 f x) :
+#print FDerivMeasurableAux.mem_A_of_differentiable /-
+theorem mem_A_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : DifferentiableAt 𝕜 f x) :
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (fderiv 𝕜 f x) r ε :=
   by
   have := hx.has_fderiv_at
@@ -206,11 +206,11 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
         (mul_le_mul_of_nonneg_left (le_of_lt (mem_ball_iff_norm.1 hz)) (le_of_lt (half_pos hε)))
         (mul_le_mul_of_nonneg_left (le_of_lt (mem_ball_iff_norm.1 hy)) (le_of_lt (half_pos hε))))
     _ = ε * r := by ring
-#align fderiv_measurable_aux.mem_A_of_differentiable FDerivMeasurableAux.mem_a_of_differentiable
+#align fderiv_measurable_aux.mem_A_of_differentiable FDerivMeasurableAux.mem_A_of_differentiable
 -/
 
-#print FDerivMeasurableAux.norm_sub_le_of_mem_a /-
-theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0 < ε) (hr : 0 < r) {x : E}
+#print FDerivMeasurableAux.norm_sub_le_of_mem_A /-
+theorem norm_sub_le_of_mem_A {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0 < ε) (hr : 0 < r) {x : E}
     {L₁ L₂ : E →L[𝕜] F} (h₁ : x ∈ A f L₁ r ε) (h₂ : x ∈ A f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ‖c‖ * ε :=
   by
   have : 0 ≤ 4 * ‖c‖ * ε :=
@@ -233,12 +233,12 @@ theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
     _ = 2 * ε * r := by ring
     _ ≤ 2 * ε * (2 * ‖c‖ * ‖y‖) := (mul_le_mul_of_nonneg_left ley (mul_nonneg (by norm_num) hε.le))
     _ = 4 * ‖c‖ * ε * ‖y‖ := by ring
-#align fderiv_measurable_aux.norm_sub_le_of_mem_A FDerivMeasurableAux.norm_sub_le_of_mem_a
+#align fderiv_measurable_aux.norm_sub_le_of_mem_A FDerivMeasurableAux.norm_sub_le_of_mem_A
 -/
 
-#print FDerivMeasurableAux.differentiable_set_subset_d /-
+#print FDerivMeasurableAux.differentiable_set_subset_D /-
 /-- Easy inclusion: a differentiability point with derivative in `K` belongs to `D f K`. -/
-theorem differentiable_set_subset_d : {x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K} ⊆ D f K :=
+theorem differentiable_set_subset_D : {x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K} ⊆ D f K :=
   by
   intro x hx
   rw [D, mem_Inter]
@@ -251,12 +251,12 @@ theorem differentiable_set_subset_d : {x | DifferentiableAt 𝕜 f x ∧ fderiv
   refine' ⟨n, fun p hp q hq => ⟨fderiv 𝕜 f x, hx.2, ⟨_, _⟩⟩⟩ <;>
     · refine' hR _ ⟨pow_pos (by norm_num) _, lt_of_le_of_lt _ hn⟩
       exact pow_le_pow_of_le_one (by norm_num) (by norm_num) (by assumption)
-#align fderiv_measurable_aux.differentiable_set_subset_D FDerivMeasurableAux.differentiable_set_subset_d
+#align fderiv_measurable_aux.differentiable_set_subset_D FDerivMeasurableAux.differentiable_set_subset_D
 -/
 
-#print FDerivMeasurableAux.d_subset_differentiable_set /-
+#print FDerivMeasurableAux.D_subset_differentiable_set /-
 /-- Harder inclusion: at a point in `D f K`, the function `f` has a derivative, in `K`. -/
-theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete K) :
+theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete K) :
     D f K ⊆ {x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K} :=
   by
   have P : ∀ {n : ℕ}, (0 : ℝ) < (1 / 2) ^ n := pow_pos (by norm_num)
@@ -415,14 +415,14 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       _ = ε * ‖y‖ := by field_simp [ne_of_gt Pos]; ring
   rw [← this.fderiv] at f'K 
   exact ⟨this.differentiable_at, f'K⟩
-#align fderiv_measurable_aux.D_subset_differentiable_set FDerivMeasurableAux.d_subset_differentiable_set
+#align fderiv_measurable_aux.D_subset_differentiable_set FDerivMeasurableAux.D_subset_differentiable_set
 -/
 
-#print FDerivMeasurableAux.differentiable_set_eq_d /-
-theorem differentiable_set_eq_d (hK : IsComplete K) :
+#print FDerivMeasurableAux.differentiable_set_eq_D /-
+theorem differentiable_set_eq_D (hK : IsComplete K) :
     {x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K} = D f K :=
-  Subset.antisymm (differentiable_set_subset_d _) (d_subset_differentiable_set hK)
-#align fderiv_measurable_aux.differentiable_set_eq_D FDerivMeasurableAux.differentiable_set_eq_d
+  Subset.antisymm (differentiable_set_subset_D _) (D_subset_differentiable_set hK)
+#align fderiv_measurable_aux.differentiable_set_eq_D FDerivMeasurableAux.differentiable_set_eq_D
 -/
 
 end FderivMeasurableAux
@@ -553,8 +553,8 @@ def D (f : ℝ → F) (K : Set F) : Set ℝ :=
 #align right_deriv_measurable_aux.D RightDerivMeasurableAux.D
 -/
 
-#print RightDerivMeasurableAux.a_mem_nhdsWithin_Ioi /-
-theorem a_mem_nhdsWithin_Ioi {L : F} {r ε x : ℝ} (hx : x ∈ A f L r ε) : A f L r ε ∈ 𝓝[>] x :=
+#print RightDerivMeasurableAux.A_mem_nhdsWithin_Ioi /-
+theorem A_mem_nhdsWithin_Ioi {L : F} {r ε x : ℝ} (hx : x ∈ A f L r ε) : A f L r ε ∈ 𝓝[>] x :=
   by
   rcases hx with ⟨r', rr', hr'⟩
   rw [mem_nhdsWithin_Ioi_iff_exists_Ioo_subset]
@@ -567,11 +567,11 @@ theorem a_mem_nhdsWithin_Ioi {L : F} {r ε x : ℝ} (hx : x ∈ A f L r ε) : A
     linarith [hx'.2]
   intro y hy z hz
   exact hr' y (A hy) z (A hz)
-#align right_deriv_measurable_aux.A_mem_nhds_within_Ioi RightDerivMeasurableAux.a_mem_nhdsWithin_Ioi
+#align right_deriv_measurable_aux.A_mem_nhds_within_Ioi RightDerivMeasurableAux.A_mem_nhdsWithin_Ioi
 -/
 
-#print RightDerivMeasurableAux.b_mem_nhdsWithin_Ioi /-
-theorem b_mem_nhdsWithin_Ioi {K : Set F} {r s ε x : ℝ} (hx : x ∈ B f K r s ε) :
+#print RightDerivMeasurableAux.B_mem_nhdsWithin_Ioi /-
+theorem B_mem_nhdsWithin_Ioi {K : Set F} {r s ε x : ℝ} (hx : x ∈ B f K r s ε) :
     B f K r s ε ∈ 𝓝[>] x :=
   by
   obtain ⟨L, LK, hL₁, hL₂⟩ : ∃ L : F, L ∈ K ∧ x ∈ A f L r ε ∧ x ∈ A f L s ε := by
@@ -579,36 +579,36 @@ theorem b_mem_nhdsWithin_Ioi {K : Set F} {r s ε x : ℝ} (hx : x ∈ B f K r s
   filter_upwards [A_mem_nhds_within_Ioi hL₁, A_mem_nhds_within_Ioi hL₂] with y hy₁ hy₂
   simp only [B, mem_Union, mem_inter_iff, exists_prop]
   exact ⟨L, LK, hy₁, hy₂⟩
-#align right_deriv_measurable_aux.B_mem_nhds_within_Ioi RightDerivMeasurableAux.b_mem_nhdsWithin_Ioi
+#align right_deriv_measurable_aux.B_mem_nhds_within_Ioi RightDerivMeasurableAux.B_mem_nhdsWithin_Ioi
 -/
 
-#print RightDerivMeasurableAux.measurableSet_b /-
-theorem measurableSet_b {K : Set F} {r s ε : ℝ} : MeasurableSet (B f K r s ε) :=
-  measurableSet_of_mem_nhdsWithin_Ioi fun x hx => b_mem_nhdsWithin_Ioi hx
-#align right_deriv_measurable_aux.measurable_set_B RightDerivMeasurableAux.measurableSet_b
+#print RightDerivMeasurableAux.measurableSet_B /-
+theorem measurableSet_B {K : Set F} {r s ε : ℝ} : MeasurableSet (B f K r s ε) :=
+  measurableSet_of_mem_nhdsWithin_Ioi fun x hx => B_mem_nhdsWithin_Ioi hx
+#align right_deriv_measurable_aux.measurable_set_B RightDerivMeasurableAux.measurableSet_B
 -/
 
-#print RightDerivMeasurableAux.a_mono /-
-theorem a_mono (L : F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : A f L r ε ⊆ A f L r δ :=
+#print RightDerivMeasurableAux.A_mono /-
+theorem A_mono (L : F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : A f L r ε ⊆ A f L r δ :=
   by
   rintro x ⟨r', r'r, hr'⟩
   refine' ⟨r', r'r, fun y hy z hz => (hr' y hy z hz).trans (mul_le_mul_of_nonneg_right h _)⟩
   linarith [hy.1, hy.2, r'r.2]
-#align right_deriv_measurable_aux.A_mono RightDerivMeasurableAux.a_mono
+#align right_deriv_measurable_aux.A_mono RightDerivMeasurableAux.A_mono
 -/
 
-#print RightDerivMeasurableAux.le_of_mem_a /-
-theorem le_of_mem_a {r ε : ℝ} {L : F} {x : ℝ} (hx : x ∈ A f L r ε) {y z : ℝ}
+#print RightDerivMeasurableAux.le_of_mem_A /-
+theorem le_of_mem_A {r ε : ℝ} {L : F} {x : ℝ} (hx : x ∈ A f L r ε) {y z : ℝ}
     (hy : y ∈ Icc x (x + r / 2)) (hz : z ∈ Icc x (x + r / 2)) : ‖f z - f y - (z - y) • L‖ ≤ ε * r :=
   by
   rcases hx with ⟨r', r'mem, hr'⟩
   have A : x + r / 2 ≤ x + r' := by linarith [r'mem.1]
   exact hr' _ ((Icc_subset_Icc le_rfl A) hy) _ ((Icc_subset_Icc le_rfl A) hz)
-#align right_deriv_measurable_aux.le_of_mem_A RightDerivMeasurableAux.le_of_mem_a
+#align right_deriv_measurable_aux.le_of_mem_A RightDerivMeasurableAux.le_of_mem_A
 -/
 
-#print RightDerivMeasurableAux.mem_a_of_differentiable /-
-theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
+#print RightDerivMeasurableAux.mem_A_of_differentiable /-
+theorem mem_A_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
     (hx : DifferentiableWithinAt ℝ f (Ici x) x) :
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (derivWithin f (Ici x) x) r ε :=
   by
@@ -637,11 +637,11 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
       · apply mul_le_mul_of_nonneg_left _ (le_of_lt (half_pos hε))
         rw [Real.norm_of_nonneg] <;> linarith [hy.1, hy.2]
     _ = ε * r := by ring
-#align right_deriv_measurable_aux.mem_A_of_differentiable RightDerivMeasurableAux.mem_a_of_differentiable
+#align right_deriv_measurable_aux.mem_A_of_differentiable RightDerivMeasurableAux.mem_A_of_differentiable
 -/
 
-#print RightDerivMeasurableAux.norm_sub_le_of_mem_a /-
-theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F} (h₁ : x ∈ A f L₁ r ε)
+#print RightDerivMeasurableAux.norm_sub_le_of_mem_A /-
+theorem norm_sub_le_of_mem_A {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F} (h₁ : x ∈ A f L₁ r ε)
     (h₂ : x ∈ A f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ε :=
   by
   suffices H : ‖(r / 2) • (L₁ - L₂)‖ ≤ r / 2 * (4 * ε)
@@ -660,12 +660,12 @@ theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F}
       · apply le_of_mem_A h₂ <;> simp [(half_pos hr).le]
       · apply le_of_mem_A h₁ <;> simp [(half_pos hr).le]
     _ = r / 2 * (4 * ε) := by ring
-#align right_deriv_measurable_aux.norm_sub_le_of_mem_A RightDerivMeasurableAux.norm_sub_le_of_mem_a
+#align right_deriv_measurable_aux.norm_sub_le_of_mem_A RightDerivMeasurableAux.norm_sub_le_of_mem_A
 -/
 
-#print RightDerivMeasurableAux.differentiable_set_subset_d /-
+#print RightDerivMeasurableAux.differentiable_set_subset_D /-
 /-- Easy inclusion: a differentiability point with derivative in `K` belongs to `D f K`. -/
-theorem differentiable_set_subset_d :
+theorem differentiable_set_subset_D :
     {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K} ⊆ D f K :=
   by
   intro x hx
@@ -679,12 +679,12 @@ theorem differentiable_set_subset_d :
   refine' ⟨n, fun p hp q hq => ⟨derivWithin f (Ici x) x, hx.2, ⟨_, _⟩⟩⟩ <;>
     · refine' hR _ ⟨pow_pos (by norm_num) _, lt_of_le_of_lt _ hn⟩
       exact pow_le_pow_of_le_one (by norm_num) (by norm_num) (by assumption)
-#align right_deriv_measurable_aux.differentiable_set_subset_D RightDerivMeasurableAux.differentiable_set_subset_d
+#align right_deriv_measurable_aux.differentiable_set_subset_D RightDerivMeasurableAux.differentiable_set_subset_D
 -/
 
-#print RightDerivMeasurableAux.d_subset_differentiable_set /-
+#print RightDerivMeasurableAux.D_subset_differentiable_set /-
 /-- Harder inclusion: at a point in `D f K`, the function `f` has a derivative, in `K`. -/
-theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
+theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     D f K ⊆ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K} :=
   by
   have P : ∀ {n : ℕ}, (0 : ℝ) < (1 / 2) ^ n := pow_pos (by norm_num)
@@ -834,14 +834,14 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
       _ = ε * ‖y - x‖ := by ring
   rw [← this.deriv_within (uniqueDiffOn_Ici x x le_rfl)] at f'K 
   exact ⟨this.differentiable_within_at, f'K⟩
-#align right_deriv_measurable_aux.D_subset_differentiable_set RightDerivMeasurableAux.d_subset_differentiable_set
+#align right_deriv_measurable_aux.D_subset_differentiable_set RightDerivMeasurableAux.D_subset_differentiable_set
 -/
 
-#print RightDerivMeasurableAux.differentiable_set_eq_d /-
-theorem differentiable_set_eq_d (hK : IsComplete K) :
+#print RightDerivMeasurableAux.differentiable_set_eq_D /-
+theorem differentiable_set_eq_D (hK : IsComplete K) :
     {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K} = D f K :=
-  Subset.antisymm (differentiable_set_subset_d _) (d_subset_differentiable_set hK)
-#align right_deriv_measurable_aux.differentiable_set_eq_D RightDerivMeasurableAux.differentiable_set_eq_d
+  Subset.antisymm (differentiable_set_subset_D _) (D_subset_differentiable_set hK)
+#align right_deriv_measurable_aux.differentiable_set_eq_D RightDerivMeasurableAux.differentiable_set_eq_D
 -/
 
 end RightDerivMeasurableAux

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

@@ -96,7 +96,7 @@ variable {𝕜 E F : Type _} [NontriviallyNormedField 𝕜] [NormedAddCommGroup
 theorem measurable_apply₂ [MeasurableSpace E] [OpensMeasurableSpace E] [SecondCountableTopology E]
     [SecondCountableTopology (E →L[𝕜] F)] [MeasurableSpace F] [BorelSpace F] :
     Measurable fun p : (E →L[𝕜] F) × E => p.1 p.2 :=
-  isBoundedBilinearMapApply.Continuous.Measurable
+  isBoundedBilinearMap_apply.Continuous.Measurable
 #align continuous_linear_map.measurable_apply₂ ContinuousLinearMap.measurable_apply₂
 -/
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.calculus.fderiv_measurable
-! leanprover-community/mathlib commit f60c6087a7275b72d5db3c5a1d0e19e35a429c0a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.Deriv.Basic
 import Mathbin.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap
 import Mathbin.MeasureTheory.Function.StronglyMeasurable.Basic
 
+#align_import analysis.calculus.fderiv_measurable from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
+
 /-!
 # Derivative is measurable
 
@@ -117,7 +114,7 @@ variable {f : E → F} (K : Set (E →L[𝕜] F))
 
 namespace FderivMeasurableAux
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y z «expr ∈ » ball[metric.ball] x r') -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » ball[metric.ball] x r') -/
 #print FDerivMeasurableAux.A /-
 /-- The set `A f L r ε` is the set of points `x` around which the function `f` is well approximated
 at scale `r` by the linear map `L`, up to an error `ε`. We tweak the definition to make sure that
@@ -525,7 +522,7 @@ variable {f : ℝ → F} (K : Set F)
 
 namespace RightDerivMeasurableAux
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y z «expr ∈ » Icc[set.Icc] x «expr + »(x, r')) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » Icc[set.Icc] x «expr + »(x, r')) -/
 #print RightDerivMeasurableAux.A /-
 /-- The set `A f L r ε` is the set of points `x` around which the function `f` is well approximated
 at scale `r` by the linear map `h ↦ h • L`, up to an error `ε`. We tweak the definition to

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

@@ -95,11 +95,13 @@ namespace ContinuousLinearMap
 variable {𝕜 E F : Type _} [NontriviallyNormedField 𝕜] [NormedAddCommGroup E] [NormedSpace 𝕜 E]
   [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
+#print ContinuousLinearMap.measurable_apply₂ /-
 theorem measurable_apply₂ [MeasurableSpace E] [OpensMeasurableSpace E] [SecondCountableTopology E]
     [SecondCountableTopology (E →L[𝕜] F)] [MeasurableSpace F] [BorelSpace F] :
     Measurable fun p : (E →L[𝕜] F) × E => p.1 p.2 :=
   isBoundedBilinearMapApply.Continuous.Measurable
 #align continuous_linear_map.measurable_apply₂ ContinuousLinearMap.measurable_apply₂
+-/
 
 end ContinuousLinearMap
 
@@ -145,6 +147,7 @@ def D (f : E → F) (K : Set (E →L[𝕜] F)) : Set E :=
 #align fderiv_measurable_aux.D FDerivMeasurableAux.D
 -/
 
+#print FDerivMeasurableAux.isOpen_a /-
 theorem isOpen_a (L : E →L[𝕜] F) (r ε : ℝ) : IsOpen (A f L r ε) :=
   by
   rw [Metric.isOpen_iff]
@@ -156,6 +159,7 @@ theorem isOpen_a (L : E →L[𝕜] F) (r ε : ℝ) : IsOpen (A f L r ε) :=
   intro y hy z hz
   exact hr' y (B hy) z (B hz)
 #align fderiv_measurable_aux.is_open_A FDerivMeasurableAux.isOpen_a
+-/
 
 #print FDerivMeasurableAux.isOpen_b /-
 theorem isOpen_b {K : Set (E →L[𝕜] F)} {r s ε : ℝ} : IsOpen (B f K r s ε) := by
@@ -163,13 +167,16 @@ theorem isOpen_b {K : Set (E →L[𝕜] F)} {r s ε : ℝ} : IsOpen (B f K r s 
 #align fderiv_measurable_aux.is_open_B FDerivMeasurableAux.isOpen_b
 -/
 
+#print FDerivMeasurableAux.a_mono /-
 theorem a_mono (L : E →L[𝕜] F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : A f L r ε ⊆ A f L r δ :=
   by
   rintro x ⟨r', r'r, hr'⟩
   refine' ⟨r', r'r, fun y hy z hz => (hr' y hy z hz).trans (mul_le_mul_of_nonneg_right h _)⟩
   linarith [mem_ball.1 hy, r'r.2, @dist_nonneg _ _ y x]
 #align fderiv_measurable_aux.A_mono FDerivMeasurableAux.a_mono
+-/
 
+#print FDerivMeasurableAux.le_of_mem_a /-
 theorem le_of_mem_a {r ε : ℝ} {L : E →L[𝕜] F} {x : E} (hx : x ∈ A f L r ε) {y z : E}
     (hy : y ∈ closedBall x (r / 2)) (hz : z ∈ closedBall x (r / 2)) :
     ‖f z - f y - L (z - y)‖ ≤ ε * r :=
@@ -177,7 +184,9 @@ theorem le_of_mem_a {r ε : ℝ} {L : E →L[𝕜] F} {x : E} (hx : x ∈ A f L
   rcases hx with ⟨r', r'mem, hr'⟩
   exact hr' _ ((mem_closed_ball.1 hy).trans_lt r'mem.1) _ ((mem_closed_ball.1 hz).trans_lt r'mem.1)
 #align fderiv_measurable_aux.le_of_mem_A FDerivMeasurableAux.le_of_mem_a
+-/
 
+#print FDerivMeasurableAux.mem_a_of_differentiable /-
 theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : DifferentiableAt 𝕜 f x) :
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (fderiv 𝕜 f x) r ε :=
   by
@@ -201,7 +210,9 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
         (mul_le_mul_of_nonneg_left (le_of_lt (mem_ball_iff_norm.1 hy)) (le_of_lt (half_pos hε))))
     _ = ε * r := by ring
 #align fderiv_measurable_aux.mem_A_of_differentiable FDerivMeasurableAux.mem_a_of_differentiable
+-/
 
+#print FDerivMeasurableAux.norm_sub_le_of_mem_a /-
 theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0 < ε) (hr : 0 < r) {x : E}
     {L₁ L₂ : E →L[𝕜] F} (h₁ : x ∈ A f L₁ r ε) (h₂ : x ∈ A f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ‖c‖ * ε :=
   by
@@ -226,7 +237,9 @@ theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
     _ ≤ 2 * ε * (2 * ‖c‖ * ‖y‖) := (mul_le_mul_of_nonneg_left ley (mul_nonneg (by norm_num) hε.le))
     _ = 4 * ‖c‖ * ε * ‖y‖ := by ring
 #align fderiv_measurable_aux.norm_sub_le_of_mem_A FDerivMeasurableAux.norm_sub_le_of_mem_a
+-/
 
+#print FDerivMeasurableAux.differentiable_set_subset_d /-
 /-- Easy inclusion: a differentiability point with derivative in `K` belongs to `D f K`. -/
 theorem differentiable_set_subset_d : {x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K} ⊆ D f K :=
   by
@@ -242,6 +255,7 @@ theorem differentiable_set_subset_d : {x | DifferentiableAt 𝕜 f x ∧ fderiv
     · refine' hR _ ⟨pow_pos (by norm_num) _, lt_of_le_of_lt _ hn⟩
       exact pow_le_pow_of_le_one (by norm_num) (by norm_num) (by assumption)
 #align fderiv_measurable_aux.differentiable_set_subset_D FDerivMeasurableAux.differentiable_set_subset_d
+-/
 
 #print FDerivMeasurableAux.d_subset_differentiable_set /-
 /-- Harder inclusion: at a point in `D f K`, the function `f` has a derivative, in `K`. -/
@@ -407,10 +421,12 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
 #align fderiv_measurable_aux.D_subset_differentiable_set FDerivMeasurableAux.d_subset_differentiable_set
 -/
 
+#print FDerivMeasurableAux.differentiable_set_eq_d /-
 theorem differentiable_set_eq_d (hK : IsComplete K) :
     {x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K} = D f K :=
   Subset.antisymm (differentiable_set_subset_d _) (d_subset_differentiable_set hK)
 #align fderiv_measurable_aux.differentiable_set_eq_D FDerivMeasurableAux.differentiable_set_eq_d
+-/
 
 end FderivMeasurableAux
 
@@ -432,6 +448,7 @@ theorem measurableSet_of_differentiableAt_of_isComplete {K : Set (E →L[𝕜] F
 
 variable [CompleteSpace F]
 
+#print measurableSet_of_differentiableAt /-
 /-- The set of differentiability points of a function taking values in a complete space is
 Borel-measurable. -/
 theorem measurableSet_of_differentiableAt : MeasurableSet {x | DifferentiableAt 𝕜 f x} :=
@@ -440,7 +457,9 @@ theorem measurableSet_of_differentiableAt : MeasurableSet {x | DifferentiableAt
   convert measurableSet_of_differentiableAt_of_isComplete 𝕜 f this
   simp
 #align measurable_set_of_differentiable_at measurableSet_of_differentiableAt
+-/
 
+#print measurable_fderiv /-
 @[measurability]
 theorem measurable_fderiv : Measurable (fderiv 𝕜 f) :=
   by
@@ -455,35 +474,46 @@ theorem measurable_fderiv : Measurable (fderiv 𝕜 f) :=
     (measurableSet_of_differentiableAt_of_isComplete _ _ hs.is_complete).union
       ((measurableSet_of_differentiableAt _ _).compl.inter (MeasurableSet.const _))
 #align measurable_fderiv measurable_fderiv
+-/
 
+#print measurable_fderiv_apply_const /-
 @[measurability]
 theorem measurable_fderiv_apply_const [MeasurableSpace F] [BorelSpace F] (y : E) :
     Measurable fun x => fderiv 𝕜 f x y :=
   (ContinuousLinearMap.measurable_apply y).comp (measurable_fderiv 𝕜 f)
 #align measurable_fderiv_apply_const measurable_fderiv_apply_const
+-/
 
 variable {𝕜}
 
+#print measurable_deriv /-
 @[measurability]
 theorem measurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜] [MeasurableSpace F]
     [BorelSpace F] (f : 𝕜 → F) : Measurable (deriv f) := by
   simpa only [fderiv_deriv] using measurable_fderiv_apply_const 𝕜 f 1
 #align measurable_deriv measurable_deriv
+-/
 
+#print stronglyMeasurable_deriv /-
 theorem stronglyMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜]
     [SecondCountableTopology F] (f : 𝕜 → F) : StronglyMeasurable (deriv f) := by borelize F;
   exact (measurable_deriv f).StronglyMeasurable
 #align strongly_measurable_deriv stronglyMeasurable_deriv
+-/
 
+#print aemeasurable_deriv /-
 theorem aemeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜] [MeasurableSpace F]
     [BorelSpace F] (f : 𝕜 → F) (μ : Measure 𝕜) : AEMeasurable (deriv f) μ :=
   (measurable_deriv f).AEMeasurable
 #align ae_measurable_deriv aemeasurable_deriv
+-/
 
+#print aestronglyMeasurable_deriv /-
 theorem aestronglyMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜]
     [SecondCountableTopology F] (f : 𝕜 → F) (μ : Measure 𝕜) : AEStronglyMeasurable (deriv f) μ :=
   (stronglyMeasurable_deriv f).AEStronglyMeasurable
 #align ae_strongly_measurable_deriv aestronglyMeasurable_deriv
+-/
 
 end fderiv
 
@@ -561,13 +591,16 @@ theorem measurableSet_b {K : Set F} {r s ε : ℝ} : MeasurableSet (B f K r s ε
 #align right_deriv_measurable_aux.measurable_set_B RightDerivMeasurableAux.measurableSet_b
 -/
 
+#print RightDerivMeasurableAux.a_mono /-
 theorem a_mono (L : F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : A f L r ε ⊆ A f L r δ :=
   by
   rintro x ⟨r', r'r, hr'⟩
   refine' ⟨r', r'r, fun y hy z hz => (hr' y hy z hz).trans (mul_le_mul_of_nonneg_right h _)⟩
   linarith [hy.1, hy.2, r'r.2]
 #align right_deriv_measurable_aux.A_mono RightDerivMeasurableAux.a_mono
+-/
 
+#print RightDerivMeasurableAux.le_of_mem_a /-
 theorem le_of_mem_a {r ε : ℝ} {L : F} {x : ℝ} (hx : x ∈ A f L r ε) {y z : ℝ}
     (hy : y ∈ Icc x (x + r / 2)) (hz : z ∈ Icc x (x + r / 2)) : ‖f z - f y - (z - y) • L‖ ≤ ε * r :=
   by
@@ -575,7 +608,9 @@ theorem le_of_mem_a {r ε : ℝ} {L : F} {x : ℝ} (hx : x ∈ A f L r ε) {y z
   have A : x + r / 2 ≤ x + r' := by linarith [r'mem.1]
   exact hr' _ ((Icc_subset_Icc le_rfl A) hy) _ ((Icc_subset_Icc le_rfl A) hz)
 #align right_deriv_measurable_aux.le_of_mem_A RightDerivMeasurableAux.le_of_mem_a
+-/
 
+#print RightDerivMeasurableAux.mem_a_of_differentiable /-
 theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
     (hx : DifferentiableWithinAt ℝ f (Ici x) x) :
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (derivWithin f (Ici x) x) r ε :=
@@ -606,7 +641,9 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
         rw [Real.norm_of_nonneg] <;> linarith [hy.1, hy.2]
     _ = ε * r := by ring
 #align right_deriv_measurable_aux.mem_A_of_differentiable RightDerivMeasurableAux.mem_a_of_differentiable
+-/
 
+#print RightDerivMeasurableAux.norm_sub_le_of_mem_a /-
 theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F} (h₁ : x ∈ A f L₁ r ε)
     (h₂ : x ∈ A f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ε :=
   by
@@ -627,6 +664,7 @@ theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F}
       · apply le_of_mem_A h₁ <;> simp [(half_pos hr).le]
     _ = r / 2 * (4 * ε) := by ring
 #align right_deriv_measurable_aux.norm_sub_le_of_mem_A RightDerivMeasurableAux.norm_sub_le_of_mem_a
+-/
 
 #print RightDerivMeasurableAux.differentiable_set_subset_d /-
 /-- Easy inclusion: a differentiability point with derivative in `K` belongs to `D f K`. -/

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

@@ -200,7 +200,6 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
         (mul_le_mul_of_nonneg_left (le_of_lt (mem_ball_iff_norm.1 hz)) (le_of_lt (half_pos hε)))
         (mul_le_mul_of_nonneg_left (le_of_lt (mem_ball_iff_norm.1 hy)) (le_of_lt (half_pos hε))))
     _ = ε * r := by ring
-    
 #align fderiv_measurable_aux.mem_A_of_differentiable FDerivMeasurableAux.mem_a_of_differentiable
 
 theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0 < ε) (hr : 0 < r) {x : E}
@@ -226,7 +225,6 @@ theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
     _ = 2 * ε * r := by ring
     _ ≤ 2 * ε * (2 * ‖c‖ * ‖y‖) := (mul_le_mul_of_nonneg_left ley (mul_nonneg (by norm_num) hε.le))
     _ = 4 * ‖c‖ * ε * ‖y‖ := by ring
-    
 #align fderiv_measurable_aux.norm_sub_le_of_mem_A FDerivMeasurableAux.norm_sub_le_of_mem_a
 
 /-- Easy inclusion: a differentiability point with derivative in `K` belongs to `D f K`. -/
@@ -314,7 +312,6 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       _ ≤ 4 * ‖c‖ * (1 / 2) ^ e + 4 * ‖c‖ * (1 / 2) ^ e + 4 * ‖c‖ * (1 / 2) ^ e := by
         apply_rules [add_le_add]
       _ = 12 * ‖c‖ * (1 / 2) ^ e := by ring
-      
   /- For definiteness, use `L0 e = L e (n e) (n e)`, to have a single sequence. We claim that this
     is a Cauchy sequence. -/
   let L0 : ℕ → E →L[𝕜] F := fun e => L e (n e) (n e)
@@ -330,7 +327,6 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       _ < 12 * ‖c‖ * (ε / (12 * ‖c‖)) :=
         (mul_lt_mul' le_rfl he (le_of_lt P) (mul_pos (by norm_num) cpos))
       _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0), ne_of_gt cpos]; ring
-      
   -- As it is Cauchy, the sequence `L0` converges, to a limit `f'` in `K`.
   obtain ⟨f', f'K, hf'⟩ : ∃ f' ∈ K, tendsto L0 at_top (𝓝 f') :=
     cauchySeq_tendsto_of_isComplete hK (fun e => (hn e (n e) (n e) le_rfl le_rfl).1) this
@@ -393,7 +389,6 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
         _ = 4 * (1 / 2) ^ e * (1 / 2) ^ (m + 2) := by field_simp; ring
         _ ≤ 4 * (1 / 2) ^ e * ‖y‖ :=
           mul_le_mul_of_nonneg_left (le_of_lt hk) (mul_nonneg (by norm_num) (le_of_lt P))
-        
     -- use the previous estimates to see that `f (x + y) - f x - f' y` is small.
     calc
       ‖f (x + y) - f x - f' y‖ = ‖f (x + y) - f x - L e (n e) m y + (L e (n e) m - f') y‖ :=
@@ -407,7 +402,6 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
           (mul_nonneg (add_nonneg (by norm_num) (mul_nonneg (by norm_num) (norm_nonneg _)))
             (norm_nonneg _)))
       _ = ε * ‖y‖ := by field_simp [ne_of_gt Pos]; ring
-      
   rw [← this.fderiv] at f'K 
   exact ⟨this.differentiable_at, f'K⟩
 #align fderiv_measurable_aux.D_subset_differentiable_set FDerivMeasurableAux.d_subset_differentiable_set
@@ -611,7 +605,6 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
       · apply mul_le_mul_of_nonneg_left _ (le_of_lt (half_pos hε))
         rw [Real.norm_of_nonneg] <;> linarith [hy.1, hy.2]
     _ = ε * r := by ring
-    
 #align right_deriv_measurable_aux.mem_A_of_differentiable RightDerivMeasurableAux.mem_a_of_differentiable
 
 theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F} (h₁ : x ∈ A f L₁ r ε)
@@ -633,7 +626,6 @@ theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F}
       · apply le_of_mem_A h₂ <;> simp [(half_pos hr).le]
       · apply le_of_mem_A h₁ <;> simp [(half_pos hr).le]
     _ = r / 2 * (4 * ε) := by ring
-    
 #align right_deriv_measurable_aux.norm_sub_le_of_mem_A RightDerivMeasurableAux.norm_sub_le_of_mem_a
 
 #print RightDerivMeasurableAux.differentiable_set_subset_d /-
@@ -720,7 +712,6 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
         (le_trans (norm_add_le _ _) (add_le_add_right (norm_add_le _ _) _))
       _ ≤ 4 * (1 / 2) ^ e + 4 * (1 / 2) ^ e + 4 * (1 / 2) ^ e := by apply_rules [add_le_add]
       _ = 12 * (1 / 2) ^ e := by ring
-      
   /- For definiteness, use `L0 e = L e (n e) (n e)`, to have a single sequence. We claim that this
     is a Cauchy sequence. -/
   let L0 : ℕ → F := fun e => L e (n e) (n e)
@@ -735,7 +726,6 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
       ‖L0 e - L0 e'‖ ≤ 12 * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
       _ < 12 * (ε / 12) := (mul_lt_mul' le_rfl he (le_of_lt P) (by norm_num))
       _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0)]; ring
-      
   -- As it is Cauchy, the sequence `L0` converges, to a limit `f'` in `K`.
   obtain ⟨f', f'K, hf'⟩ : ∃ f' ∈ K, tendsto L0 at_top (𝓝 f') :=
     cauchySeq_tendsto_of_isComplete hK (fun e => (hn e (n e) (n e) le_rfl le_rfl).1) this
@@ -796,7 +786,6 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
         _ ≤ 4 * (1 / 2) ^ e * (y - x) :=
           (mul_le_mul_of_nonneg_left (le_of_lt hk) (mul_nonneg (by norm_num) (le_of_lt P)))
         _ = 4 * (1 / 2) ^ e * ‖y - x‖ := by rw [Real.norm_of_nonneg yzero.le]
-        
     calc
       ‖f y - f x - (y - x) • f'‖ =
           ‖f y - f x - (y - x) • L e (n e) m + (y - x) • (L e (n e) m - f')‖ :=
@@ -808,7 +797,6 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
       _ ≤ 16 * ‖y - x‖ * (ε / 16) :=
         (mul_le_mul_of_nonneg_left he.le (mul_nonneg (by norm_num) (norm_nonneg _)))
       _ = ε * ‖y - x‖ := by ring
-      
   rw [← this.deriv_within (uniqueDiffOn_Ici x x le_rfl)] at f'K 
   exact ⟨this.differentiable_within_at, f'K⟩
 #align right_deriv_measurable_aux.D_subset_differentiable_set RightDerivMeasurableAux.d_subset_differentiable_set

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -115,7 +115,7 @@ variable {f : E → F} (K : Set (E →L[𝕜] F))
 
 namespace FderivMeasurableAux
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » ball[metric.ball] x r') -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y z «expr ∈ » ball[metric.ball] x r') -/
 #print FDerivMeasurableAux.A /-
 /-- The set `A f L r ε` is the set of points `x` around which the function `f` is well approximated
 at scale `r` by the linear map `L`, up to an error `ε`. We tweak the definition to make sure that
@@ -501,7 +501,7 @@ variable {f : ℝ → F} (K : Set F)
 
 namespace RightDerivMeasurableAux
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » Icc[set.Icc] x «expr + »(x, r')) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y z «expr ∈ » Icc[set.Icc] x «expr + »(x, r')) -/
 #print RightDerivMeasurableAux.A /-
 /-- The set `A f L r ε` is the set of points `x` around which the function `f` is well approximated
 at scale `r` by the linear map `h ↦ h • L`, up to an error `ε`. We tweak the definition to

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

@@ -121,9 +121,9 @@ namespace FderivMeasurableAux
 at scale `r` by the linear map `L`, up to an error `ε`. We tweak the definition to make sure that
 this is an open set.-/
 def A (f : E → F) (L : E →L[𝕜] F) (r ε : ℝ) : Set E :=
-  { x |
+  {x |
     ∃ r' ∈ Ioc (r / 2) r,
-      ∀ (y) (_ : y ∈ ball x r') (z) (_ : z ∈ ball x r'), ‖f z - f y - L (z - y)‖ ≤ ε * r }
+      ∀ (y) (_ : y ∈ ball x r') (z) (_ : z ∈ ball x r'), ‖f z - f y - L (z - y)‖ ≤ ε * r}
 #align fderiv_measurable_aux.A FDerivMeasurableAux.A
 -/
 
@@ -230,7 +230,7 @@ theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
 #align fderiv_measurable_aux.norm_sub_le_of_mem_A FDerivMeasurableAux.norm_sub_le_of_mem_a
 
 /-- Easy inclusion: a differentiability point with derivative in `K` belongs to `D f K`. -/
-theorem differentiable_set_subset_d : { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } ⊆ D f K :=
+theorem differentiable_set_subset_d : {x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K} ⊆ D f K :=
   by
   intro x hx
   rw [D, mem_Inter]
@@ -248,7 +248,7 @@ theorem differentiable_set_subset_d : { x | DifferentiableAt 𝕜 f x ∧ fderiv
 #print FDerivMeasurableAux.d_subset_differentiable_set /-
 /-- Harder inclusion: at a point in `D f K`, the function `f` has a derivative, in `K`. -/
 theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete K) :
-    D f K ⊆ { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } :=
+    D f K ⊆ {x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K} :=
   by
   have P : ∀ {n : ℕ}, (0 : ℝ) < (1 / 2) ^ n := pow_pos (by norm_num)
   rcases NormedField.exists_one_lt_norm 𝕜 with ⟨c, hc⟩
@@ -414,7 +414,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
 -/
 
 theorem differentiable_set_eq_d (hK : IsComplete K) :
-    { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } = D f K :=
+    {x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K} = D f K :=
   Subset.antisymm (differentiable_set_subset_d _) (d_subset_differentiable_set hK)
 #align fderiv_measurable_aux.differentiable_set_eq_D FDerivMeasurableAux.differentiable_set_eq_d
 
@@ -430,7 +430,7 @@ variable (𝕜 f)
 /-- The set of differentiability points of a function, with derivative in a given complete set,
 is Borel-measurable. -/
 theorem measurableSet_of_differentiableAt_of_isComplete {K : Set (E →L[𝕜] F)} (hK : IsComplete K) :
-    MeasurableSet { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } := by
+    MeasurableSet {x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K} := by
   simp [differentiable_set_eq_D K hK, D, is_open_B.measurable_set, MeasurableSet.iInter,
     MeasurableSet.iUnion]
 #align measurable_set_of_differentiable_at_of_is_complete measurableSet_of_differentiableAt_of_isComplete
@@ -440,7 +440,7 @@ variable [CompleteSpace F]
 
 /-- The set of differentiability points of a function taking values in a complete space is
 Borel-measurable. -/
-theorem measurableSet_of_differentiableAt : MeasurableSet { x | DifferentiableAt 𝕜 f x } :=
+theorem measurableSet_of_differentiableAt : MeasurableSet {x | DifferentiableAt 𝕜 f x} :=
   by
   have : IsComplete (univ : Set (E →L[𝕜] F)) := complete_univ
   convert measurableSet_of_differentiableAt_of_isComplete 𝕜 f this
@@ -453,8 +453,8 @@ theorem measurable_fderiv : Measurable (fderiv 𝕜 f) :=
   refine' measurable_of_isClosed fun s hs => _
   have :
     fderiv 𝕜 f ⁻¹' s =
-      { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ s } ∪
-        { x | ¬DifferentiableAt 𝕜 f x } ∩ { x | (0 : E →L[𝕜] F) ∈ s } :=
+      {x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ s} ∪
+        {x | ¬DifferentiableAt 𝕜 f x} ∩ {x | (0 : E →L[𝕜] F) ∈ s} :=
     Set.ext fun x => mem_preimage.trans fderiv_mem_iff
   rw [this]
   exact
@@ -507,10 +507,10 @@ namespace RightDerivMeasurableAux
 at scale `r` by the linear map `h ↦ h • L`, up to an error `ε`. We tweak the definition to
 make sure that this is open on the right. -/
 def A (f : ℝ → F) (L : F) (r ε : ℝ) : Set ℝ :=
-  { x |
+  {x |
     ∃ r' ∈ Ioc (r / 2) r,
       ∀ (y) (_ : y ∈ Icc x (x + r')) (z) (_ : z ∈ Icc x (x + r')),
-        ‖f z - f y - (z - y) • L‖ ≤ ε * r }
+        ‖f z - f y - (z - y) • L‖ ≤ ε * r}
 #align right_deriv_measurable_aux.A RightDerivMeasurableAux.A
 -/
 
@@ -555,7 +555,7 @@ theorem b_mem_nhdsWithin_Ioi {K : Set F} {r s ε x : ℝ} (hx : x ∈ B f K r s
   by
   obtain ⟨L, LK, hL₁, hL₂⟩ : ∃ L : F, L ∈ K ∧ x ∈ A f L r ε ∧ x ∈ A f L s ε := by
     simpa only [B, mem_Union, mem_inter_iff, exists_prop] using hx
-  filter_upwards [A_mem_nhds_within_Ioi hL₁, A_mem_nhds_within_Ioi hL₂]with y hy₁ hy₂
+  filter_upwards [A_mem_nhds_within_Ioi hL₁, A_mem_nhds_within_Ioi hL₂] with y hy₁ hy₂
   simp only [B, mem_Union, mem_inter_iff, exists_prop]
   exact ⟨L, LK, hy₁, hy₂⟩
 #align right_deriv_measurable_aux.B_mem_nhds_within_Ioi RightDerivMeasurableAux.b_mem_nhdsWithin_Ioi
@@ -639,7 +639,7 @@ theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F}
 #print RightDerivMeasurableAux.differentiable_set_subset_d /-
 /-- Easy inclusion: a differentiability point with derivative in `K` belongs to `D f K`. -/
 theorem differentiable_set_subset_d :
-    { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } ⊆ D f K :=
+    {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K} ⊆ D f K :=
   by
   intro x hx
   rw [D, mem_Inter]
@@ -658,7 +658,7 @@ theorem differentiable_set_subset_d :
 #print RightDerivMeasurableAux.d_subset_differentiable_set /-
 /-- Harder inclusion: at a point in `D f K`, the function `f` has a derivative, in `K`. -/
 theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
-    D f K ⊆ { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } :=
+    D f K ⊆ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K} :=
   by
   have P : ∀ {n : ℕ}, (0 : ℝ) < (1 / 2) ^ n := pow_pos (by norm_num)
   intro x hx
@@ -759,7 +759,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     have xmem : x ∈ Ico x (x + (1 / 2) ^ (n e + 1)) := by
       simp only [one_div, left_mem_Ico, lt_add_iff_pos_right, inv_pos, pow_pos, zero_lt_bit0,
         zero_lt_one]
-    filter_upwards [Icc_mem_nhdsWithin_Ici xmem]with y hy
+    filter_upwards [Icc_mem_nhdsWithin_Ici xmem] with y hy
     -- We need to show that `f y - f x - f' (y - x)` is small. For this, we will work at scale
     -- `k` where `k` is chosen with `‖y - x‖ ∼ 2 ^ (-k)`.
     rcases eq_or_lt_of_le hy.1 with (rfl | xy)
@@ -816,7 +816,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
 
 #print RightDerivMeasurableAux.differentiable_set_eq_d /-
 theorem differentiable_set_eq_d (hK : IsComplete K) :
-    { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } = D f K :=
+    {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K} = D f K :=
   Subset.antisymm (differentiable_set_subset_d _) (d_subset_differentiable_set hK)
 #align right_deriv_measurable_aux.differentiable_set_eq_D RightDerivMeasurableAux.differentiable_set_eq_d
 -/
@@ -831,7 +831,7 @@ variable (f)
 /-- The set of right differentiability points of a function, with derivative in a given complete
 set, is Borel-measurable. -/
 theorem measurableSet_of_differentiableWithinAt_Ici_of_isComplete {K : Set F} (hK : IsComplete K) :
-    MeasurableSet { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } := by
+    MeasurableSet {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K} := by
   simp [differentiable_set_eq_D K hK, D, measurable_set_B, MeasurableSet.iInter,
     MeasurableSet.iUnion]
 #align measurable_set_of_differentiable_within_at_Ici_of_is_complete measurableSet_of_differentiableWithinAt_Ici_of_isComplete
@@ -843,7 +843,7 @@ variable [CompleteSpace F]
 /-- The set of right differentiability points of a function taking values in a complete space is
 Borel-measurable. -/
 theorem measurableSet_of_differentiableWithinAt_Ici :
-    MeasurableSet { x | DifferentiableWithinAt ℝ f (Ici x) x } :=
+    MeasurableSet {x | DifferentiableWithinAt ℝ f (Ici x) x} :=
   by
   have : IsComplete (univ : Set F) := complete_univ
   convert measurableSet_of_differentiableWithinAt_Ici_of_isComplete f this
@@ -859,8 +859,8 @@ theorem measurable_derivWithin_Ici [MeasurableSpace F] [BorelSpace F] :
   refine' measurable_of_isClosed fun s hs => _
   have :
     (fun x => derivWithin f (Ici x) x) ⁻¹' s =
-      { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ s } ∪
-        { x | ¬DifferentiableWithinAt ℝ f (Ici x) x } ∩ { x | (0 : F) ∈ s } :=
+      {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ s} ∪
+        {x | ¬DifferentiableWithinAt ℝ f (Ici x) x} ∩ {x | (0 : F) ∈ s} :=
     Set.ext fun x => mem_preimage.trans derivWithin_mem_iff
   rw [this]
   exact
@@ -894,7 +894,7 @@ theorem aestronglyMeasurable_derivWithin_Ici [SecondCountableTopology F] (μ : M
 /-- The set of right differentiability points of a function taking values in a complete space is
 Borel-measurable. -/
 theorem measurableSet_of_differentiableWithinAt_Ioi :
-    MeasurableSet { x | DifferentiableWithinAt ℝ f (Ioi x) x } := by
+    MeasurableSet {x | DifferentiableWithinAt ℝ f (Ioi x) x} := by
   simpa [differentiableWithinAt_Ioi_iff_Ici] using measurableSet_of_differentiableWithinAt_Ici f
 #align measurable_set_of_differentiable_within_at_Ioi measurableSet_of_differentiableWithinAt_Ioi
 -/

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

@@ -182,7 +182,7 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (fderiv 𝕜 f x) r ε :=
   by
   have := hx.has_fderiv_at
-  simp only [HasFDerivAt, HasFDerivAtFilter, is_o_iff] at this
+  simp only [HasFDerivAt, HasFDerivAtFilter, is_o_iff] at this 
   rcases eventually_nhds_iff_ball.1 (this (half_pos hε)) with ⟨R, R_pos, hR⟩
   refine' ⟨R, R_pos, fun r hr => _⟩
   have : r ∈ Ioc (r / 2) r := ⟨half_lt_self hr.1, le_rfl⟩
@@ -210,7 +210,7 @@ theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
     mul_nonneg (mul_nonneg (by norm_num : (0 : ℝ) ≤ 4) (norm_nonneg _)) hε.le
   refine' op_norm_le_of_shell (half_pos hr) this hc _
   intro y ley ylt
-  rw [div_div, div_le_iff' (mul_pos (by norm_num : (0 : ℝ) < 2) (zero_lt_one.trans hc))] at ley
+  rw [div_div, div_le_iff' (mul_pos (by norm_num : (0 : ℝ) < 2) (zero_lt_one.trans hc))] at ley 
   calc
     ‖(L₁ - L₂) y‖ = ‖f (x + y) - f x - L₂ (x + y - x) - (f (x + y) - f x - L₁ (x + y - x))‖ := by
       simp
@@ -266,7 +266,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     have := mem_Inter.1 hx e
     rcases mem_Union.1 this with ⟨n, hn⟩
     refine' ⟨n, fun p q hp hq => _⟩
-    simp only [mem_Inter, ge_iff_le] at hn
+    simp only [mem_Inter, ge_iff_le] at hn 
     rcases mem_Union.1 (hn p hp q hq) with ⟨L, hL⟩
     exact ⟨L, mem_Union.1 hL⟩
   /- Recast the assumptions: for each `e`, there exist `n e` and linear maps `L e p q` in `K`
@@ -329,7 +329,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       ‖L0 e - L0 e'‖ ≤ 12 * ‖c‖ * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
       _ < 12 * ‖c‖ * (ε / (12 * ‖c‖)) :=
         (mul_lt_mul' le_rfl he (le_of_lt P) (mul_pos (by norm_num) cpos))
-      _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0), ne_of_gt cpos] ; ring
+      _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0), ne_of_gt cpos]; ring
       
   -- As it is Cauchy, the sequence `L0` converges, to a limit `f'` in `K`.
   obtain ⟨f', f'K, hf'⟩ : ∃ f' ∈ K, tendsto L0 at_top (𝓝 f') :=
@@ -370,12 +370,12 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     have k_gt : n e < k :=
       by
       have : ((1 : ℝ) / 2) ^ (k + 1) < (1 / 2) ^ (n e + 1) := lt_trans hk y_lt
-      rw [pow_lt_pow_iff_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this
+      rw [pow_lt_pow_iff_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this 
       linarith
     set m := k - 1 with hl
     have m_ge : n e ≤ m := Nat.le_pred_of_lt k_gt
     have km : k = m + 1 := (Nat.succ_pred_eq_of_pos (lt_of_le_of_lt (zero_le _) k_gt)).symm
-    rw [km] at hk h'k
+    rw [km] at hk h'k 
     -- `f` is well approximated by `L e (n e) k` at the relevant scale
     -- (in fact, we use `m = k - 1` instead of `k` because of the precise definition of `A`).
     have J1 : ‖f (x + y) - f x - L e (n e) m (x + y - x)‖ ≤ (1 / 2) ^ e * (1 / 2) ^ m :=
@@ -406,9 +406,9 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
         (mul_le_mul_of_nonneg_left he.le
           (mul_nonneg (add_nonneg (by norm_num) (mul_nonneg (by norm_num) (norm_nonneg _)))
             (norm_nonneg _)))
-      _ = ε * ‖y‖ := by field_simp [ne_of_gt Pos] ; ring
+      _ = ε * ‖y‖ := by field_simp [ne_of_gt Pos]; ring
       
-  rw [← this.fderiv] at f'K
+  rw [← this.fderiv] at f'K 
   exact ⟨this.differentiable_at, f'K⟩
 #align fderiv_measurable_aux.D_subset_differentiable_set FDerivMeasurableAux.d_subset_differentiable_set
 -/
@@ -587,7 +587,7 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (derivWithin f (Ici x) x) r ε :=
   by
   have := hx.has_deriv_within_at
-  simp_rw [hasDerivWithinAt_iff_isLittleO, is_o_iff] at this
+  simp_rw [hasDerivWithinAt_iff_isLittleO, is_o_iff] at this 
   rcases mem_nhdsWithin_Ici_iff_exists_Ico_subset.1 (this (half_pos hε)) with ⟨m, xm, hm⟩
   refine' ⟨m - x, by linarith [show x < m from xm], fun r hr => _⟩
   have : r ∈ Ioc (r / 2) r := ⟨half_lt_self hr.1, le_rfl⟩
@@ -618,7 +618,7 @@ theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F}
     (h₂ : x ∈ A f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ε :=
   by
   suffices H : ‖(r / 2) • (L₁ - L₂)‖ ≤ r / 2 * (4 * ε)
-  · rwa [norm_smul, Real.norm_of_nonneg (half_pos hr).le, mul_le_mul_left (half_pos hr)] at H
+  · rwa [norm_smul, Real.norm_of_nonneg (half_pos hr).le, mul_le_mul_left (half_pos hr)] at H 
   calc
     ‖(r / 2) • (L₁ - L₂)‖ =
         ‖f (x + r / 2) - f x - (x + r / 2 - x) • L₂ -
@@ -674,7 +674,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     have := mem_Inter.1 hx e
     rcases mem_Union.1 this with ⟨n, hn⟩
     refine' ⟨n, fun p q hp hq => _⟩
-    simp only [mem_Inter, ge_iff_le] at hn
+    simp only [mem_Inter, ge_iff_le] at hn 
     rcases mem_Union.1 (hn p hp q hq) with ⟨L, hL⟩
     exact ⟨L, mem_Union.1 hL⟩
   /- Recast the assumptions: for each `e`, there exist `n e` and linear maps `L e p q` in `K`
@@ -734,7 +734,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     calc
       ‖L0 e - L0 e'‖ ≤ 12 * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
       _ < 12 * (ε / 12) := (mul_lt_mul' le_rfl he (le_of_lt P) (by norm_num))
-      _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0)] ; ring
+      _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0)]; ring
       
   -- As it is Cauchy, the sequence `L0` converges, to a limit `f'` in `K`.
   obtain ⟨f', f'K, hf'⟩ : ∃ f' ∈ K, tendsto L0 at_top (𝓝 f') :=
@@ -775,12 +775,12 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     have k_gt : n e < k :=
       by
       have : ((1 : ℝ) / 2) ^ (k + 1) < (1 / 2) ^ (n e + 1) := lt_of_lt_of_le hk y_le
-      rw [pow_lt_pow_iff_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this
+      rw [pow_lt_pow_iff_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this 
       linarith
     set m := k - 1 with hl
     have m_ge : n e ≤ m := Nat.le_pred_of_lt k_gt
     have km : k = m + 1 := (Nat.succ_pred_eq_of_pos (lt_of_le_of_lt (zero_le _) k_gt)).symm
-    rw [km] at hk h'k
+    rw [km] at hk h'k 
     -- `f` is well approximated by `L e (n e) k` at the relevant scale
     -- (in fact, we use `m = k - 1` instead of `k` because of the precise definition of `A`).
     have J : ‖f y - f x - (y - x) • L e (n e) m‖ ≤ 4 * (1 / 2) ^ e * ‖y - x‖ :=
@@ -790,7 +790,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
           apply le_of_mem_A (hn e (n e) m le_rfl m_ge).2.2
           · simp only [one_div, inv_pow, left_mem_Icc, le_add_iff_nonneg_right]
             exact div_nonneg (inv_nonneg.2 (pow_nonneg zero_le_two _)) zero_le_two
-          · simp only [pow_add, tsub_le_iff_left] at h'k
+          · simp only [pow_add, tsub_le_iff_left] at h'k 
             simpa only [hy.1, mem_Icc, true_and_iff, one_div, pow_one] using h'k
         _ = 4 * (1 / 2) ^ e * (1 / 2) ^ (m + 2) := by field_simp; ring
         _ ≤ 4 * (1 / 2) ^ e * (y - x) :=
@@ -809,7 +809,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
         (mul_le_mul_of_nonneg_left he.le (mul_nonneg (by norm_num) (norm_nonneg _)))
       _ = ε * ‖y - x‖ := by ring
       
-  rw [← this.deriv_within (uniqueDiffOn_Ici x x le_rfl)] at f'K
+  rw [← this.deriv_within (uniqueDiffOn_Ici x x le_rfl)] at f'K 
   exact ⟨this.differentiable_within_at, f'K⟩
 #align right_deriv_measurable_aux.D_subset_differentiable_set RightDerivMeasurableAux.d_subset_differentiable_set
 -/

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.calculus.fderiv_measurable
-! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
+! leanprover-community/mathlib commit f60c6087a7275b72d5db3c5a1d0e19e35a429c0a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.MeasureTheory.Function.StronglyMeasurable.Basic
 /-!
 # Derivative is measurable
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove that the derivative of any function with complete codomain is a measurable
 function. Namely, we prove:
 
@@ -113,30 +116,36 @@ variable {f : E → F} (K : Set (E →L[𝕜] F))
 namespace FderivMeasurableAux
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » ball[metric.ball] x r') -/
+#print FDerivMeasurableAux.A /-
 /-- The set `A f L r ε` is the set of points `x` around which the function `f` is well approximated
 at scale `r` by the linear map `L`, up to an error `ε`. We tweak the definition to make sure that
 this is an open set.-/
-def a (f : E → F) (L : E →L[𝕜] F) (r ε : ℝ) : Set E :=
+def A (f : E → F) (L : E →L[𝕜] F) (r ε : ℝ) : Set E :=
   { x |
     ∃ r' ∈ Ioc (r / 2) r,
       ∀ (y) (_ : y ∈ ball x r') (z) (_ : z ∈ ball x r'), ‖f z - f y - L (z - y)‖ ≤ ε * r }
-#align fderiv_measurable_aux.A FderivMeasurableAux.a
+#align fderiv_measurable_aux.A FDerivMeasurableAux.A
+-/
 
+#print FDerivMeasurableAux.B /-
 /-- The set `B f K r s ε` is the set of points `x` around which there exists a continuous linear map
 `L` belonging to `K` (a given set of continuous linear maps) that approximates well the
 function `f` (up to an error `ε`), simultaneously at scales `r` and `s`. -/
-def b (f : E → F) (K : Set (E →L[𝕜] F)) (r s ε : ℝ) : Set E :=
-  ⋃ L ∈ K, a f L r ε ∩ a f L s ε
-#align fderiv_measurable_aux.B FderivMeasurableAux.b
+def B (f : E → F) (K : Set (E →L[𝕜] F)) (r s ε : ℝ) : Set E :=
+  ⋃ L ∈ K, A f L r ε ∩ A f L s ε
+#align fderiv_measurable_aux.B FDerivMeasurableAux.B
+-/
 
+#print FDerivMeasurableAux.D /-
 /-- The set `D f K` is a complicated set constructed using countable intersections and unions. Its
 main use is that, when `K` is complete, it is exactly the set of points where `f` is differentiable,
 with a derivative in `K`. -/
-def d (f : E → F) (K : Set (E →L[𝕜] F)) : Set E :=
-  ⋂ e : ℕ, ⋃ n : ℕ, ⋂ (p ≥ n) (q ≥ n), b f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ e)
-#align fderiv_measurable_aux.D FderivMeasurableAux.d
+def D (f : E → F) (K : Set (E →L[𝕜] F)) : Set E :=
+  ⋂ e : ℕ, ⋃ n : ℕ, ⋂ (p ≥ n) (q ≥ n), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ e)
+#align fderiv_measurable_aux.D FDerivMeasurableAux.D
+-/
 
-theorem isOpen_a (L : E →L[𝕜] F) (r ε : ℝ) : IsOpen (a f L r ε) :=
+theorem isOpen_a (L : E →L[𝕜] F) (r ε : ℝ) : IsOpen (A f L r ε) :=
   by
   rw [Metric.isOpen_iff]
   rintro x ⟨r', r'_mem, hr'⟩
@@ -146,29 +155,31 @@ theorem isOpen_a (L : E →L[𝕜] F) (r ε : ℝ) : IsOpen (a f L r ε) :=
   have B : ball x' s ⊆ ball x r' := ball_subset (le_of_lt hx')
   intro y hy z hz
   exact hr' y (B hy) z (B hz)
-#align fderiv_measurable_aux.is_open_A FderivMeasurableAux.isOpen_a
+#align fderiv_measurable_aux.is_open_A FDerivMeasurableAux.isOpen_a
 
-theorem isOpen_b {K : Set (E →L[𝕜] F)} {r s ε : ℝ} : IsOpen (b f K r s ε) := by
+#print FDerivMeasurableAux.isOpen_b /-
+theorem isOpen_b {K : Set (E →L[𝕜] F)} {r s ε : ℝ} : IsOpen (B f K r s ε) := by
   simp [B, isOpen_iUnion, IsOpen.inter, is_open_A]
-#align fderiv_measurable_aux.is_open_B FderivMeasurableAux.isOpen_b
+#align fderiv_measurable_aux.is_open_B FDerivMeasurableAux.isOpen_b
+-/
 
-theorem a_mono (L : E →L[𝕜] F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : a f L r ε ⊆ a f L r δ :=
+theorem a_mono (L : E →L[𝕜] F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : A f L r ε ⊆ A f L r δ :=
   by
   rintro x ⟨r', r'r, hr'⟩
   refine' ⟨r', r'r, fun y hy z hz => (hr' y hy z hz).trans (mul_le_mul_of_nonneg_right h _)⟩
   linarith [mem_ball.1 hy, r'r.2, @dist_nonneg _ _ y x]
-#align fderiv_measurable_aux.A_mono FderivMeasurableAux.a_mono
+#align fderiv_measurable_aux.A_mono FDerivMeasurableAux.a_mono
 
-theorem le_of_mem_a {r ε : ℝ} {L : E →L[𝕜] F} {x : E} (hx : x ∈ a f L r ε) {y z : E}
+theorem le_of_mem_a {r ε : ℝ} {L : E →L[𝕜] F} {x : E} (hx : x ∈ A f L r ε) {y z : E}
     (hy : y ∈ closedBall x (r / 2)) (hz : z ∈ closedBall x (r / 2)) :
     ‖f z - f y - L (z - y)‖ ≤ ε * r :=
   by
   rcases hx with ⟨r', r'mem, hr'⟩
   exact hr' _ ((mem_closed_ball.1 hy).trans_lt r'mem.1) _ ((mem_closed_ball.1 hz).trans_lt r'mem.1)
-#align fderiv_measurable_aux.le_of_mem_A FderivMeasurableAux.le_of_mem_a
+#align fderiv_measurable_aux.le_of_mem_A FDerivMeasurableAux.le_of_mem_a
 
 theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : DifferentiableAt 𝕜 f x) :
-    ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ a f (fderiv 𝕜 f x) r ε :=
+    ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (fderiv 𝕜 f x) r ε :=
   by
   have := hx.has_fderiv_at
   simp only [HasFDerivAt, HasFDerivAtFilter, is_o_iff] at this
@@ -190,10 +201,10 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
         (mul_le_mul_of_nonneg_left (le_of_lt (mem_ball_iff_norm.1 hy)) (le_of_lt (half_pos hε))))
     _ = ε * r := by ring
     
-#align fderiv_measurable_aux.mem_A_of_differentiable FderivMeasurableAux.mem_a_of_differentiable
+#align fderiv_measurable_aux.mem_A_of_differentiable FDerivMeasurableAux.mem_a_of_differentiable
 
 theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0 < ε) (hr : 0 < r) {x : E}
-    {L₁ L₂ : E →L[𝕜] F} (h₁ : x ∈ a f L₁ r ε) (h₂ : x ∈ a f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ‖c‖ * ε :=
+    {L₁ L₂ : E →L[𝕜] F} (h₁ : x ∈ A f L₁ r ε) (h₂ : x ∈ A f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ‖c‖ * ε :=
   by
   have : 0 ≤ 4 * ‖c‖ * ε :=
     mul_nonneg (mul_nonneg (by norm_num : (0 : ℝ) ≤ 4) (norm_nonneg _)) hε.le
@@ -216,10 +227,10 @@ theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
     _ ≤ 2 * ε * (2 * ‖c‖ * ‖y‖) := (mul_le_mul_of_nonneg_left ley (mul_nonneg (by norm_num) hε.le))
     _ = 4 * ‖c‖ * ε * ‖y‖ := by ring
     
-#align fderiv_measurable_aux.norm_sub_le_of_mem_A FderivMeasurableAux.norm_sub_le_of_mem_a
+#align fderiv_measurable_aux.norm_sub_le_of_mem_A FDerivMeasurableAux.norm_sub_le_of_mem_a
 
 /-- Easy inclusion: a differentiability point with derivative in `K` belongs to `D f K`. -/
-theorem differentiable_set_subset_d : { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } ⊆ d f K :=
+theorem differentiable_set_subset_d : { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } ⊆ D f K :=
   by
   intro x hx
   rw [D, mem_Inter]
@@ -232,11 +243,12 @@ theorem differentiable_set_subset_d : { x | DifferentiableAt 𝕜 f x ∧ fderiv
   refine' ⟨n, fun p hp q hq => ⟨fderiv 𝕜 f x, hx.2, ⟨_, _⟩⟩⟩ <;>
     · refine' hR _ ⟨pow_pos (by norm_num) _, lt_of_le_of_lt _ hn⟩
       exact pow_le_pow_of_le_one (by norm_num) (by norm_num) (by assumption)
-#align fderiv_measurable_aux.differentiable_set_subset_D FderivMeasurableAux.differentiable_set_subset_d
+#align fderiv_measurable_aux.differentiable_set_subset_D FDerivMeasurableAux.differentiable_set_subset_d
 
+#print FDerivMeasurableAux.d_subset_differentiable_set /-
 /-- Harder inclusion: at a point in `D f K`, the function `f` has a derivative, in `K`. -/
 theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete K) :
-    d f K ⊆ { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } :=
+    D f K ⊆ { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } :=
   by
   have P : ∀ {n : ℕ}, (0 : ℝ) < (1 / 2) ^ n := pow_pos (by norm_num)
   rcases NormedField.exists_one_lt_norm 𝕜 with ⟨c, hc⟩
@@ -398,12 +410,13 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       
   rw [← this.fderiv] at f'K
   exact ⟨this.differentiable_at, f'K⟩
-#align fderiv_measurable_aux.D_subset_differentiable_set FderivMeasurableAux.d_subset_differentiable_set
+#align fderiv_measurable_aux.D_subset_differentiable_set FDerivMeasurableAux.d_subset_differentiable_set
+-/
 
 theorem differentiable_set_eq_d (hK : IsComplete K) :
-    { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } = d f K :=
+    { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } = D f K :=
   Subset.antisymm (differentiable_set_subset_d _) (d_subset_differentiable_set hK)
-#align fderiv_measurable_aux.differentiable_set_eq_D FderivMeasurableAux.differentiable_set_eq_d
+#align fderiv_measurable_aux.differentiable_set_eq_D FDerivMeasurableAux.differentiable_set_eq_d
 
 end FderivMeasurableAux
 
@@ -413,6 +426,7 @@ variable [MeasurableSpace E] [OpensMeasurableSpace E]
 
 variable (𝕜 f)
 
+#print measurableSet_of_differentiableAt_of_isComplete /-
 /-- The set of differentiability points of a function, with derivative in a given complete set,
 is Borel-measurable. -/
 theorem measurableSet_of_differentiableAt_of_isComplete {K : Set (E →L[𝕜] F)} (hK : IsComplete K) :
@@ -420,6 +434,7 @@ theorem measurableSet_of_differentiableAt_of_isComplete {K : Set (E →L[𝕜] F
   simp [differentiable_set_eq_D K hK, D, is_open_B.measurable_set, MeasurableSet.iInter,
     MeasurableSet.iUnion]
 #align measurable_set_of_differentiable_at_of_is_complete measurableSet_of_differentiableAt_of_isComplete
+-/
 
 variable [CompleteSpace F]
 
@@ -466,15 +481,15 @@ theorem stronglyMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 
   exact (measurable_deriv f).StronglyMeasurable
 #align strongly_measurable_deriv stronglyMeasurable_deriv
 
-theorem aEMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜] [MeasurableSpace F]
+theorem aemeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜] [MeasurableSpace F]
     [BorelSpace F] (f : 𝕜 → F) (μ : Measure 𝕜) : AEMeasurable (deriv f) μ :=
   (measurable_deriv f).AEMeasurable
-#align ae_measurable_deriv aEMeasurable_deriv
+#align ae_measurable_deriv aemeasurable_deriv
 
-theorem aEStronglyMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜]
+theorem aestronglyMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜]
     [SecondCountableTopology F] (f : 𝕜 → F) (μ : Measure 𝕜) : AEStronglyMeasurable (deriv f) μ :=
   (stronglyMeasurable_deriv f).AEStronglyMeasurable
-#align ae_strongly_measurable_deriv aEStronglyMeasurable_deriv
+#align ae_strongly_measurable_deriv aestronglyMeasurable_deriv
 
 end fderiv
 
@@ -487,31 +502,38 @@ variable {f : ℝ → F} (K : Set F)
 namespace RightDerivMeasurableAux
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » Icc[set.Icc] x «expr + »(x, r')) -/
+#print RightDerivMeasurableAux.A /-
 /-- The set `A f L r ε` is the set of points `x` around which the function `f` is well approximated
 at scale `r` by the linear map `h ↦ h • L`, up to an error `ε`. We tweak the definition to
 make sure that this is open on the right. -/
-def a (f : ℝ → F) (L : F) (r ε : ℝ) : Set ℝ :=
+def A (f : ℝ → F) (L : F) (r ε : ℝ) : Set ℝ :=
   { x |
     ∃ r' ∈ Ioc (r / 2) r,
       ∀ (y) (_ : y ∈ Icc x (x + r')) (z) (_ : z ∈ Icc x (x + r')),
         ‖f z - f y - (z - y) • L‖ ≤ ε * r }
-#align right_deriv_measurable_aux.A RightDerivMeasurableAux.a
+#align right_deriv_measurable_aux.A RightDerivMeasurableAux.A
+-/
 
+#print RightDerivMeasurableAux.B /-
 /-- The set `B f K r s ε` is the set of points `x` around which there exists a vector
 `L` belonging to `K` (a given set of vectors) such that `h • L` approximates well `f (x + h)`
 (up to an error `ε`), simultaneously at scales `r` and `s`. -/
-def b (f : ℝ → F) (K : Set F) (r s ε : ℝ) : Set ℝ :=
-  ⋃ L ∈ K, a f L r ε ∩ a f L s ε
-#align right_deriv_measurable_aux.B RightDerivMeasurableAux.b
+def B (f : ℝ → F) (K : Set F) (r s ε : ℝ) : Set ℝ :=
+  ⋃ L ∈ K, A f L r ε ∩ A f L s ε
+#align right_deriv_measurable_aux.B RightDerivMeasurableAux.B
+-/
 
+#print RightDerivMeasurableAux.D /-
 /-- The set `D f K` is a complicated set constructed using countable intersections and unions. Its
 main use is that, when `K` is complete, it is exactly the set of points where `f` is differentiable,
 with a derivative in `K`. -/
-def d (f : ℝ → F) (K : Set F) : Set ℝ :=
-  ⋂ e : ℕ, ⋃ n : ℕ, ⋂ (p ≥ n) (q ≥ n), b f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ e)
-#align right_deriv_measurable_aux.D RightDerivMeasurableAux.d
+def D (f : ℝ → F) (K : Set F) : Set ℝ :=
+  ⋂ e : ℕ, ⋃ n : ℕ, ⋂ (p ≥ n) (q ≥ n), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ e)
+#align right_deriv_measurable_aux.D RightDerivMeasurableAux.D
+-/
 
-theorem a_mem_nhdsWithin_Ioi {L : F} {r ε x : ℝ} (hx : x ∈ a f L r ε) : a f L r ε ∈ 𝓝[>] x :=
+#print RightDerivMeasurableAux.a_mem_nhdsWithin_Ioi /-
+theorem a_mem_nhdsWithin_Ioi {L : F} {r ε x : ℝ} (hx : x ∈ A f L r ε) : A f L r ε ∈ 𝓝[>] x :=
   by
   rcases hx with ⟨r', rr', hr'⟩
   rw [mem_nhdsWithin_Ioi_iff_exists_Ioo_subset]
@@ -525,9 +547,11 @@ theorem a_mem_nhdsWithin_Ioi {L : F} {r ε x : ℝ} (hx : x ∈ a f L r ε) : a
   intro y hy z hz
   exact hr' y (A hy) z (A hz)
 #align right_deriv_measurable_aux.A_mem_nhds_within_Ioi RightDerivMeasurableAux.a_mem_nhdsWithin_Ioi
+-/
 
-theorem b_mem_nhdsWithin_Ioi {K : Set F} {r s ε x : ℝ} (hx : x ∈ b f K r s ε) :
-    b f K r s ε ∈ 𝓝[>] x :=
+#print RightDerivMeasurableAux.b_mem_nhdsWithin_Ioi /-
+theorem b_mem_nhdsWithin_Ioi {K : Set F} {r s ε x : ℝ} (hx : x ∈ B f K r s ε) :
+    B f K r s ε ∈ 𝓝[>] x :=
   by
   obtain ⟨L, LK, hL₁, hL₂⟩ : ∃ L : F, L ∈ K ∧ x ∈ A f L r ε ∧ x ∈ A f L s ε := by
     simpa only [B, mem_Union, mem_inter_iff, exists_prop] using hx
@@ -535,19 +559,22 @@ theorem b_mem_nhdsWithin_Ioi {K : Set F} {r s ε x : ℝ} (hx : x ∈ b f K r s
   simp only [B, mem_Union, mem_inter_iff, exists_prop]
   exact ⟨L, LK, hy₁, hy₂⟩
 #align right_deriv_measurable_aux.B_mem_nhds_within_Ioi RightDerivMeasurableAux.b_mem_nhdsWithin_Ioi
+-/
 
-theorem measurableSet_b {K : Set F} {r s ε : ℝ} : MeasurableSet (b f K r s ε) :=
+#print RightDerivMeasurableAux.measurableSet_b /-
+theorem measurableSet_b {K : Set F} {r s ε : ℝ} : MeasurableSet (B f K r s ε) :=
   measurableSet_of_mem_nhdsWithin_Ioi fun x hx => b_mem_nhdsWithin_Ioi hx
 #align right_deriv_measurable_aux.measurable_set_B RightDerivMeasurableAux.measurableSet_b
+-/
 
-theorem a_mono (L : F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : a f L r ε ⊆ a f L r δ :=
+theorem a_mono (L : F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : A f L r ε ⊆ A f L r δ :=
   by
   rintro x ⟨r', r'r, hr'⟩
   refine' ⟨r', r'r, fun y hy z hz => (hr' y hy z hz).trans (mul_le_mul_of_nonneg_right h _)⟩
   linarith [hy.1, hy.2, r'r.2]
 #align right_deriv_measurable_aux.A_mono RightDerivMeasurableAux.a_mono
 
-theorem le_of_mem_a {r ε : ℝ} {L : F} {x : ℝ} (hx : x ∈ a f L r ε) {y z : ℝ}
+theorem le_of_mem_a {r ε : ℝ} {L : F} {x : ℝ} (hx : x ∈ A f L r ε) {y z : ℝ}
     (hy : y ∈ Icc x (x + r / 2)) (hz : z ∈ Icc x (x + r / 2)) : ‖f z - f y - (z - y) • L‖ ≤ ε * r :=
   by
   rcases hx with ⟨r', r'mem, hr'⟩
@@ -557,7 +584,7 @@ theorem le_of_mem_a {r ε : ℝ} {L : F} {x : ℝ} (hx : x ∈ a f L r ε) {y z
 
 theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
     (hx : DifferentiableWithinAt ℝ f (Ici x) x) :
-    ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ a f (derivWithin f (Ici x) x) r ε :=
+    ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (derivWithin f (Ici x) x) r ε :=
   by
   have := hx.has_deriv_within_at
   simp_rw [hasDerivWithinAt_iff_isLittleO, is_o_iff] at this
@@ -587,8 +614,8 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
     
 #align right_deriv_measurable_aux.mem_A_of_differentiable RightDerivMeasurableAux.mem_a_of_differentiable
 
-theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F} (h₁ : x ∈ a f L₁ r ε)
-    (h₂ : x ∈ a f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ε :=
+theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F} (h₁ : x ∈ A f L₁ r ε)
+    (h₂ : x ∈ A f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ε :=
   by
   suffices H : ‖(r / 2) • (L₁ - L₂)‖ ≤ r / 2 * (4 * ε)
   · rwa [norm_smul, Real.norm_of_nonneg (half_pos hr).le, mul_le_mul_left (half_pos hr)] at H
@@ -609,9 +636,10 @@ theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F}
     
 #align right_deriv_measurable_aux.norm_sub_le_of_mem_A RightDerivMeasurableAux.norm_sub_le_of_mem_a
 
+#print RightDerivMeasurableAux.differentiable_set_subset_d /-
 /-- Easy inclusion: a differentiability point with derivative in `K` belongs to `D f K`. -/
 theorem differentiable_set_subset_d :
-    { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } ⊆ d f K :=
+    { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } ⊆ D f K :=
   by
   intro x hx
   rw [D, mem_Inter]
@@ -625,10 +653,12 @@ theorem differentiable_set_subset_d :
     · refine' hR _ ⟨pow_pos (by norm_num) _, lt_of_le_of_lt _ hn⟩
       exact pow_le_pow_of_le_one (by norm_num) (by norm_num) (by assumption)
 #align right_deriv_measurable_aux.differentiable_set_subset_D RightDerivMeasurableAux.differentiable_set_subset_d
+-/
 
+#print RightDerivMeasurableAux.d_subset_differentiable_set /-
 /-- Harder inclusion: at a point in `D f K`, the function `f` has a derivative, in `K`. -/
 theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
-    d f K ⊆ { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } :=
+    D f K ⊆ { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } :=
   by
   have P : ∀ {n : ℕ}, (0 : ℝ) < (1 / 2) ^ n := pow_pos (by norm_num)
   intro x hx
@@ -782,11 +812,14 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
   rw [← this.deriv_within (uniqueDiffOn_Ici x x le_rfl)] at f'K
   exact ⟨this.differentiable_within_at, f'K⟩
 #align right_deriv_measurable_aux.D_subset_differentiable_set RightDerivMeasurableAux.d_subset_differentiable_set
+-/
 
+#print RightDerivMeasurableAux.differentiable_set_eq_d /-
 theorem differentiable_set_eq_d (hK : IsComplete K) :
-    { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } = d f K :=
+    { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } = D f K :=
   Subset.antisymm (differentiable_set_subset_d _) (d_subset_differentiable_set hK)
 #align right_deriv_measurable_aux.differentiable_set_eq_D RightDerivMeasurableAux.differentiable_set_eq_d
+-/
 
 end RightDerivMeasurableAux
 
@@ -794,6 +827,7 @@ open RightDerivMeasurableAux
 
 variable (f)
 
+#print measurableSet_of_differentiableWithinAt_Ici_of_isComplete /-
 /-- The set of right differentiability points of a function, with derivative in a given complete
 set, is Borel-measurable. -/
 theorem measurableSet_of_differentiableWithinAt_Ici_of_isComplete {K : Set F} (hK : IsComplete K) :
@@ -801,9 +835,11 @@ theorem measurableSet_of_differentiableWithinAt_Ici_of_isComplete {K : Set F} (h
   simp [differentiable_set_eq_D K hK, D, measurable_set_B, MeasurableSet.iInter,
     MeasurableSet.iUnion]
 #align measurable_set_of_differentiable_within_at_Ici_of_is_complete measurableSet_of_differentiableWithinAt_Ici_of_isComplete
+-/
 
 variable [CompleteSpace F]
 
+#print measurableSet_of_differentiableWithinAt_Ici /-
 /-- The set of right differentiability points of a function taking values in a complete space is
 Borel-measurable. -/
 theorem measurableSet_of_differentiableWithinAt_Ici :
@@ -813,7 +849,9 @@ theorem measurableSet_of_differentiableWithinAt_Ici :
   convert measurableSet_of_differentiableWithinAt_Ici_of_isComplete f this
   simp
 #align measurable_set_of_differentiable_within_at_Ici measurableSet_of_differentiableWithinAt_Ici
+-/
 
+#print measurable_derivWithin_Ici /-
 @[measurability]
 theorem measurable_derivWithin_Ici [MeasurableSpace F] [BorelSpace F] :
     Measurable fun x => derivWithin f (Ici x) x :=
@@ -829,49 +867,66 @@ theorem measurable_derivWithin_Ici [MeasurableSpace F] [BorelSpace F] :
     (measurableSet_of_differentiableWithinAt_Ici_of_isComplete _ hs.is_complete).union
       ((measurableSet_of_differentiableWithinAt_Ici _).compl.inter (MeasurableSet.const _))
 #align measurable_deriv_within_Ici measurable_derivWithin_Ici
+-/
 
+#print stronglyMeasurable_derivWithin_Ici /-
 theorem stronglyMeasurable_derivWithin_Ici [SecondCountableTopology F] :
     StronglyMeasurable fun x => derivWithin f (Ici x) x := by borelize F;
   exact (measurable_derivWithin_Ici f).StronglyMeasurable
 #align strongly_measurable_deriv_within_Ici stronglyMeasurable_derivWithin_Ici
+-/
 
-theorem aEMeasurable_derivWithin_Ici [MeasurableSpace F] [BorelSpace F] (μ : Measure ℝ) :
+#print aemeasurable_derivWithin_Ici /-
+theorem aemeasurable_derivWithin_Ici [MeasurableSpace F] [BorelSpace F] (μ : Measure ℝ) :
     AEMeasurable (fun x => derivWithin f (Ici x) x) μ :=
   (measurable_derivWithin_Ici f).AEMeasurable
-#align ae_measurable_deriv_within_Ici aEMeasurable_derivWithin_Ici
+#align ae_measurable_deriv_within_Ici aemeasurable_derivWithin_Ici
+-/
 
-theorem aEStronglyMeasurable_derivWithin_Ici [SecondCountableTopology F] (μ : Measure ℝ) :
+#print aestronglyMeasurable_derivWithin_Ici /-
+theorem aestronglyMeasurable_derivWithin_Ici [SecondCountableTopology F] (μ : Measure ℝ) :
     AEStronglyMeasurable (fun x => derivWithin f (Ici x) x) μ :=
   (stronglyMeasurable_derivWithin_Ici f).AEStronglyMeasurable
-#align ae_strongly_measurable_deriv_within_Ici aEStronglyMeasurable_derivWithin_Ici
+#align ae_strongly_measurable_deriv_within_Ici aestronglyMeasurable_derivWithin_Ici
+-/
 
+#print measurableSet_of_differentiableWithinAt_Ioi /-
 /-- The set of right differentiability points of a function taking values in a complete space is
 Borel-measurable. -/
 theorem measurableSet_of_differentiableWithinAt_Ioi :
     MeasurableSet { x | DifferentiableWithinAt ℝ f (Ioi x) x } := by
   simpa [differentiableWithinAt_Ioi_iff_Ici] using measurableSet_of_differentiableWithinAt_Ici f
 #align measurable_set_of_differentiable_within_at_Ioi measurableSet_of_differentiableWithinAt_Ioi
+-/
 
+#print measurable_derivWithin_Ioi /-
 @[measurability]
 theorem measurable_derivWithin_Ioi [MeasurableSpace F] [BorelSpace F] :
     Measurable fun x => derivWithin f (Ioi x) x := by
   simpa [derivWithin_Ioi_eq_Ici] using measurable_derivWithin_Ici f
 #align measurable_deriv_within_Ioi measurable_derivWithin_Ioi
+-/
 
+#print stronglyMeasurable_derivWithin_Ioi /-
 theorem stronglyMeasurable_derivWithin_Ioi [SecondCountableTopology F] :
     StronglyMeasurable fun x => derivWithin f (Ioi x) x := by borelize F;
   exact (measurable_derivWithin_Ioi f).StronglyMeasurable
 #align strongly_measurable_deriv_within_Ioi stronglyMeasurable_derivWithin_Ioi
+-/
 
-theorem aEMeasurable_derivWithin_Ioi [MeasurableSpace F] [BorelSpace F] (μ : Measure ℝ) :
+#print aemeasurable_derivWithin_Ioi /-
+theorem aemeasurable_derivWithin_Ioi [MeasurableSpace F] [BorelSpace F] (μ : Measure ℝ) :
     AEMeasurable (fun x => derivWithin f (Ioi x) x) μ :=
   (measurable_derivWithin_Ioi f).AEMeasurable
-#align ae_measurable_deriv_within_Ioi aEMeasurable_derivWithin_Ioi
+#align ae_measurable_deriv_within_Ioi aemeasurable_derivWithin_Ioi
+-/
 
-theorem aEStronglyMeasurable_derivWithin_Ioi [SecondCountableTopology F] (μ : Measure ℝ) :
+#print aestronglyMeasurable_derivWithin_Ioi /-
+theorem aestronglyMeasurable_derivWithin_Ioi [SecondCountableTopology F] (μ : Measure ℝ) :
     AEStronglyMeasurable (fun x => derivWithin f (Ioi x) x) μ :=
   (stronglyMeasurable_derivWithin_Ioi f).AEStronglyMeasurable
-#align ae_strongly_measurable_deriv_within_Ioi aEStronglyMeasurable_derivWithin_Ioi
+#align ae_strongly_measurable_deriv_within_Ioi aestronglyMeasurable_derivWithin_Ioi
+-/
 
 end RightDeriv
 

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

@@ -85,7 +85,7 @@ open TopologicalSpace (SecondCountableTopology)
 
 open MeasureTheory
 
-open Topology
+open scoped Topology
 
 namespace ContinuousLinearMap
 

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

@@ -179,10 +179,7 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
   calc
     ‖f z - f y - (fderiv 𝕜 f x) (z - y)‖ =
         ‖f z - f x - (fderiv 𝕜 f x) (z - x) - (f y - f x - (fderiv 𝕜 f x) (y - x))‖ :=
-      by
-      congr 1
-      simp only [ContinuousLinearMap.map_sub]
-      abel
+      by congr 1; simp only [ContinuousLinearMap.map_sub]; abel
     _ ≤ ‖f z - f x - (fderiv 𝕜 f x) (z - x)‖ + ‖f y - f x - (fderiv 𝕜 f x) (y - x)‖ :=
       (norm_sub_le _ _)
     _ ≤ ε / 2 * ‖z - x‖ + ε / 2 * ‖y - x‖ :=
@@ -299,9 +296,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     calc
       ‖L e p q - L e' p' q'‖ =
           ‖L e p q - L e p r + (L e p r - L e' p' r) + (L e' p' r - L e' p' q')‖ :=
-        by
-        congr 1
-        abel
+        by congr 1; abel
       _ ≤ ‖L e p q - L e p r‖ + ‖L e p r - L e' p' r‖ + ‖L e' p' r - L e' p' q'‖ :=
         (le_trans (norm_add_le _ _) (add_le_add_right (norm_add_le _ _) _))
       _ ≤ 4 * ‖c‖ * (1 / 2) ^ e + 4 * ‖c‖ * (1 / 2) ^ e + 4 * ‖c‖ * (1 / 2) ^ e := by
@@ -322,9 +317,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       ‖L0 e - L0 e'‖ ≤ 12 * ‖c‖ * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
       _ < 12 * ‖c‖ * (ε / (12 * ‖c‖)) :=
         (mul_lt_mul' le_rfl he (le_of_lt P) (mul_pos (by norm_num) cpos))
-      _ = ε := by
-        field_simp [(by norm_num : (12 : ℝ) ≠ 0), ne_of_gt cpos]
-        ring
+      _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0), ne_of_gt cpos] ; ring
       
   -- As it is Cauchy, the sequence `L0` converges, to a limit `f'` in `K`.
   obtain ⟨f', f'K, hf'⟩ : ∃ f' ∈ K, tendsto L0 at_top (𝓝 f') :=
@@ -352,7 +345,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     refine' ⟨(1 / 2) ^ (n e + 1), P, fun y hy => _⟩
     -- We need to show that `f (x + y) - f x - f' y` is small. For this, we will work at scale
     -- `k` where `k` is chosen with `‖y‖ ∼ 2 ^ (-k)`.
-    by_cases y_pos : y = 0
+    by_cases y_pos : y = 0;
     · simp [y_pos]
     have yzero : 0 < ‖y‖ := norm_pos_iff.mpr y_pos
     have y_lt : ‖y‖ < (1 / 2) ^ (n e + 1) := by simpa using mem_ball_iff_norm.1 hy
@@ -385,10 +378,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       calc
         ‖f (x + y) - f x - L e (n e) m y‖ ≤ (1 / 2) ^ e * (1 / 2) ^ m := by
           simpa only [add_sub_cancel'] using J1
-        _ = 4 * (1 / 2) ^ e * (1 / 2) ^ (m + 2) :=
-          by
-          field_simp
-          ring
+        _ = 4 * (1 / 2) ^ e * (1 / 2) ^ (m + 2) := by field_simp; ring
         _ ≤ 4 * (1 / 2) ^ e * ‖y‖ :=
           mul_le_mul_of_nonneg_left (le_of_lt hk) (mul_nonneg (by norm_num) (le_of_lt P))
         
@@ -404,9 +394,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
         (mul_le_mul_of_nonneg_left he.le
           (mul_nonneg (add_nonneg (by norm_num) (mul_nonneg (by norm_num) (norm_nonneg _)))
             (norm_nonneg _)))
-      _ = ε * ‖y‖ := by
-        field_simp [ne_of_gt Pos]
-        ring
+      _ = ε * ‖y‖ := by field_simp [ne_of_gt Pos] ; ring
       
   rw [← this.fderiv] at f'K
   exact ⟨this.differentiable_at, f'K⟩
@@ -474,9 +462,7 @@ theorem measurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜] [Mea
 #align measurable_deriv measurable_deriv
 
 theorem stronglyMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜]
-    [SecondCountableTopology F] (f : 𝕜 → F) : StronglyMeasurable (deriv f) :=
-  by
-  borelize F
+    [SecondCountableTopology F] (f : 𝕜 → F) : StronglyMeasurable (deriv f) := by borelize F;
   exact (measurable_deriv f).StronglyMeasurable
 #align strongly_measurable_deriv stronglyMeasurable_deriv
 
@@ -531,10 +517,7 @@ theorem a_mem_nhdsWithin_Ioi {L : F} {r ε x : ℝ} (hx : x ∈ a f L r ε) : a
   rw [mem_nhdsWithin_Ioi_iff_exists_Ioo_subset]
   obtain ⟨s, s_gt, s_lt⟩ : ∃ s : ℝ, r / 2 < s ∧ s < r' := exists_between rr'.1
   have : s ∈ Ioc (r / 2) r := ⟨s_gt, le_of_lt (s_lt.trans_le rr'.2)⟩
-  refine'
-    ⟨x + r' - s, by
-      simp only [mem_Ioi]
-      linarith, fun x' hx' => ⟨s, this, _⟩⟩
+  refine' ⟨x + r' - s, by simp only [mem_Ioi]; linarith, fun x' hx' => ⟨s, this, _⟩⟩
   have A : Icc x' (x' + s) ⊆ Icc x (x + r') :=
     by
     apply Icc_subset_Icc hx'.1.le
@@ -586,10 +569,7 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
     ‖f z - f y - (z - y) • derivWithin f (Ici x) x‖ =
         ‖f z - f x - (z - x) • derivWithin f (Ici x) x -
             (f y - f x - (y - x) • derivWithin f (Ici x) x)‖ :=
-      by
-      congr 1
-      simp only [sub_smul]
-      abel
+      by congr 1; simp only [sub_smul]; abel
     _ ≤
         ‖f z - f x - (z - x) • derivWithin f (Ici x) x‖ +
           ‖f y - f x - (y - x) • derivWithin f (Ici x) x‖ :=
@@ -705,9 +685,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     calc
       ‖L e p q - L e' p' q'‖ =
           ‖L e p q - L e p r + (L e p r - L e' p' r) + (L e' p' r - L e' p' q')‖ :=
-        by
-        congr 1
-        abel
+        by congr 1; abel
       _ ≤ ‖L e p q - L e p r‖ + ‖L e p r - L e' p' r‖ + ‖L e' p' r - L e' p' q'‖ :=
         (le_trans (norm_add_le _ _) (add_le_add_right (norm_add_le _ _) _))
       _ ≤ 4 * (1 / 2) ^ e + 4 * (1 / 2) ^ e + 4 * (1 / 2) ^ e := by apply_rules [add_le_add]
@@ -726,9 +704,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     calc
       ‖L0 e - L0 e'‖ ≤ 12 * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
       _ < 12 * (ε / 12) := (mul_lt_mul' le_rfl he (le_of_lt P) (by norm_num))
-      _ = ε := by
-        field_simp [(by norm_num : (12 : ℝ) ≠ 0)]
-        ring
+      _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0)] ; ring
       
   -- As it is Cauchy, the sequence `L0` converges, to a limit `f'` in `K`.
   obtain ⟨f', f'K, hf'⟩ : ∃ f' ∈ K, tendsto L0 at_top (𝓝 f') :=
@@ -786,10 +762,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
             exact div_nonneg (inv_nonneg.2 (pow_nonneg zero_le_two _)) zero_le_two
           · simp only [pow_add, tsub_le_iff_left] at h'k
             simpa only [hy.1, mem_Icc, true_and_iff, one_div, pow_one] using h'k
-        _ = 4 * (1 / 2) ^ e * (1 / 2) ^ (m + 2) :=
-          by
-          field_simp
-          ring
+        _ = 4 * (1 / 2) ^ e * (1 / 2) ^ (m + 2) := by field_simp; ring
         _ ≤ 4 * (1 / 2) ^ e * (y - x) :=
           (mul_le_mul_of_nonneg_left (le_of_lt hk) (mul_nonneg (by norm_num) (le_of_lt P)))
         _ = 4 * (1 / 2) ^ e * ‖y - x‖ := by rw [Real.norm_of_nonneg yzero.le]
@@ -800,9 +773,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
         by simp only [smul_sub, sub_add_sub_cancel]
       _ ≤ 4 * (1 / 2) ^ e * ‖y - x‖ + ‖y - x‖ * (12 * (1 / 2) ^ e) :=
         (norm_add_le_of_le J
-          (by
-            rw [norm_smul]
-            exact mul_le_mul_of_nonneg_left (Lf' _ _ m_ge) (norm_nonneg _)))
+          (by rw [norm_smul]; exact mul_le_mul_of_nonneg_left (Lf' _ _ m_ge) (norm_nonneg _)))
       _ = 16 * ‖y - x‖ * (1 / 2) ^ e := by ring
       _ ≤ 16 * ‖y - x‖ * (ε / 16) :=
         (mul_le_mul_of_nonneg_left he.le (mul_nonneg (by norm_num) (norm_nonneg _)))
@@ -860,9 +831,7 @@ theorem measurable_derivWithin_Ici [MeasurableSpace F] [BorelSpace F] :
 #align measurable_deriv_within_Ici measurable_derivWithin_Ici
 
 theorem stronglyMeasurable_derivWithin_Ici [SecondCountableTopology F] :
-    StronglyMeasurable fun x => derivWithin f (Ici x) x :=
-  by
-  borelize F
+    StronglyMeasurable fun x => derivWithin f (Ici x) x := by borelize F;
   exact (measurable_derivWithin_Ici f).StronglyMeasurable
 #align strongly_measurable_deriv_within_Ici stronglyMeasurable_derivWithin_Ici
 
@@ -890,9 +859,7 @@ theorem measurable_derivWithin_Ioi [MeasurableSpace F] [BorelSpace F] :
 #align measurable_deriv_within_Ioi measurable_derivWithin_Ioi
 
 theorem stronglyMeasurable_derivWithin_Ioi [SecondCountableTopology F] :
-    StronglyMeasurable fun x => derivWithin f (Ioi x) x :=
-  by
-  borelize F
+    StronglyMeasurable fun x => derivWithin f (Ioi x) x := by borelize F;
   exact (measurable_derivWithin_Ioi f).StronglyMeasurable
 #align strongly_measurable_deriv_within_Ioi stronglyMeasurable_derivWithin_Ioi
 

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

@@ -4,11 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.calculus.fderiv_measurable
-! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
+! 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.Deriv
+import Mathbin.Analysis.Calculus.Deriv.Basic
 import Mathbin.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap
 import Mathbin.MeasureTheory.Function.StronglyMeasurable.Basic
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -485,10 +485,10 @@ theorem aEMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜] [M
   (measurable_deriv f).AEMeasurable
 #align ae_measurable_deriv aEMeasurable_deriv
 
-theorem aeStronglyMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜]
-    [SecondCountableTopology F] (f : 𝕜 → F) (μ : Measure 𝕜) : AeStronglyMeasurable (deriv f) μ :=
-  (stronglyMeasurable_deriv f).AeStronglyMeasurable
-#align ae_strongly_measurable_deriv aeStronglyMeasurable_deriv
+theorem aEStronglyMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜]
+    [SecondCountableTopology F] (f : 𝕜 → F) (μ : Measure 𝕜) : AEStronglyMeasurable (deriv f) μ :=
+  (stronglyMeasurable_deriv f).AEStronglyMeasurable
+#align ae_strongly_measurable_deriv aEStronglyMeasurable_deriv
 
 end fderiv
 
@@ -871,10 +871,10 @@ theorem aEMeasurable_derivWithin_Ici [MeasurableSpace F] [BorelSpace F] (μ : Me
   (measurable_derivWithin_Ici f).AEMeasurable
 #align ae_measurable_deriv_within_Ici aEMeasurable_derivWithin_Ici
 
-theorem aeStronglyMeasurable_derivWithin_Ici [SecondCountableTopology F] (μ : Measure ℝ) :
-    AeStronglyMeasurable (fun x => derivWithin f (Ici x) x) μ :=
-  (stronglyMeasurable_derivWithin_Ici f).AeStronglyMeasurable
-#align ae_strongly_measurable_deriv_within_Ici aeStronglyMeasurable_derivWithin_Ici
+theorem aEStronglyMeasurable_derivWithin_Ici [SecondCountableTopology F] (μ : Measure ℝ) :
+    AEStronglyMeasurable (fun x => derivWithin f (Ici x) x) μ :=
+  (stronglyMeasurable_derivWithin_Ici f).AEStronglyMeasurable
+#align ae_strongly_measurable_deriv_within_Ici aEStronglyMeasurable_derivWithin_Ici
 
 /-- The set of right differentiability points of a function taking values in a complete space is
 Borel-measurable. -/
@@ -901,10 +901,10 @@ theorem aEMeasurable_derivWithin_Ioi [MeasurableSpace F] [BorelSpace F] (μ : Me
   (measurable_derivWithin_Ioi f).AEMeasurable
 #align ae_measurable_deriv_within_Ioi aEMeasurable_derivWithin_Ioi
 
-theorem aeStronglyMeasurable_derivWithin_Ioi [SecondCountableTopology F] (μ : Measure ℝ) :
-    AeStronglyMeasurable (fun x => derivWithin f (Ioi x) x) μ :=
-  (stronglyMeasurable_derivWithin_Ioi f).AeStronglyMeasurable
-#align ae_strongly_measurable_deriv_within_Ioi aeStronglyMeasurable_derivWithin_Ioi
+theorem aEStronglyMeasurable_derivWithin_Ioi [SecondCountableTopology F] (μ : Measure ℝ) :
+    AEStronglyMeasurable (fun x => derivWithin f (Ioi x) x) μ :=
+  (stronglyMeasurable_derivWithin_Ioi f).AEStronglyMeasurable
+#align ae_strongly_measurable_deriv_within_Ioi aEStronglyMeasurable_derivWithin_Ioi
 
 end RightDeriv
 

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

@@ -171,7 +171,7 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ a f (fderiv 𝕜 f x) r ε :=
   by
   have := hx.has_fderiv_at
-  simp only [HasFderivAt, HasFderivAtFilter, is_o_iff] at this
+  simp only [HasFDerivAt, HasFDerivAtFilter, is_o_iff] at this
   rcases eventually_nhds_iff_ball.1 (this (half_pos hε)) with ⟨R, R_pos, hR⟩
   refine' ⟨R, R_pos, fun r hr => _⟩
   have : r ∈ Ioc (r / 2) r := ⟨half_lt_self hr.1, le_rfl⟩
@@ -336,9 +336,9 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     rw [eventually_at_top]
     exact ⟨e, fun e' he' => M _ _ _ _ _ _ le_rfl hp le_rfl le_rfl he'⟩
   -- Let us show that `f` has derivative `f'` at `x`.
-  have : HasFderivAt f f' x :=
+  have : HasFDerivAt f f' x :=
     by
-    simp only [hasFderivAt_iff_isLittleO_nhds_zero, is_o_iff]
+    simp only [hasFDerivAt_iff_isLittleO_nhds_zero, is_o_iff]
     /- to get an approximation with a precision `ε`, we will replace `f` with `L e (n e) m` for
         some large enough `e` (yielding a small error by uniform approximation). As one can vary `m`,
         this makes it possible to cover all scales, and thus to obtain a good linear approximation in

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -4,11 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.calculus.fderiv_measurable
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
+! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.Deriv
+import Mathbin.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap
 import Mathbin.MeasureTheory.Function.StronglyMeasurable.Basic
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -148,7 +148,7 @@ theorem isOpen_a (L : E →L[𝕜] F) (r ε : ℝ) : IsOpen (a f L r ε) :=
 #align fderiv_measurable_aux.is_open_A FderivMeasurableAux.isOpen_a
 
 theorem isOpen_b {K : Set (E →L[𝕜] F)} {r s ε : ℝ} : IsOpen (b f K r s ε) := by
-  simp [B, isOpen_unionᵢ, IsOpen.inter, is_open_A]
+  simp [B, isOpen_iUnion, IsOpen.inter, is_open_A]
 #align fderiv_measurable_aux.is_open_B FderivMeasurableAux.isOpen_b
 
 theorem a_mono (L : E →L[𝕜] F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : a f L r ε ⊆ a f L r δ :=
@@ -428,8 +428,8 @@ variable (𝕜 f)
 is Borel-measurable. -/
 theorem measurableSet_of_differentiableAt_of_isComplete {K : Set (E →L[𝕜] F)} (hK : IsComplete K) :
     MeasurableSet { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } := by
-  simp [differentiable_set_eq_D K hK, D, is_open_B.measurable_set, MeasurableSet.interᵢ,
-    MeasurableSet.unionᵢ]
+  simp [differentiable_set_eq_D K hK, D, is_open_B.measurable_set, MeasurableSet.iInter,
+    MeasurableSet.iUnion]
 #align measurable_set_of_differentiable_at_of_is_complete measurableSet_of_differentiableAt_of_isComplete
 
 variable [CompleteSpace F]
@@ -826,8 +826,8 @@ variable (f)
 set, is Borel-measurable. -/
 theorem measurableSet_of_differentiableWithinAt_Ici_of_isComplete {K : Set F} (hK : IsComplete K) :
     MeasurableSet { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } := by
-  simp [differentiable_set_eq_D K hK, D, measurable_set_B, MeasurableSet.interᵢ,
-    MeasurableSet.unionᵢ]
+  simp [differentiable_set_eq_D K hK, D, measurable_set_B, MeasurableSet.iInter,
+    MeasurableSet.iUnion]
 #align measurable_set_of_differentiable_within_at_Ici_of_is_complete measurableSet_of_differentiableWithinAt_Ici_of_isComplete
 
 variable [CompleteSpace F]

mathlib commit https://github.com/leanprover-community/mathlib/commit/92c69b77c5a7dc0f7eeddb552508633305157caa

@@ -479,15 +479,15 @@ theorem stronglyMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 
   exact (measurable_deriv f).StronglyMeasurable
 #align strongly_measurable_deriv stronglyMeasurable_deriv
 
-theorem aeMeasurableDeriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜] [MeasurableSpace F]
-    [BorelSpace F] (f : 𝕜 → F) (μ : Measure 𝕜) : AeMeasurable (deriv f) μ :=
-  (measurable_deriv f).AeMeasurable
-#align ae_measurable_deriv aeMeasurableDeriv
+theorem aEMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜] [MeasurableSpace F]
+    [BorelSpace F] (f : 𝕜 → F) (μ : Measure 𝕜) : AEMeasurable (deriv f) μ :=
+  (measurable_deriv f).AEMeasurable
+#align ae_measurable_deriv aEMeasurable_deriv
 
-theorem aeStronglyMeasurableDeriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜]
+theorem aeStronglyMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜]
     [SecondCountableTopology F] (f : 𝕜 → F) (μ : Measure 𝕜) : AeStronglyMeasurable (deriv f) μ :=
   (stronglyMeasurable_deriv f).AeStronglyMeasurable
-#align ae_strongly_measurable_deriv aeStronglyMeasurableDeriv
+#align ae_strongly_measurable_deriv aeStronglyMeasurable_deriv
 
 end fderiv
 
@@ -865,15 +865,15 @@ theorem stronglyMeasurable_derivWithin_Ici [SecondCountableTopology F] :
   exact (measurable_derivWithin_Ici f).StronglyMeasurable
 #align strongly_measurable_deriv_within_Ici stronglyMeasurable_derivWithin_Ici
 
-theorem aeMeasurableDerivWithinIci [MeasurableSpace F] [BorelSpace F] (μ : Measure ℝ) :
-    AeMeasurable (fun x => derivWithin f (Ici x) x) μ :=
-  (measurable_derivWithin_Ici f).AeMeasurable
-#align ae_measurable_deriv_within_Ici aeMeasurableDerivWithinIci
+theorem aEMeasurable_derivWithin_Ici [MeasurableSpace F] [BorelSpace F] (μ : Measure ℝ) :
+    AEMeasurable (fun x => derivWithin f (Ici x) x) μ :=
+  (measurable_derivWithin_Ici f).AEMeasurable
+#align ae_measurable_deriv_within_Ici aEMeasurable_derivWithin_Ici
 
-theorem aeStronglyMeasurableDerivWithinIci [SecondCountableTopology F] (μ : Measure ℝ) :
+theorem aeStronglyMeasurable_derivWithin_Ici [SecondCountableTopology F] (μ : Measure ℝ) :
     AeStronglyMeasurable (fun x => derivWithin f (Ici x) x) μ :=
   (stronglyMeasurable_derivWithin_Ici f).AeStronglyMeasurable
-#align ae_strongly_measurable_deriv_within_Ici aeStronglyMeasurableDerivWithinIci
+#align ae_strongly_measurable_deriv_within_Ici aeStronglyMeasurable_derivWithin_Ici
 
 /-- The set of right differentiability points of a function taking values in a complete space is
 Borel-measurable. -/
@@ -895,15 +895,15 @@ theorem stronglyMeasurable_derivWithin_Ioi [SecondCountableTopology F] :
   exact (measurable_derivWithin_Ioi f).StronglyMeasurable
 #align strongly_measurable_deriv_within_Ioi stronglyMeasurable_derivWithin_Ioi
 
-theorem aeMeasurableDerivWithinIoi [MeasurableSpace F] [BorelSpace F] (μ : Measure ℝ) :
-    AeMeasurable (fun x => derivWithin f (Ioi x) x) μ :=
-  (measurable_derivWithin_Ioi f).AeMeasurable
-#align ae_measurable_deriv_within_Ioi aeMeasurableDerivWithinIoi
+theorem aEMeasurable_derivWithin_Ioi [MeasurableSpace F] [BorelSpace F] (μ : Measure ℝ) :
+    AEMeasurable (fun x => derivWithin f (Ioi x) x) μ :=
+  (measurable_derivWithin_Ioi f).AEMeasurable
+#align ae_measurable_deriv_within_Ioi aEMeasurable_derivWithin_Ioi
 
-theorem aeStronglyMeasurableDerivWithinIoi [SecondCountableTopology F] (μ : Measure ℝ) :
+theorem aeStronglyMeasurable_derivWithin_Ioi [SecondCountableTopology F] (μ : Measure ℝ) :
     AeStronglyMeasurable (fun x => derivWithin f (Ioi x) x) μ :=
   (stronglyMeasurable_derivWithin_Ioi f).AeStronglyMeasurable
-#align ae_strongly_measurable_deriv_within_Ioi aeStronglyMeasurableDerivWithinIoi
+#align ae_strongly_measurable_deriv_within_Ioi aeStronglyMeasurable_derivWithin_Ioi
 
 end RightDeriv
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -4,14 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.calculus.fderiv_measurable
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.Deriv
-import Mathbin.MeasureTheory.Constructions.BorelSpace
 import Mathbin.MeasureTheory.Function.StronglyMeasurable.Basic
-import Mathbin.Tactic.RingExp
 
 /-!
 # Derivative is measurable

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

@@ -339,7 +339,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
   -- Let us show that `f` has derivative `f'` at `x`.
   have : HasFderivAt f f' x :=
     by
-    simp only [hasFderivAt_iff_isOCat_nhds_zero, is_o_iff]
+    simp only [hasFderivAt_iff_isLittleO_nhds_zero, is_o_iff]
     /- to get an approximation with a precision `ε`, we will replace `f` with `L e (n e) m` for
         some large enough `e` (yielding a small error by uniform approximation). As one can vary `m`,
         this makes it possible to cover all scales, and thus to obtain a good linear approximation in
@@ -578,7 +578,7 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ a f (derivWithin f (Ici x) x) r ε :=
   by
   have := hx.has_deriv_within_at
-  simp_rw [hasDerivWithinAt_iff_isOCat, is_o_iff] at this
+  simp_rw [hasDerivWithinAt_iff_isLittleO, is_o_iff] at this
   rcases mem_nhdsWithin_Ici_iff_exists_Ico_subset.1 (this (half_pos hε)) with ⟨m, xm, hm⟩
   refine' ⟨m - x, by linarith [show x < m from xm], fun r hr => _⟩
   have : r ∈ Ioc (r / 2) r := ⟨half_lt_self hr.1, le_rfl⟩
@@ -743,7 +743,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
   -- Let us show that `f` has right derivative `f'` at `x`.
   have : HasDerivWithinAt f f' (Ici x) x :=
     by
-    simp only [hasDerivWithinAt_iff_isOCat, is_o_iff]
+    simp only [hasDerivWithinAt_iff_isLittleO, is_o_iff]
     /- to get an approximation with a precision `ε`, we will replace `f` with `L e (n e) m` for
         some large enough `e` (yielding a small error by uniform approximation). As one can vary `m`,
         this makes it possible to cover all scales, and thus to obtain a good linear approximation in

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

@@ -758,7 +758,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     -- We need to show that `f y - f x - f' (y - x)` is small. For this, we will work at scale
     -- `k` where `k` is chosen with `‖y - x‖ ∼ 2 ^ (-k)`.
     rcases eq_or_lt_of_le hy.1 with (rfl | xy)
-    · simp only [sub_self, zero_smul, norm_zero, mul_zero]
+    · simp only [sub_self, zero_smul, norm_zero, MulZeroClass.mul_zero]
     have yzero : 0 < y - x := sub_pos.2 xy
     have y_le : y - x ≤ (1 / 2) ^ (n e + 1) := by linarith [hy.2]
     have yone : y - x ≤ 1 := le_trans y_le (pow_le_one _ (by norm_num) (by norm_num))

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -113,7 +113,7 @@ variable {f : E → F} (K : Set (E →L[𝕜] F))
 
 namespace FderivMeasurableAux
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (y z «expr ∈ » ball[metric.ball] x r') -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » ball[metric.ball] x r') -/
 /-- The set `A f L r ε` is the set of points `x` around which the function `f` is well approximated
 at scale `r` by the linear map `L`, up to an error `ε`. We tweak the definition to make sure that
 this is an open set.-/
@@ -185,13 +185,13 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
       simp only [ContinuousLinearMap.map_sub]
       abel
     _ ≤ ‖f z - f x - (fderiv 𝕜 f x) (z - x)‖ + ‖f y - f x - (fderiv 𝕜 f x) (y - x)‖ :=
-      norm_sub_le _ _
+      (norm_sub_le _ _)
     _ ≤ ε / 2 * ‖z - x‖ + ε / 2 * ‖y - x‖ :=
-      add_le_add (hR _ (lt_trans (mem_ball.1 hz) hr.2)) (hR _ (lt_trans (mem_ball.1 hy) hr.2))
+      (add_le_add (hR _ (lt_trans (mem_ball.1 hz) hr.2)) (hR _ (lt_trans (mem_ball.1 hy) hr.2)))
     _ ≤ ε / 2 * r + ε / 2 * r :=
-      add_le_add
+      (add_le_add
         (mul_le_mul_of_nonneg_left (le_of_lt (mem_ball_iff_norm.1 hz)) (le_of_lt (half_pos hε)))
-        (mul_le_mul_of_nonneg_left (le_of_lt (mem_ball_iff_norm.1 hy)) (le_of_lt (half_pos hε)))
+        (mul_le_mul_of_nonneg_left (le_of_lt (mem_ball_iff_norm.1 hy)) (le_of_lt (half_pos hε))))
     _ = ε * r := by ring
     
 #align fderiv_measurable_aux.mem_A_of_differentiable FderivMeasurableAux.mem_a_of_differentiable
@@ -207,7 +207,7 @@ theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
   calc
     ‖(L₁ - L₂) y‖ = ‖f (x + y) - f x - L₂ (x + y - x) - (f (x + y) - f x - L₁ (x + y - x))‖ := by
       simp
-    _ ≤ ‖f (x + y) - f x - L₂ (x + y - x)‖ + ‖f (x + y) - f x - L₁ (x + y - x)‖ := norm_sub_le _ _
+    _ ≤ ‖f (x + y) - f x - L₂ (x + y - x)‖ + ‖f (x + y) - f x - L₁ (x + y - x)‖ := (norm_sub_le _ _)
     _ ≤ ε * r + ε * r := by
       apply add_le_add
       · apply le_of_mem_A h₂
@@ -217,7 +217,7 @@ theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
         · simp only [le_of_lt (half_pos hr), mem_closed_ball, dist_self]
         · simp only [dist_eq_norm, add_sub_cancel', mem_closed_ball, ylt.le]
     _ = 2 * ε * r := by ring
-    _ ≤ 2 * ε * (2 * ‖c‖ * ‖y‖) := mul_le_mul_of_nonneg_left ley (mul_nonneg (by norm_num) hε.le)
+    _ ≤ 2 * ε * (2 * ‖c‖ * ‖y‖) := (mul_le_mul_of_nonneg_left ley (mul_nonneg (by norm_num) hε.le))
     _ = 4 * ‖c‖ * ε * ‖y‖ := by ring
     
 #align fderiv_measurable_aux.norm_sub_le_of_mem_A FderivMeasurableAux.norm_sub_le_of_mem_a
@@ -304,7 +304,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
         congr 1
         abel
       _ ≤ ‖L e p q - L e p r‖ + ‖L e p r - L e' p' r‖ + ‖L e' p' r - L e' p' q'‖ :=
-        le_trans (norm_add_le _ _) (add_le_add_right (norm_add_le _ _) _)
+        (le_trans (norm_add_le _ _) (add_le_add_right (norm_add_le _ _) _))
       _ ≤ 4 * ‖c‖ * (1 / 2) ^ e + 4 * ‖c‖ * (1 / 2) ^ e + 4 * ‖c‖ * (1 / 2) ^ e := by
         apply_rules [add_le_add]
       _ = 12 * ‖c‖ * (1 / 2) ^ e := by ring
@@ -322,7 +322,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     calc
       ‖L0 e - L0 e'‖ ≤ 12 * ‖c‖ * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
       _ < 12 * ‖c‖ * (ε / (12 * ‖c‖)) :=
-        mul_lt_mul' le_rfl he (le_of_lt P) (mul_pos (by norm_num) cpos)
+        (mul_lt_mul' le_rfl he (le_of_lt P) (mul_pos (by norm_num) cpos))
       _ = ε := by
         field_simp [(by norm_num : (12 : ℝ) ≠ 0), ne_of_gt cpos]
         ring
@@ -398,13 +398,13 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       ‖f (x + y) - f x - f' y‖ = ‖f (x + y) - f x - L e (n e) m y + (L e (n e) m - f') y‖ :=
         congr_arg _ (by simp)
       _ ≤ 4 * (1 / 2) ^ e * ‖y‖ + 12 * ‖c‖ * (1 / 2) ^ e * ‖y‖ :=
-        norm_add_le_of_le J2
-          ((le_op_norm _ _).trans (mul_le_mul_of_nonneg_right (Lf' _ _ m_ge) (norm_nonneg _)))
+        (norm_add_le_of_le J2
+          ((le_op_norm _ _).trans (mul_le_mul_of_nonneg_right (Lf' _ _ m_ge) (norm_nonneg _))))
       _ = (4 + 12 * ‖c‖) * ‖y‖ * (1 / 2) ^ e := by ring
       _ ≤ (4 + 12 * ‖c‖) * ‖y‖ * (ε / (4 + 12 * ‖c‖)) :=
-        mul_le_mul_of_nonneg_left he.le
+        (mul_le_mul_of_nonneg_left he.le
           (mul_nonneg (add_nonneg (by norm_num) (mul_nonneg (by norm_num) (norm_nonneg _)))
-            (norm_nonneg _))
+            (norm_nonneg _)))
       _ = ε * ‖y‖ := by
         field_simp [ne_of_gt Pos]
         ring
@@ -501,7 +501,7 @@ variable {f : ℝ → F} (K : Set F)
 
 namespace RightDerivMeasurableAux
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (y z «expr ∈ » Icc[set.Icc] x «expr + »(x, r')) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » Icc[set.Icc] x «expr + »(x, r')) -/
 /-- The set `A f L r ε` is the set of points `x` around which the function `f` is well approximated
 at scale `r` by the linear map `h ↦ h • L`, up to an error `ε`. We tweak the definition to
 make sure that this is open on the right. -/
@@ -594,10 +594,10 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
     _ ≤
         ‖f z - f x - (z - x) • derivWithin f (Ici x) x‖ +
           ‖f y - f x - (y - x) • derivWithin f (Ici x) x‖ :=
-      norm_sub_le _ _
+      (norm_sub_le _ _)
     _ ≤ ε / 2 * ‖z - x‖ + ε / 2 * ‖y - x‖ :=
-      add_le_add (hm ⟨hz.1, hz.2.trans_lt (by linarith [hr.2])⟩)
-        (hm ⟨hy.1, hy.2.trans_lt (by linarith [hr.2])⟩)
+      (add_le_add (hm ⟨hz.1, hz.2.trans_lt (by linarith [hr.2])⟩)
+        (hm ⟨hy.1, hy.2.trans_lt (by linarith [hr.2])⟩))
     _ ≤ ε / 2 * r + ε / 2 * r := by
       apply add_le_add
       · apply mul_le_mul_of_nonneg_left _ (le_of_lt (half_pos hε))
@@ -621,7 +621,7 @@ theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F}
     _ ≤
         ‖f (x + r / 2) - f x - (x + r / 2 - x) • L₂‖ +
           ‖f (x + r / 2) - f x - (x + r / 2 - x) • L₁‖ :=
-      norm_sub_le _ _
+      (norm_sub_le _ _)
     _ ≤ ε * r + ε * r := by
       apply add_le_add
       · apply le_of_mem_A h₂ <;> simp [(half_pos hr).le]
@@ -710,7 +710,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
         congr 1
         abel
       _ ≤ ‖L e p q - L e p r‖ + ‖L e p r - L e' p' r‖ + ‖L e' p' r - L e' p' q'‖ :=
-        le_trans (norm_add_le _ _) (add_le_add_right (norm_add_le _ _) _)
+        (le_trans (norm_add_le _ _) (add_le_add_right (norm_add_le _ _) _))
       _ ≤ 4 * (1 / 2) ^ e + 4 * (1 / 2) ^ e + 4 * (1 / 2) ^ e := by apply_rules [add_le_add]
       _ = 12 * (1 / 2) ^ e := by ring
       
@@ -726,7 +726,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     rw [dist_comm, dist_eq_norm]
     calc
       ‖L0 e - L0 e'‖ ≤ 12 * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
-      _ < 12 * (ε / 12) := mul_lt_mul' le_rfl he (le_of_lt P) (by norm_num)
+      _ < 12 * (ε / 12) := (mul_lt_mul' le_rfl he (le_of_lt P) (by norm_num))
       _ = ε := by
         field_simp [(by norm_num : (12 : ℝ) ≠ 0)]
         ring
@@ -792,7 +792,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
           field_simp
           ring
         _ ≤ 4 * (1 / 2) ^ e * (y - x) :=
-          mul_le_mul_of_nonneg_left (le_of_lt hk) (mul_nonneg (by norm_num) (le_of_lt P))
+          (mul_le_mul_of_nonneg_left (le_of_lt hk) (mul_nonneg (by norm_num) (le_of_lt P)))
         _ = 4 * (1 / 2) ^ e * ‖y - x‖ := by rw [Real.norm_of_nonneg yzero.le]
         
     calc
@@ -800,13 +800,13 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
           ‖f y - f x - (y - x) • L e (n e) m + (y - x) • (L e (n e) m - f')‖ :=
         by simp only [smul_sub, sub_add_sub_cancel]
       _ ≤ 4 * (1 / 2) ^ e * ‖y - x‖ + ‖y - x‖ * (12 * (1 / 2) ^ e) :=
-        norm_add_le_of_le J
+        (norm_add_le_of_le J
           (by
             rw [norm_smul]
-            exact mul_le_mul_of_nonneg_left (Lf' _ _ m_ge) (norm_nonneg _))
+            exact mul_le_mul_of_nonneg_left (Lf' _ _ m_ge) (norm_nonneg _)))
       _ = 16 * ‖y - x‖ * (1 / 2) ^ e := by ring
       _ ≤ 16 * ‖y - x‖ * (ε / 16) :=
-        mul_le_mul_of_nonneg_left he.le (mul_nonneg (by norm_num) (norm_nonneg _))
+        (mul_le_mul_of_nonneg_left he.le (mul_nonneg (by norm_num) (norm_nonneg _)))
       _ = ε * ‖y - x‖ := by ring
       
   rw [← this.deriv_within (uniqueDiffOn_Ici x x le_rfl)] at f'K

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

This lets us unify a few lemmas between GroupWithZero and EuclideanDomain and two lemmas that were previously proved separately for Nat, Int, Polynomial.

@@ -288,7 +288,7 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     calc
       ‖L0 e - L0 e'‖ ≤ 12 * ‖c‖ * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
       _ < 12 * ‖c‖ * (ε / (12 * ‖c‖)) := by gcongr
-      _ = ε := by field_simp; ring
+      _ = ε := by field_simp
   -- As it is Cauchy, the sequence `L0` converges, to a limit `f'` in `K`.
   obtain ⟨f', f'K, hf'⟩ : ∃ f' ∈ K, Tendsto L0 atTop (𝓝 f') :=
     cauchySeq_tendsto_of_isComplete hK (fun e => (hn e (n e) (n e) le_rfl le_rfl).1) this
@@ -642,7 +642,7 @@ theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     calc
       ‖L0 e - L0 e'‖ ≤ 12 * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
       _ < 12 * (ε / 12) := mul_lt_mul' le_rfl he (le_of_lt P) (by norm_num)
-      _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0)]; ring
+      _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0)]
 
   -- As it is Cauchy, the sequence `L0` converges, to a limit `f'` in `K`.
   obtain ⟨f', f'K, hf'⟩ : ∃ f' ∈ K, Tendsto L0 atTop (𝓝 f') :=

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -189,7 +189,7 @@ theorem norm_sub_le_of_mem_A {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
   calc
     ‖(L₁ - L₂) y‖ = ‖f (x + y) - f x - L₂ (x + y - x) - (f (x + y) - f x - L₁ (x + y - x))‖ := by
       simp
-    _ ≤ ‖f (x + y) - f x - L₂ (x + y - x)‖ + ‖f (x + y) - f x - L₁ (x + y - x)‖ := (norm_sub_le _ _)
+    _ ≤ ‖f (x + y) - f x - L₂ (x + y - x)‖ + ‖f (x + y) - f x - L₁ (x + y - x)‖ := norm_sub_le _ _
     _ ≤ ε * r + ε * r := by
       apply add_le_add
       · apply le_of_mem_A h₂
@@ -641,7 +641,7 @@ theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     rw [dist_comm, dist_eq_norm]
     calc
       ‖L0 e - L0 e'‖ ≤ 12 * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
-      _ < 12 * (ε / 12) := (mul_lt_mul' le_rfl he (le_of_lt P) (by norm_num))
+      _ < 12 * (ε / 12) := mul_lt_mul' le_rfl he (le_of_lt P) (by norm_num)
       _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0)]; ring
 
   -- As it is Cauchy, the sequence `L0` converges, to a limit `f'` in `K`.

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -111,7 +111,7 @@ namespace FDerivMeasurableAux
 
 /-- The set `A f L r ε` is the set of points `x` around which the function `f` is well approximated
 at scale `r` by the linear map `L`, up to an error `ε`. We tweak the definition to make sure that
-this is an open set.-/
+this is an open set. -/
 def A (f : E → F) (L : E →L[𝕜] F) (r ε : ℝ) : Set E :=
   { x | ∃ r' ∈ Ioc (r / 2) r, ∀ y ∈ ball x r', ∀ z ∈ ball x r', ‖f z - f y - L (z - y)‖ < ε * r }
 #align fderiv_measurable_aux.A FDerivMeasurableAux.A

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -336,7 +336,7 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       apply le_of_mem_A (hn e (n e) m le_rfl m_ge).2.2
       · simp only [mem_closedBall, dist_self]
         positivity
-      · simpa only [dist_eq_norm, add_sub_cancel_left, mem_closedBall, pow_succ', mul_one_div] using
+      · simpa only [dist_eq_norm, add_sub_cancel_left, mem_closedBall, pow_succ, mul_one_div] using
           h'k
     have J2 : ‖f (x + y) - f x - L e (n e) m y‖ ≤ 4 * (1 / 2) ^ e * ‖y‖ :=
       calc

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -194,10 +194,10 @@ theorem norm_sub_le_of_mem_A {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
       apply add_le_add
       · apply le_of_mem_A h₂
         · simp only [le_of_lt (half_pos hr), mem_closedBall, dist_self]
-        · simp only [dist_eq_norm, add_sub_cancel', mem_closedBall, ylt.le]
+        · simp only [dist_eq_norm, add_sub_cancel_left, mem_closedBall, ylt.le]
       · apply le_of_mem_A h₁
         · simp only [le_of_lt (half_pos hr), mem_closedBall, dist_self]
-        · simp only [dist_eq_norm, add_sub_cancel', mem_closedBall, ylt.le]
+        · simp only [dist_eq_norm, add_sub_cancel_left, mem_closedBall, ylt.le]
     _ = 2 * ε * r := by ring
     _ ≤ 2 * ε * (2 * ‖c‖ * ‖y‖) := by gcongr
     _ = 4 * ‖c‖ * ε * ‖y‖ := by ring
@@ -336,12 +336,12 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       apply le_of_mem_A (hn e (n e) m le_rfl m_ge).2.2
       · simp only [mem_closedBall, dist_self]
         positivity
-      · simpa only [dist_eq_norm, add_sub_cancel', mem_closedBall, pow_succ', mul_one_div] using
+      · simpa only [dist_eq_norm, add_sub_cancel_left, mem_closedBall, pow_succ', mul_one_div] using
           h'k
     have J2 : ‖f (x + y) - f x - L e (n e) m y‖ ≤ 4 * (1 / 2) ^ e * ‖y‖ :=
       calc
         ‖f (x + y) - f x - L e (n e) m y‖ ≤ (1 / 2) ^ e * (1 / 2) ^ m := by
-          simpa only [add_sub_cancel'] using J1
+          simpa only [add_sub_cancel_left] using J1
         _ = 4 * (1 / 2) ^ e * (1 / 2) ^ (m + 2) := by field_simp; ring
         _ ≤ 4 * (1 / 2) ^ e * ‖y‖ := by gcongr
     -- use the previous estimates to see that `f (x + y) - f x - f' y` is small.

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -103,11 +103,8 @@ end ContinuousLinearMap
 section fderiv
 
 variable {𝕜 : Type*} [NontriviallyNormedField 𝕜]
-
 variable {E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
-
 variable {F : Type*} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
-
 variable {f : E → F} (K : Set (E →L[𝕜] F))
 
 namespace FDerivMeasurableAux
@@ -370,7 +367,6 @@ end FDerivMeasurableAux
 open FDerivMeasurableAux
 
 variable [MeasurableSpace E] [OpensMeasurableSpace E]
-
 variable (𝕜 f)
 
 /-- The set of differentiability points of a function, with derivative in a given complete set,
@@ -448,7 +444,6 @@ end fderiv
 section RightDeriv
 
 variable {F : Type*} [NormedAddCommGroup F] [NormedSpace ℝ F]
-
 variable {f : ℝ → F} (K : Set F)
 
 namespace RightDerivMeasurableAux

1. ContinuousAt.comp₂, ContinuousAt.comp₂_continuousWithinAt, and _of_eq versions.
2. ContinuousAt.along_{fst,snd}: Continuous functions are continuous in their first and second arguments.

@@ -853,7 +853,7 @@ lemma isOpen_A_with_param {r s : ℝ} (hf : Continuous f.uncurry) (L : E →L[
   simp only [A, half_lt_self_iff, not_lt, mem_Ioc, mem_ball, map_sub, mem_setOf_eq]
   apply isOpen_iff_mem_nhds.2
   rintro ⟨a, x⟩ ⟨r', ⟨Irr', Ir'r⟩, hr⟩
-  have ha : Continuous (f a) := continuous_uncurry_left a hf
+  have ha : Continuous (f a) := hf.uncurry_left a
   rcases exists_between Irr' with ⟨t, hrt, htr'⟩
   rcases exists_between hrt with ⟨t', hrt', ht't⟩
   obtain ⟨b, b_lt, hb⟩ : ∃ b, b < s * r ∧ ∀ y ∈ closedBall x t, ∀ z ∈ closedBall x t,

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

@@ -328,7 +328,7 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     have k_gt : n e < k := by
       have : ((1 : ℝ) / 2) ^ (k + 1) < (1 / 2) ^ (n e + 1) := lt_trans hk y_lt
       rw [pow_lt_pow_iff_right_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this
-      linarith
+      omega
     set m := k - 1
     have m_ge : n e ≤ m := Nat.le_sub_one_of_lt k_gt
     have km : k = m + 1 := (Nat.succ_pred_eq_of_pos (lt_of_le_of_lt (zero_le _) k_gt)).symm
@@ -686,7 +686,7 @@ theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     have k_gt : n e < k := by
       have : ((1 : ℝ) / 2) ^ (k + 1) < (1 / 2) ^ (n e + 1) := lt_of_lt_of_le hk y_le
       rw [pow_lt_pow_iff_right_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this
-      linarith
+      omega
     set m := k - 1
     have m_ge : n e ≤ m := Nat.le_sub_one_of_lt k_gt
     have km : k = m + 1 := (Nat.succ_pred_eq_of_pos (lt_of_le_of_lt (zero_le _) k_gt)).symm

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>

@@ -545,8 +545,8 @@ theorem mem_A_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
 
 theorem norm_sub_le_of_mem_A {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F} (h₁ : x ∈ A f L₁ r ε)
     (h₂ : x ∈ A f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ε := by
-  suffices H : ‖(r / 2) • (L₁ - L₂)‖ ≤ r / 2 * (4 * ε)
-  · rwa [norm_smul, Real.norm_of_nonneg (half_pos hr).le, mul_le_mul_left (half_pos hr)] at H
+  suffices H : ‖(r / 2) • (L₁ - L₂)‖ ≤ r / 2 * (4 * ε) by
+    rwa [norm_smul, Real.norm_of_nonneg (half_pos hr).le, mul_le_mul_left (half_pos hr)] at H
   calc
     ‖(r / 2) • (L₁ - L₂)‖ =
         ‖f (x + r / 2) - f x - (x + r / 2 - x) • L₂ -

• upgrade isSeparable_iUnion to an Iff lemma, restore the original version as IsSeparable.iUnion;
• add isSeparable_union and isSeparable_closure;
• upgrade isSeparable_pi from [Finite ι] to [Countable ι], add IsSeparable.univ_pi version;
• add Dense.isSeparable_iff and isSeparable_range;
• rename isSeparable_of_separableSpace_subtype to IsSeparable.of_subtype;
• rename isSeparable_of_separableSpace to IsSeparable.of_separableSpace.

@@ -1003,9 +1003,7 @@ theorem stronglyMeasurable_deriv_with_param [LocallyCompactSpace 𝕜] [Measurab
         rintro - ⟨x, rfl⟩
         exact mem_range_self (p.1, x)
       exact closure_mono (Submodule.span_mono B) A
-    apply (IsSeparable.span _).closure.mono this
-    rw [← image_univ]
-    exact (isSeparable_of_separableSpace univ).image hf
+    exact (isSeparable_range hf).span.closure.mono this
   · exact (measurable_deriv_with_param hf).stronglyMeasurable
 
 theorem aemeasurable_deriv_with_param [LocallyCompactSpace 𝕜] [MeasurableSpace 𝕜]

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

@@ -186,7 +186,7 @@ theorem mem_A_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
 
 theorem norm_sub_le_of_mem_A {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0 < ε) (hr : 0 < r) {x : E}
     {L₁ L₂ : E →L[𝕜] F} (h₁ : x ∈ A f L₁ r ε) (h₂ : x ∈ A f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ‖c‖ * ε := by
-  refine' op_norm_le_of_shell (half_pos hr) (by positivity) hc _
+  refine' opNorm_le_of_shell (half_pos hr) (by positivity) hc _
   intro y ley ylt
   rw [div_div, div_le_iff' (mul_pos (by norm_num : (0 : ℝ) < 2) (zero_lt_one.trans hc))] at ley
   calc
@@ -352,7 +352,7 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       ‖f (x + y) - f x - f' y‖ = ‖f (x + y) - f x - L e (n e) m y + (L e (n e) m - f') y‖ :=
         congr_arg _ (by simp)
       _ ≤ 4 * (1 / 2) ^ e * ‖y‖ + 12 * ‖c‖ * (1 / 2) ^ e * ‖y‖ :=
-        norm_add_le_of_le J2 <| (le_op_norm _ _).trans <| by gcongr; exact Lf' _ _ m_ge
+        norm_add_le_of_le J2 <| (le_opNorm _ _).trans <| by gcongr; exact Lf' _ _ m_ge
       _ = (4 + 12 * ‖c‖) * ‖y‖ * (1 / 2) ^ e := by ring
       _ ≤ (4 + 12 * ‖c‖) * ‖y‖ * (ε / (4 + 12 * ‖c‖)) := by gcongr
       _ = ε * ‖y‖ := by field_simp [ne_of_gt pos]; ring

Rename properSpace_of_* to ProperSpace.of_*, restore old names as deprecated aliases. This affects:

• properSpace_of_locallyCompactSpace -> ProperSpace.of_locallyCompactSpace, also golf using new ProperSpace.of_seq_closedBall;
• properSpace_of_locallyCompact_module -> ProperSpace.of_locallyCompact_module;
• properSpace_of_compact_closedBall_of_le -> ProperSpace.of_isCompact_closedBall_of_le, also changed compact -> isCompact in the name.

@@ -849,7 +849,7 @@ open Uniformity
 
 lemma isOpen_A_with_param {r s : ℝ} (hf : Continuous f.uncurry) (L : E →L[𝕜] F) :
     IsOpen {p : α × E | p.2 ∈ A (f p.1) L r s} := by
-  have : ProperSpace E := properSpace_of_locallyCompactSpace 𝕜
+  have : ProperSpace E := .of_locallyCompactSpace 𝕜
   simp only [A, half_lt_self_iff, not_lt, mem_Ioc, mem_ball, map_sub, mem_setOf_eq]
   apply isOpen_iff_mem_nhds.2
   rintro ⟨a, x⟩ ⟨r', ⟨Irr', Ir'r⟩, hr⟩
@@ -945,7 +945,7 @@ theorem measurableSet_of_differentiableAt_of_isComplete_with_param
   refine MeasurableSet.iInter (fun _ ↦ ?_)
   refine MeasurableSet.iInter (fun _ ↦ ?_)
   refine MeasurableSet.iInter (fun _ ↦ ?_)
-  have : ProperSpace E := properSpace_of_locallyCompactSpace 𝕜
+  have : ProperSpace E := .of_locallyCompactSpace 𝕜
   exact (isOpen_B_with_param hf K).measurableSet
 
 variable (𝕜)
@@ -991,7 +991,7 @@ theorem stronglyMeasurable_deriv_with_param [LocallyCompactSpace 𝕜] [Measurab
     StronglyMeasurable (fun (p : α × 𝕜) ↦ deriv (f p.1) p.2) := by
   borelize F
   rcases h.out with hα|hF
-  · have : ProperSpace 𝕜 := properSpace_of_locallyCompactSpace 𝕜
+  · have : ProperSpace 𝕜 := .of_locallyCompactSpace 𝕜
     apply stronglyMeasurable_iff_measurable_separable.2 ⟨measurable_deriv_with_param hf, ?_⟩
     have : range (fun (p : α × 𝕜) ↦ deriv (f p.1) p.2)
         ⊆ closure (Submodule.span 𝕜 (range f.uncurry)) := by

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -5,6 +5,7 @@ Authors: Sébastien Gouëzel, Yury Kudryashov
 -/
 import Mathlib.Analysis.Calculus.Deriv.Basic
 import Mathlib.Analysis.Calculus.Deriv.Slope
+import Mathlib.Analysis.NormedSpace.FiniteDimension
 import Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap
 import Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic
 

@@ -201,7 +201,7 @@ theorem norm_sub_le_of_mem_A {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
         · simp only [le_of_lt (half_pos hr), mem_closedBall, dist_self]
         · simp only [dist_eq_norm, add_sub_cancel', mem_closedBall, ylt.le]
     _ = 2 * ε * r := by ring
-    _ ≤ 2 * ε * (2 * ‖c‖ * ‖y‖) := (mul_le_mul_of_nonneg_left ley (mul_nonneg (by norm_num) hε.le))
+    _ ≤ 2 * ε * (2 * ‖c‖ * ‖y‖) := by gcongr
     _ = 4 * ‖c‖ * ε * ‖y‖ := by ring
 #align fderiv_measurable_aux.norm_sub_le_of_mem_A FDerivMeasurableAux.norm_sub_le_of_mem_A
 
@@ -211,7 +211,7 @@ theorem differentiable_set_subset_D :
   intro x hx
   rw [D, mem_iInter]
   intro e
-  have : (0 : ℝ) < (1 / 2) ^ e := pow_pos (by norm_num) _
+  have : (0 : ℝ) < (1 / 2) ^ e := by positivity
   rcases mem_A_of_differentiable this hx.1 with ⟨R, R_pos, hR⟩
   obtain ⟨n, hn⟩ : ∃ n : ℕ, (1 / 2) ^ n < R :=
     exists_pow_lt_of_lt_one R_pos (by norm_num : (1 : ℝ) / 2 < 1)
@@ -226,7 +226,6 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     D f K ⊆ { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } := by
   have P : ∀ {n : ℕ}, (0 : ℝ) < (1 / 2) ^ n := fun {n} => pow_pos (by norm_num) n
   rcases NormedField.exists_one_lt_norm 𝕜 with ⟨c, hc⟩
-  have cpos : 0 < ‖c‖ := lt_trans zero_lt_one hc
   intro x hx
   have :
     ∀ e : ℕ, ∃ n : ℕ, ∀ p q, n ≤ p → n ≤ q →
@@ -285,13 +284,13 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     rw [Metric.cauchySeq_iff']
     intro ε εpos
     obtain ⟨e, he⟩ : ∃ e : ℕ, (1 / 2) ^ e < ε / (12 * ‖c‖) :=
-      exists_pow_lt_of_lt_one (div_pos εpos (mul_pos (by norm_num) cpos)) (by norm_num)
+      exists_pow_lt_of_lt_one (by positivity) (by norm_num)
     refine' ⟨e, fun e' he' => _⟩
     rw [dist_comm, dist_eq_norm]
     calc
       ‖L0 e - L0 e'‖ ≤ 12 * ‖c‖ * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
       _ < 12 * ‖c‖ * (ε / (12 * ‖c‖)) := by gcongr
-      _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0), ne_of_gt cpos]; ring
+      _ = ε := by field_simp; ring
   -- As it is Cauchy, the sequence `L0` converges, to a limit `f'` in `K`.
   obtain ⟨f', f'K, hf'⟩ : ∃ f' ∈ K, Tendsto L0 atTop (𝓝 f') :=
     cauchySeq_tendsto_of_isComplete hK (fun e => (hn e (n e) (n e) le_rfl le_rfl).1) this
@@ -338,7 +337,7 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     have J1 : ‖f (x + y) - f x - L e (n e) m (x + y - x)‖ ≤ (1 / 2) ^ e * (1 / 2) ^ m := by
       apply le_of_mem_A (hn e (n e) m le_rfl m_ge).2.2
       · simp only [mem_closedBall, dist_self]
-        exact div_nonneg (le_of_lt P) zero_le_two
+        positivity
       · simpa only [dist_eq_norm, add_sub_cancel', mem_closedBall, pow_succ', mul_one_div] using
           h'k
     have J2 : ‖f (x + y) - f x - L e (n e) m y‖ ≤ 4 * (1 / 2) ^ e * ‖y‖ :=
@@ -346,15 +345,13 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
         ‖f (x + y) - f x - L e (n e) m y‖ ≤ (1 / 2) ^ e * (1 / 2) ^ m := by
           simpa only [add_sub_cancel'] using J1
         _ = 4 * (1 / 2) ^ e * (1 / 2) ^ (m + 2) := by field_simp; ring
-        _ ≤ 4 * (1 / 2) ^ e * ‖y‖ :=
-          mul_le_mul_of_nonneg_left (le_of_lt hk) (mul_nonneg (by norm_num) (le_of_lt P))
+        _ ≤ 4 * (1 / 2) ^ e * ‖y‖ := by gcongr
     -- use the previous estimates to see that `f (x + y) - f x - f' y` is small.
     calc
       ‖f (x + y) - f x - f' y‖ = ‖f (x + y) - f x - L e (n e) m y + (L e (n e) m - f') y‖ :=
         congr_arg _ (by simp)
       _ ≤ 4 * (1 / 2) ^ e * ‖y‖ + 12 * ‖c‖ * (1 / 2) ^ e * ‖y‖ :=
-        (norm_add_le_of_le J2
-          ((le_op_norm _ _).trans (mul_le_mul_of_nonneg_right (Lf' _ _ m_ge) (norm_nonneg _))))
+        norm_add_le_of_le J2 <| (le_op_norm _ _).trans <| by gcongr; exact Lf' _ _ m_ge
       _ = (4 + 12 * ‖c‖) * ‖y‖ * (1 / 2) ^ e := by ring
       _ ≤ (4 + 12 * ‖c‖) * ‖y‖ * (ε / (4 + 12 * ‖c‖)) := by gcongr
       _ = ε * ‖y‖ := by field_simp [ne_of_gt pos]; ring
@@ -505,7 +502,7 @@ theorem measurableSet_B {K : Set F} {r s ε : ℝ} : MeasurableSet (B f K r s ε
 
 theorem A_mono (L : F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : A f L r ε ⊆ A f L r δ := by
   rintro x ⟨r', r'r, hr'⟩
-  refine' ⟨r', r'r, fun y hy z hz => (hr' y hy z hz).trans (mul_le_mul_of_nonneg_right h _)⟩
+  refine ⟨r', r'r, fun y hy z hz => (hr' y hy z hz).trans (mul_le_mul_of_nonneg_right h ?_)⟩
   linarith [hy.1, hy.2, r'r.2]
 #align right_deriv_measurable_aux.A_mono RightDerivMeasurableAux.A_mono
 
@@ -554,10 +551,9 @@ theorem norm_sub_le_of_mem_A {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F}
         ‖f (x + r / 2) - f x - (x + r / 2 - x) • L₂ -
             (f (x + r / 2) - f x - (x + r / 2 - x) • L₁)‖ :=
       by simp [smul_sub]
-    _ ≤
-        ‖f (x + r / 2) - f x - (x + r / 2 - x) • L₂‖ +
+    _ ≤ ‖f (x + r / 2) - f x - (x + r / 2 - x) • L₂‖ +
           ‖f (x + r / 2) - f x - (x + r / 2 - x) • L₁‖ :=
-      (norm_sub_le _ _)
+      norm_sub_le _ _
     _ ≤ ε * r + ε * r := by
       apply add_le_add
       · apply le_of_mem_A h₂ <;> simp [(half_pos hr).le]
@@ -701,24 +697,20 @@ theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
         ‖f y - f x - (y - x) • L e (n e) m‖ ≤ (1 / 2) ^ e * (1 / 2) ^ m := by
           apply le_of_mem_A (hn e (n e) m le_rfl m_ge).2.2
           · simp only [one_div, inv_pow, left_mem_Icc, le_add_iff_nonneg_right]
-            exact div_nonneg (inv_nonneg.2 (pow_nonneg zero_le_two _)) zero_le_two
+            positivity
           · simp only [pow_add, tsub_le_iff_left] at h'k
             simpa only [hy.1, mem_Icc, true_and_iff, one_div, pow_one] using h'k
         _ = 4 * (1 / 2) ^ e * (1 / 2) ^ (m + 2) := by field_simp; ring
-        _ ≤ 4 * (1 / 2) ^ e * (y - x) :=
-          (mul_le_mul_of_nonneg_left (le_of_lt hk) (mul_nonneg (by norm_num) (le_of_lt P)))
+        _ ≤ 4 * (1 / 2) ^ e * (y - x) := by gcongr
         _ = 4 * (1 / 2) ^ e * ‖y - x‖ := by rw [Real.norm_of_nonneg yzero.le]
-
     calc
       ‖f y - f x - (y - x) • f'‖ =
           ‖f y - f x - (y - x) • L e (n e) m + (y - x) • (L e (n e) m - f')‖ :=
         by simp only [smul_sub, sub_add_sub_cancel]
       _ ≤ 4 * (1 / 2) ^ e * ‖y - x‖ + ‖y - x‖ * (12 * (1 / 2) ^ e) :=
-        (norm_add_le_of_le J
-          (by rw [norm_smul]; exact mul_le_mul_of_nonneg_left (Lf' _ _ m_ge) (norm_nonneg _)))
+        norm_add_le_of_le J <| by rw [norm_smul]; gcongr; exact Lf' _ _ m_ge
       _ = 16 * ‖y - x‖ * (1 / 2) ^ e := by ring
-      _ ≤ 16 * ‖y - x‖ * (ε / 16) :=
-        (mul_le_mul_of_nonneg_left he.le (mul_nonneg (by norm_num) (norm_nonneg _)))
+      _ ≤ 16 * ‖y - x‖ * (ε / 16) := by gcongr
       _ = ε * ‖y - x‖ := by ring
 
   rw [← this.derivWithin (uniqueDiffOn_Ici x x Set.left_mem_Ici)] at f'K

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

@@ -459,10 +459,8 @@ namespace RightDerivMeasurableAux
 at scale `r` by the linear map `h ↦ h • L`, up to an error `ε`. We tweak the definition to
 make sure that this is open on the right. -/
 def A (f : ℝ → F) (L : F) (r ε : ℝ) : Set ℝ :=
-  { x |
-    ∃ r' ∈ Ioc (r / 2) r,
-      ∀ (y) (_ : y ∈ Icc x (x + r')) (z) (_ : z ∈ Icc x (x + r')),
-        ‖f z - f y - (z - y) • L‖ ≤ ε * r }
+  { x | ∃ r' ∈ Ioc (r / 2) r, ∀ᵉ (y ∈ Icc x (x + r')) (z ∈ Icc x (x + r')),
+    ‖f z - f y - (z - y) • L‖ ≤ ε * r }
 #align right_deriv_measurable_aux.A RightDerivMeasurableAux.A
 
 /-- The set `B f K r s ε` is the set of points `x` around which there exists a vector

This way we can easily change the definition so that it works for topological vector spaces without generalizing any of the theorems right away.

@@ -163,22 +163,21 @@ theorem le_of_mem_A {r ε : ℝ} {L : E →L[𝕜] F} {x : E} (hx : x ∈ A f L
 
 theorem mem_A_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : DifferentiableAt 𝕜 f x) :
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (fderiv 𝕜 f x) r ε := by
-  have := hx.hasFDerivAt
-  simp only [HasFDerivAt, HasFDerivAtFilter, isLittleO_iff] at this
   let δ := (ε / 2) / 2
-  have hδ : 0 < δ := by positivity
-  rcases eventually_nhds_iff_ball.1 (this hδ) with ⟨R, R_pos, hR⟩
+  obtain ⟨R, R_pos, hR⟩ :
+      ∃ R > 0, ∀ y ∈ ball x R, ‖f y - f x - fderiv 𝕜 f x (y - x)‖ ≤ δ * ‖y - x‖ :=
+    eventually_nhds_iff_ball.1 <| hx.hasFDerivAt.isLittleO.bound <| by positivity
   refine' ⟨R, R_pos, fun r hr => _⟩
-  have : r ∈ Ioc (r / 2) r := ⟨half_lt_self hr.1, le_rfl⟩
+  have : r ∈ Ioc (r / 2) r := right_mem_Ioc.2 <| half_lt_self hr.1
   refine' ⟨r, this, fun y hy z hz => _⟩
   calc
     ‖f z - f y - (fderiv 𝕜 f x) (z - y)‖ =
         ‖f z - f x - (fderiv 𝕜 f x) (z - x) - (f y - f x - (fderiv 𝕜 f x) (y - x))‖ :=
-      by congr 1; simp only [ContinuousLinearMap.map_sub]; abel
+      by simp only [map_sub]; abel_nf
     _ ≤ ‖f z - f x - (fderiv 𝕜 f x) (z - x)‖ + ‖f y - f x - (fderiv 𝕜 f x) (y - x)‖ :=
-      (norm_sub_le _ _)
+      norm_sub_le _ _
     _ ≤ δ * ‖z - x‖ + δ * ‖y - x‖ :=
-      (add_le_add (hR _ (lt_trans (mem_ball.1 hz) hr.2)) (hR _ (lt_trans (mem_ball.1 hy) hr.2)))
+      add_le_add (hR _ (ball_subset_ball hr.2.le hz)) (hR _ (ball_subset_ball hr.2.le hy))
     _ ≤ δ * r + δ * r := by rw [mem_ball_iff_norm] at hz hy; gcongr
     _ = (ε / 2) * r := by ring
     _ < ε * r := by gcongr; exacts [hr.1, half_lt_self hε]

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

Algebra.GroupPower.Order

• pow_mono → pow_right_mono
• pow_le_pow → pow_le_pow_right
• pow_le_pow_of_le_left → pow_le_pow_left
• pow_lt_pow_of_lt_left → pow_lt_pow_left
• strictMonoOn_pow → pow_left_strictMonoOn
• pow_strictMono_right → pow_right_strictMono
• pow_lt_pow → pow_lt_pow_right
• pow_lt_pow_iff → pow_lt_pow_iff_right
• pow_le_pow_iff → pow_le_pow_iff_right
• self_lt_pow → lt_self_pow
• strictAnti_pow → pow_right_strictAnti
• pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
• pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
• lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
• le_of_pow_le_pow → le_of_pow_le_pow_left
• pow_lt_pow₀ → pow_lt_pow_right₀

Algebra.GroupPower.CovariantClass

• pow_le_pow_of_le_left' → pow_le_pow_left'
• nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
• pow_lt_pow' → pow_lt_pow_right'
• nsmul_lt_nsmul → nsmul_lt_nsmul_left
• pow_strictMono_left → pow_right_strictMono'
• nsmul_strictMono_right → nsmul_left_strictMono
• StrictMono.pow_right' → StrictMono.pow_const
• StrictMono.nsmul_left → StrictMono.const_nsmul
• pow_strictMono_right' → pow_left_strictMono
• nsmul_strictMono_left → nsmul_right_strictMono
• Monotone.pow_right → Monotone.pow_const
• Monotone.nsmul_left → Monotone.const_nsmul
• lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
• lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
• pow_le_pow' → pow_le_pow_right'
• nsmul_le_nsmul → nsmul_le_nsmul_left
• pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
• nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
• le_of_pow_le_pow' → le_of_pow_le_pow_left'
• le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
• pow_le_pow_iff' → pow_le_pow_iff_right'
• nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
• pow_lt_pow_iff' → pow_lt_pow_iff_right'
• nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

Data.Nat.Pow

• Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
• Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
• Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

• pow_le_pow_iff_left
• pow_lt_pow_iff_left
• pow_right_injective
• pow_right_inj
• Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
• Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

• self_le_pow was a duplicate of le_self_pow.
• Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
• Nat.pow_right_strictMono is defeq to pow_right_strictMono.
• Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
• Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

• A bunch of proofs have been golfed.
• Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
• A few Nat lemmas have been protected.
• One docstring has been fixed.

@@ -328,7 +328,7 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     -- the scale is large enough (as `y` is small enough)
     have k_gt : n e < k := by
       have : ((1 : ℝ) / 2) ^ (k + 1) < (1 / 2) ^ (n e + 1) := lt_trans hk y_lt
-      rw [pow_lt_pow_iff_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this
+      rw [pow_lt_pow_iff_right_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this
       linarith
     set m := k - 1
     have m_ge : n e ≤ m := Nat.le_sub_one_of_lt k_gt
@@ -691,7 +691,7 @@ theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     -- the scale is large enough (as `y - x` is small enough)
     have k_gt : n e < k := by
       have : ((1 : ℝ) / 2) ^ (k + 1) < (1 / 2) ^ (n e + 1) := lt_of_lt_of_le hk y_le
-      rw [pow_lt_pow_iff_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this
+      rw [pow_lt_pow_iff_right_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this
       linarith
     set m := k - 1
     have m_ge : n e ≤ m := Nat.le_sub_one_of_lt k_gt

Assorted golf I did while working on a refactor. Submitting as a separate PR.

• Move not_differentiableAt_abs_zero to Calculus.Deriv.Add, golf.
• Rename HasFDerivWithinAt_of_nhdsWithin_eq_bot to HasFDerivWithinAt.of_nhdsWithin_eq_bot, golf.
• Protect Filter.EventuallyEq.rfl.
• Golf here and there.

@@ -115,9 +115,7 @@ namespace FDerivMeasurableAux
 at scale `r` by the linear map `L`, up to an error `ε`. We tweak the definition to make sure that
 this is an open set.-/
 def A (f : E → F) (L : E →L[𝕜] F) (r ε : ℝ) : Set E :=
-  { x |
-    ∃ r' ∈ Ioc (r / 2) r,
-      ∀ (y) (_ : y ∈ ball x r') (z) (_ : z ∈ ball x r'), ‖f z - f y - L (z - y)‖ < ε * r }
+  { x | ∃ r' ∈ Ioc (r / 2) r, ∀ y ∈ ball x r', ∀ z ∈ ball x r', ‖f z - f y - L (z - y)‖ < ε * r }
 #align fderiv_measurable_aux.A FDerivMeasurableAux.A
 
 /-- The set `B f K r s ε` is the set of points `x` around which there exists a continuous linear map
@@ -386,12 +384,7 @@ theorem measurableSet_of_differentiableAt_of_isComplete {K : Set (E →L[𝕜] F
   -- simp [differentiable_set_eq_D K hK, D, isOpen_B.measurableSet, MeasurableSet.iInter,
   --   MeasurableSet.iUnion]
   simp only [D, differentiable_set_eq_D K hK]
-  refine MeasurableSet.iInter fun _ => ?_
-  refine MeasurableSet.iUnion fun _ => ?_
-  refine MeasurableSet.iInter fun _ => ?_
-  refine MeasurableSet.iInter fun _ => ?_
-  refine MeasurableSet.iInter fun _ => ?_
-  refine MeasurableSet.iInter fun _ => ?_
+  repeat apply_rules [MeasurableSet.iUnion, MeasurableSet.iInter] <;> intro
   exact isOpen_B.measurableSet
 #align measurable_set_of_differentiable_at_of_is_complete measurableSet_of_differentiableAt_of_isComplete
 
@@ -753,12 +746,7 @@ theorem measurableSet_of_differentiableWithinAt_Ici_of_isComplete {K : Set F} (h
   -- simp [differentiable_set_eq_d K hK, D, measurableSet_b, MeasurableSet.iInter,
   --   MeasurableSet.iUnion]
   simp only [differentiable_set_eq_D K hK, D]
-  refine MeasurableSet.iInter fun _ => ?_
-  refine MeasurableSet.iUnion fun _ => ?_
-  refine MeasurableSet.iInter fun _ => ?_
-  refine MeasurableSet.iInter fun _ => ?_
-  refine MeasurableSet.iInter fun _ => ?_
-  refine MeasurableSet.iInter fun _ => ?_
+  repeat apply_rules [MeasurableSet.iUnion, MeasurableSet.iInter] <;> intro
   exact measurableSet_B
 #align measurable_set_of_differentiable_within_at_Ici_of_is_complete measurableSet_of_differentiableWithinAt_Ici_of_isComplete
 

@@ -333,7 +333,7 @@ theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       rw [pow_lt_pow_iff_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this
       linarith
     set m := k - 1
-    have m_ge : n e ≤ m := Nat.le_pred_of_lt k_gt
+    have m_ge : n e ≤ m := Nat.le_sub_one_of_lt k_gt
     have km : k = m + 1 := (Nat.succ_pred_eq_of_pos (lt_of_le_of_lt (zero_le _) k_gt)).symm
     rw [km] at hk h'k
     -- `f` is well approximated by `L e (n e) k` at the relevant scale
@@ -701,7 +701,7 @@ theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
       rw [pow_lt_pow_iff_of_lt_one (by norm_num : (0 : ℝ) < 1 / 2) (by norm_num)] at this
       linarith
     set m := k - 1
-    have m_ge : n e ≤ m := Nat.le_pred_of_lt k_gt
+    have m_ge : n e ≤ m := Nat.le_sub_one_of_lt k_gt
     have km : k = m + 1 := (Nat.succ_pred_eq_of_pos (lt_of_le_of_lt (zero_le _) k_gt)).symm
     rw [km] at hk h'k
     -- `f` is well approximated by `L e (n e) k` at the relevant scale

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

@@ -504,7 +504,7 @@ theorem B_mem_nhdsWithin_Ioi {K : Set F} {r s ε x : ℝ} (hx : x ∈ B f K r s
     B f K r s ε ∈ 𝓝[>] x := by
   obtain ⟨L, LK, hL₁, hL₂⟩ : ∃ L : F, L ∈ K ∧ x ∈ A f L r ε ∧ x ∈ A f L s ε := by
     simpa only [B, mem_iUnion, mem_inter_iff, exists_prop] using hx
-  filter_upwards [A_mem_nhdsWithin_Ioi hL₁, A_mem_nhdsWithin_Ioi hL₂]with y hy₁ hy₂
+  filter_upwards [A_mem_nhdsWithin_Ioi hL₁, A_mem_nhdsWithin_Ioi hL₂] with y hy₁ hy₂
   simp only [B, mem_iUnion, mem_inter_iff, exists_prop]
   exact ⟨L, LK, hy₁, hy₂⟩
 #align right_deriv_measurable_aux.B_mem_nhds_within_Ioi RightDerivMeasurableAux.B_mem_nhdsWithin_Ioi
@@ -683,7 +683,7 @@ theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     have xmem : x ∈ Ico x (x + (1 / 2) ^ (n e + 1)) := by
       simp only [one_div, left_mem_Ico, lt_add_iff_pos_right, inv_pos, pow_pos, zero_lt_two,
         zero_lt_one]
-    filter_upwards [Icc_mem_nhdsWithin_Ici xmem]with y hy
+    filter_upwards [Icc_mem_nhdsWithin_Ici xmem] with y hy
     -- We need to show that `f y - f x - f' (y - x)` is small. For this, we will work at scale
     -- `k` where `k` is chosen with `‖y - x‖ ∼ 2 ^ (-k)`.
     rcases eq_or_lt_of_le hy.1 with (rfl | xy)

@@ -167,7 +167,7 @@ theorem mem_A_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (fderiv 𝕜 f x) r ε := by
   have := hx.hasFDerivAt
   simp only [HasFDerivAt, HasFDerivAtFilter, isLittleO_iff] at this
-  let δ := (ε/2)/2
+  let δ := (ε / 2) / 2
   have hδ : 0 < δ := by positivity
   rcases eventually_nhds_iff_ball.1 (this hδ) with ⟨R, R_pos, hR⟩
   refine' ⟨R, R_pos, fun r hr => _⟩
@@ -182,15 +182,13 @@ theorem mem_A_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
     _ ≤ δ * ‖z - x‖ + δ * ‖y - x‖ :=
       (add_le_add (hR _ (lt_trans (mem_ball.1 hz) hr.2)) (hR _ (lt_trans (mem_ball.1 hy) hr.2)))
     _ ≤ δ * r + δ * r := by rw [mem_ball_iff_norm] at hz hy; gcongr
-    _ = (ε /2) * r := by ring
+    _ = (ε / 2) * r := by ring
     _ < ε * r := by gcongr; exacts [hr.1, half_lt_self hε]
 #align fderiv_measurable_aux.mem_A_of_differentiable FDerivMeasurableAux.mem_A_of_differentiable
 
 theorem norm_sub_le_of_mem_A {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0 < ε) (hr : 0 < r) {x : E}
     {L₁ L₂ : E →L[𝕜] F} (h₁ : x ∈ A f L₁ r ε) (h₂ : x ∈ A f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ‖c‖ * ε := by
-  have : 0 ≤ 4 * ‖c‖ * ε :=
-    mul_nonneg (mul_nonneg (by norm_num : (0 : ℝ) ≤ 4) (norm_nonneg _)) hε.le
-  refine' op_norm_le_of_shell (half_pos hr) this hc _
+  refine' op_norm_le_of_shell (half_pos hr) (by positivity) hc _
   intro y ley ylt
   rw [div_div, div_le_iff' (mul_pos (by norm_num : (0 : ℝ) < 2) (zero_lt_one.trans hc))] at ley
   calc
@@ -883,7 +881,10 @@ lemma isOpen_A_with_param {r s : ℝ} (hf : Continuous f.uncurry) (L : E →L[
   obtain ⟨b, b_lt, hb⟩ : ∃ b, b < s * r ∧ ∀ y ∈ closedBall x t, ∀ z ∈ closedBall x t,
       ‖f a z - f a y - (L z - L y)‖ ≤ b := by
     have B : Continuous (fun (p : E × E) ↦ ‖f a p.2 - f a p.1 - (L p.2 - L p.1)‖) := by
-      continuity
+      -- `continuity` took several seconds to solve this.
+      refine continuous_norm.comp' <| Continuous.sub ?_ ?_
+      · exact ha.comp' continuous_snd |>.sub <| ha.comp' continuous_fst
+      · exact L.continuous.comp' continuous_snd |>.sub <| L.continuous.comp' continuous_fst
     have C : (closedBall x t ×ˢ closedBall x t).Nonempty := by simp; linarith
     rcases ((isCompact_closedBall x t).prod (isCompact_closedBall x t)).exists_isMaxOn
       C B.continuousOn with ⟨p, pt, hp⟩
@@ -892,13 +893,16 @@ lemma isOpen_A_with_param {r s : ℝ} (hf : Continuous f.uncurry) (L : E →L[
       hr p.1 (pt.1.trans_lt htr') p.2 (pt.2.trans_lt htr'), fun y hy z hz ↦ ?_⟩
     have D : (y, z) ∈ closedBall x t ×ˢ closedBall x t := mem_prod.2 ⟨hy, hz⟩
     exact hp D
-  obtain ⟨ε, εpos, hε⟩ : ∃ ε, 0 < ε ∧ b + 2 * ε < s * r := ⟨(s * r - b)/3, by linarith, by linarith⟩
+  obtain ⟨ε, εpos, hε⟩ : ∃ ε, 0 < ε ∧ b + 2 * ε < s * r :=
+    ⟨(s * r - b) / 3, by linarith, by linarith⟩
   obtain ⟨u, u_open, au, hu⟩ : ∃ u, IsOpen u ∧ a ∈ u ∧ ∀ (p : α × E),
       p.1 ∈ u → p.2 ∈ closedBall x t → dist (f.uncurry p) (f.uncurry (a, p.2)) < ε := by
-    have C : Continuous (fun (p : α × E) ↦ f a p.2) := by continuity
+    have C : Continuous (fun (p : α × E) ↦ f a p.2) :=
+      -- `continuity` took several seconds to solve this.
+      ha.comp' continuous_snd
     have D : ({a} ×ˢ closedBall x t).EqOn f.uncurry (fun p ↦ f a p.2) := by
       rintro ⟨b, y⟩ ⟨hb, -⟩
-      simp at hb
+      simp only [mem_singleton_iff] at hb
       simp [hb]
     obtain ⟨v, v_open, sub_v, hv⟩ : ∃ v, IsOpen v ∧ {a} ×ˢ closedBall x t ⊆ v ∧
         ∀ p ∈ v, dist (Function.uncurry f p) (f a p.2) < ε :=

Last prerequisite for Rademacher theorem in #7003.

Along the way, we weaken the second-countability assumptions for strong measurability of the derivative and the right derivative.

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yury Kudryashov
 -/
 import Mathlib.Analysis.Calculus.Deriv.Basic
+import Mathlib.Analysis.Calculus.Deriv.Slope
 import Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap
 import Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic
 
@@ -82,8 +83,7 @@ set_option linter.uppercaseLean3 false -- A B D
 
 noncomputable section
 
-open Set Metric Asymptotics Filter ContinuousLinearMap MeasureTheory
-open TopologicalSpace (SecondCountableTopology)
+open Set Metric Asymptotics Filter ContinuousLinearMap MeasureTheory TopologicalSpace
 open scoped Topology
 
 namespace ContinuousLinearMap
@@ -436,9 +436,12 @@ theorem measurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜] [Mea
 #align measurable_deriv measurable_deriv
 
 theorem stronglyMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜]
-    [SecondCountableTopology F] (f : 𝕜 → F) : StronglyMeasurable (deriv f) := by
+    [h : SecondCountableTopologyEither 𝕜 F] (f : 𝕜 → F) : StronglyMeasurable (deriv f) := by
   borelize F
-  exact (measurable_deriv f).stronglyMeasurable
+  rcases h.out with h𝕜|hF
+  · exact stronglyMeasurable_iff_measurable_separable.2
+      ⟨measurable_deriv f, isSeparable_range_deriv _⟩
+  · exact (measurable_deriv f).stronglyMeasurable
 #align strongly_measurable_deriv stronglyMeasurable_deriv
 
 theorem aemeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜] [MeasurableSpace F]
@@ -447,7 +450,8 @@ theorem aemeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜] [M
 #align ae_measurable_deriv aemeasurable_deriv
 
 theorem aestronglyMeasurable_deriv [MeasurableSpace 𝕜] [OpensMeasurableSpace 𝕜]
-    [SecondCountableTopology F] (f : 𝕜 → F) (μ : Measure 𝕜) : AEStronglyMeasurable (deriv f) μ :=
+    [SecondCountableTopologyEither 𝕜 F] (f : 𝕜 → F) (μ : Measure 𝕜) :
+    AEStronglyMeasurable (deriv f) μ :=
   (stronglyMeasurable_deriv f).aestronglyMeasurable
 #align ae_strongly_measurable_deriv aestronglyMeasurable_deriv
 
@@ -786,10 +790,25 @@ theorem measurable_derivWithin_Ici [MeasurableSpace F] [BorelSpace F] :
       ((measurableSet_of_differentiableWithinAt_Ici _).compl.inter (MeasurableSet.const _))
 #align measurable_deriv_within_Ici measurable_derivWithin_Ici
 
-theorem stronglyMeasurable_derivWithin_Ici [SecondCountableTopology F] :
-    StronglyMeasurable fun x => derivWithin f (Ici x) x := by
+theorem stronglyMeasurable_derivWithin_Ici :
+    StronglyMeasurable (fun x ↦ derivWithin f (Ici x) x) := by
   borelize F
-  exact (measurable_derivWithin_Ici f).stronglyMeasurable
+  apply stronglyMeasurable_iff_measurable_separable.2 ⟨measurable_derivWithin_Ici f, ?_⟩
+  obtain ⟨t, t_count, ht⟩ : ∃ t : Set ℝ, t.Countable ∧ Dense t := exists_countable_dense ℝ
+  suffices H : range (fun x ↦ derivWithin f (Ici x) x) ⊆ closure (Submodule.span ℝ (f '' t)) from
+    IsSeparable.mono (t_count.image f).isSeparable.span.closure H
+  rintro - ⟨x, rfl⟩
+  suffices H' : range (fun y ↦ derivWithin f (Ici x) y) ⊆ closure (Submodule.span ℝ (f '' t)) from
+    H' (mem_range_self _)
+  apply range_derivWithin_subset_closure_span_image
+  calc Ici x
+    = closure (Ioi x ∩ closure t) := by simp [dense_iff_closure_eq.1 ht]
+  _ ⊆ closure (closure (Ioi x ∩ t)) := by
+      apply closure_mono
+      simpa [inter_comm] using (isOpen_Ioi (a := x)).closure_inter (s := t)
+  _ ⊆ closure (Ici x ∩ t) := by
+      rw [closure_closure]
+      exact closure_mono (inter_subset_inter_left _ Ioi_subset_Ici_self)
 #align strongly_measurable_deriv_within_Ici stronglyMeasurable_derivWithin_Ici
 
 theorem aemeasurable_derivWithin_Ici [MeasurableSpace F] [BorelSpace F] (μ : Measure ℝ) :
@@ -797,7 +816,7 @@ theorem aemeasurable_derivWithin_Ici [MeasurableSpace F] [BorelSpace F] (μ : Me
   (measurable_derivWithin_Ici f).aemeasurable
 #align ae_measurable_deriv_within_Ici aemeasurable_derivWithin_Ici
 
-theorem aestronglyMeasurable_derivWithin_Ici [SecondCountableTopology F] (μ : Measure ℝ) :
+theorem aestronglyMeasurable_derivWithin_Ici (μ : Measure ℝ) :
     AEStronglyMeasurable (fun x => derivWithin f (Ici x) x) μ :=
   (stronglyMeasurable_derivWithin_Ici f).aestronglyMeasurable
 #align ae_strongly_measurable_deriv_within_Ici aestronglyMeasurable_derivWithin_Ici
@@ -815,10 +834,9 @@ theorem measurable_derivWithin_Ioi [MeasurableSpace F] [BorelSpace F] :
   simpa [derivWithin_Ioi_eq_Ici] using measurable_derivWithin_Ici f
 #align measurable_deriv_within_Ioi measurable_derivWithin_Ioi
 
-theorem stronglyMeasurable_derivWithin_Ioi [SecondCountableTopology F] :
-    StronglyMeasurable fun x => derivWithin f (Ioi x) x := by
-  borelize F
-  exact (measurable_derivWithin_Ioi f).stronglyMeasurable
+theorem stronglyMeasurable_derivWithin_Ioi :
+    StronglyMeasurable (fun x ↦ derivWithin f (Ioi x) x) := by
+  simpa [derivWithin_Ioi_eq_Ici] using stronglyMeasurable_derivWithin_Ici f
 #align strongly_measurable_deriv_within_Ioi stronglyMeasurable_derivWithin_Ioi
 
 theorem aemeasurable_derivWithin_Ioi [MeasurableSpace F] [BorelSpace F] (μ : Measure ℝ) :
@@ -826,7 +844,7 @@ theorem aemeasurable_derivWithin_Ioi [MeasurableSpace F] [BorelSpace F] (μ : Me
   (measurable_derivWithin_Ioi f).aemeasurable
 #align ae_measurable_deriv_within_Ioi aemeasurable_derivWithin_Ioi
 
-theorem aestronglyMeasurable_derivWithin_Ioi [SecondCountableTopology F] (μ : Measure ℝ) :
+theorem aestronglyMeasurable_derivWithin_Ioi (μ : Measure ℝ) :
     AEStronglyMeasurable (fun x => derivWithin f (Ioi x) x) μ :=
   (stronglyMeasurable_derivWithin_Ioi f).aestronglyMeasurable
 #align ae_strongly_measurable_deriv_within_Ioi aestronglyMeasurable_derivWithin_Ioi
@@ -986,11 +1004,27 @@ theorem measurable_deriv_with_param [LocallyCompactSpace 𝕜] [MeasurableSpace
   simpa only [fderiv_deriv] using measurable_fderiv_apply_const_with_param 𝕜 hf 1
 
 theorem stronglyMeasurable_deriv_with_param [LocallyCompactSpace 𝕜] [MeasurableSpace 𝕜]
-    [OpensMeasurableSpace 𝕜] [SecondCountableTopology F]
+    [OpensMeasurableSpace 𝕜] [h : SecondCountableTopologyEither α F]
     {f : α → 𝕜 → F} (hf : Continuous f.uncurry) :
     StronglyMeasurable (fun (p : α × 𝕜) ↦ deriv (f p.1) p.2) := by
   borelize F
-  exact (measurable_deriv_with_param hf).stronglyMeasurable
+  rcases h.out with hα|hF
+  · have : ProperSpace 𝕜 := properSpace_of_locallyCompactSpace 𝕜
+    apply stronglyMeasurable_iff_measurable_separable.2 ⟨measurable_deriv_with_param hf, ?_⟩
+    have : range (fun (p : α × 𝕜) ↦ deriv (f p.1) p.2)
+        ⊆ closure (Submodule.span 𝕜 (range f.uncurry)) := by
+      rintro - ⟨p, rfl⟩
+      have A : deriv (f p.1) p.2 ∈ closure (Submodule.span 𝕜 (range (f p.1))) := by
+        rw [← image_univ]
+        apply range_deriv_subset_closure_span_image _ dense_univ (mem_range_self _)
+      have B : range (f p.1) ⊆ range (f.uncurry) := by
+        rintro - ⟨x, rfl⟩
+        exact mem_range_self (p.1, x)
+      exact closure_mono (Submodule.span_mono B) A
+    apply (IsSeparable.span _).closure.mono this
+    rw [← image_univ]
+    exact (isSeparable_of_separableSpace univ).image hf
+  · exact (measurable_deriv_with_param hf).stronglyMeasurable
 
 theorem aemeasurable_deriv_with_param [LocallyCompactSpace 𝕜] [MeasurableSpace 𝕜]
     [OpensMeasurableSpace 𝕜] [MeasurableSpace F]
@@ -999,7 +1033,7 @@ theorem aemeasurable_deriv_with_param [LocallyCompactSpace 𝕜] [MeasurableSpac
   (measurable_deriv_with_param hf).aemeasurable
 
 theorem aestronglyMeasurable_deriv_with_param [LocallyCompactSpace 𝕜] [MeasurableSpace 𝕜]
-    [OpensMeasurableSpace 𝕜] [SecondCountableTopology F]
+    [OpensMeasurableSpace 𝕜] [SecondCountableTopologyEither α F]
     {f : α → 𝕜 → F} (hf : Continuous f.uncurry) (μ : Measure (α × 𝕜)) :
     AEStronglyMeasurable (fun (p : α × 𝕜) ↦ deriv (f p.1) p.2) μ :=
   (stronglyMeasurable_deriv_with_param hf).aestronglyMeasurable

We reuse the main results that were proved for functions not depending on a parameter (but we need to tweak the definition of the set A to let it cover all cases, replacing a large inequality by a strict one).

@@ -25,6 +25,11 @@ We also show the same results for the right derivative on the real line
 (see `measurable_derivWithin_Ici` and `measurable_derivWithin_Ioi`), following the same
 proof strategy.
 
+We also prove measurability statements for functions depending on a parameter: for `f : α → E → F`,
+we show the measurability of `(p : α × E) ↦ fderiv 𝕜 (f p.1) p.2`. This requires additional
+assumptions. We give versions of the above statements (appending `with_param` to their names) when
+`f` is continuous and `E` is locally compact.
+
 ## Implementation
 
 We give a proof that avoids second-countability issues, by expressing the differentiability set
@@ -112,7 +117,7 @@ this is an open set.-/
 def A (f : E → F) (L : E →L[𝕜] F) (r ε : ℝ) : Set E :=
   { x |
     ∃ r' ∈ Ioc (r / 2) r,
-      ∀ (y) (_ : y ∈ ball x r') (z) (_ : z ∈ ball x r'), ‖f z - f y - L (z - y)‖ ≤ ε * r }
+      ∀ (y) (_ : y ∈ ball x r') (z) (_ : z ∈ ball x r'), ‖f z - f y - L (z - y)‖ < ε * r }
 #align fderiv_measurable_aux.A FDerivMeasurableAux.A
 
 /-- The set `B f K r s ε` is the set of points `x` around which there exists a continuous linear map
@@ -129,7 +134,7 @@ def D (f : E → F) (K : Set (E →L[𝕜] F)) : Set E :=
   ⋂ e : ℕ, ⋃ n : ℕ, ⋂ (p ≥ n) (q ≥ n), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ e)
 #align fderiv_measurable_aux.D FDerivMeasurableAux.D
 
-theorem isOpen_a (L : E →L[𝕜] F) (r ε : ℝ) : IsOpen (A f L r ε) := by
+theorem isOpen_A (L : E →L[𝕜] F) (r ε : ℝ) : IsOpen (A f L r ε) := by
   rw [Metric.isOpen_iff]
   rintro x ⟨r', r'_mem, hr'⟩
   obtain ⟨s, s_gt, s_lt⟩ : ∃ s : ℝ, r / 2 < s ∧ s < r' := exists_between r'_mem.1
@@ -138,33 +143,33 @@ theorem isOpen_a (L : E →L[𝕜] F) (r ε : ℝ) : IsOpen (A f L r ε) := by
   have B : ball x' s ⊆ ball x r' := ball_subset (le_of_lt hx')
   intro y hy z hz
   exact hr' y (B hy) z (B hz)
-#align fderiv_measurable_aux.is_open_A FDerivMeasurableAux.isOpen_a
+#align fderiv_measurable_aux.is_open_A FDerivMeasurableAux.isOpen_A
 
-theorem isOpen_b {K : Set (E →L[𝕜] F)} {r s ε : ℝ} : IsOpen (B f K r s ε) := by
-  -- Porting note: was
-  -- simp [B, isOpen_iUnion, IsOpen.inter, isOpen_a]
-  simp only [B]
-  exact isOpen_iUnion fun _ => isOpen_iUnion fun _ => (isOpen_a _ _ _).inter (isOpen_a _ _ _)
-#align fderiv_measurable_aux.is_open_B FDerivMeasurableAux.isOpen_b
+theorem isOpen_B {K : Set (E →L[𝕜] F)} {r s ε : ℝ} : IsOpen (B f K r s ε) := by
+  simp [B, isOpen_biUnion, IsOpen.inter, isOpen_A]
+#align fderiv_measurable_aux.is_open_B FDerivMeasurableAux.isOpen_B
 
-theorem a_mono (L : E →L[𝕜] F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : A f L r ε ⊆ A f L r δ := by
+theorem A_mono (L : E →L[𝕜] F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : A f L r ε ⊆ A f L r δ := by
   rintro x ⟨r', r'r, hr'⟩
-  refine' ⟨r', r'r, fun y hy z hz => (hr' y hy z hz).trans (mul_le_mul_of_nonneg_right h _)⟩
+  refine' ⟨r', r'r, fun y hy z hz => (hr' y hy z hz).trans_le (mul_le_mul_of_nonneg_right h _)⟩
   linarith [mem_ball.1 hy, r'r.2, @dist_nonneg _ _ y x]
-#align fderiv_measurable_aux.A_mono FDerivMeasurableAux.a_mono
+#align fderiv_measurable_aux.A_mono FDerivMeasurableAux.A_mono
 
-theorem le_of_mem_a {r ε : ℝ} {L : E →L[𝕜] F} {x : E} (hx : x ∈ A f L r ε) {y z : E}
+theorem le_of_mem_A {r ε : ℝ} {L : E →L[𝕜] F} {x : E} (hx : x ∈ A f L r ε) {y z : E}
     (hy : y ∈ closedBall x (r / 2)) (hz : z ∈ closedBall x (r / 2)) :
     ‖f z - f y - L (z - y)‖ ≤ ε * r := by
   rcases hx with ⟨r', r'mem, hr'⟩
+  apply le_of_lt
   exact hr' _ ((mem_closedBall.1 hy).trans_lt r'mem.1) _ ((mem_closedBall.1 hz).trans_lt r'mem.1)
-#align fderiv_measurable_aux.le_of_mem_A FDerivMeasurableAux.le_of_mem_a
+#align fderiv_measurable_aux.le_of_mem_A FDerivMeasurableAux.le_of_mem_A
 
-theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : DifferentiableAt 𝕜 f x) :
+theorem mem_A_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : DifferentiableAt 𝕜 f x) :
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (fderiv 𝕜 f x) r ε := by
   have := hx.hasFDerivAt
   simp only [HasFDerivAt, HasFDerivAtFilter, isLittleO_iff] at this
-  rcases eventually_nhds_iff_ball.1 (this (half_pos hε)) with ⟨R, R_pos, hR⟩
+  let δ := (ε/2)/2
+  have hδ : 0 < δ := by positivity
+  rcases eventually_nhds_iff_ball.1 (this hδ) with ⟨R, R_pos, hR⟩
   refine' ⟨R, R_pos, fun r hr => _⟩
   have : r ∈ Ioc (r / 2) r := ⟨half_lt_self hr.1, le_rfl⟩
   refine' ⟨r, this, fun y hy z hz => _⟩
@@ -174,13 +179,14 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
       by congr 1; simp only [ContinuousLinearMap.map_sub]; abel
     _ ≤ ‖f z - f x - (fderiv 𝕜 f x) (z - x)‖ + ‖f y - f x - (fderiv 𝕜 f x) (y - x)‖ :=
       (norm_sub_le _ _)
-    _ ≤ ε / 2 * ‖z - x‖ + ε / 2 * ‖y - x‖ :=
+    _ ≤ δ * ‖z - x‖ + δ * ‖y - x‖ :=
       (add_le_add (hR _ (lt_trans (mem_ball.1 hz) hr.2)) (hR _ (lt_trans (mem_ball.1 hy) hr.2)))
-    _ ≤ ε / 2 * r + ε / 2 * r := by rw [mem_ball_iff_norm] at hz hy; gcongr
-    _ = ε * r := by ring
-#align fderiv_measurable_aux.mem_A_of_differentiable FDerivMeasurableAux.mem_a_of_differentiable
+    _ ≤ δ * r + δ * r := by rw [mem_ball_iff_norm] at hz hy; gcongr
+    _ = (ε /2) * r := by ring
+    _ < ε * r := by gcongr; exacts [hr.1, half_lt_self hε]
+#align fderiv_measurable_aux.mem_A_of_differentiable FDerivMeasurableAux.mem_A_of_differentiable
 
-theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0 < ε) (hr : 0 < r) {x : E}
+theorem norm_sub_le_of_mem_A {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0 < ε) (hr : 0 < r) {x : E}
     {L₁ L₂ : E →L[𝕜] F} (h₁ : x ∈ A f L₁ r ε) (h₂ : x ∈ A f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ‖c‖ * ε := by
   have : 0 ≤ 4 * ‖c‖ * ε :=
     mul_nonneg (mul_nonneg (by norm_num : (0 : ℝ) ≤ 4) (norm_nonneg _)) hε.le
@@ -193,35 +199,35 @@ theorem norm_sub_le_of_mem_a {c : 𝕜} (hc : 1 < ‖c‖) {r ε : ℝ} (hε : 0
     _ ≤ ‖f (x + y) - f x - L₂ (x + y - x)‖ + ‖f (x + y) - f x - L₁ (x + y - x)‖ := (norm_sub_le _ _)
     _ ≤ ε * r + ε * r := by
       apply add_le_add
-      · apply le_of_mem_a h₂
+      · apply le_of_mem_A h₂
         · simp only [le_of_lt (half_pos hr), mem_closedBall, dist_self]
         · simp only [dist_eq_norm, add_sub_cancel', mem_closedBall, ylt.le]
-      · apply le_of_mem_a h₁
+      · apply le_of_mem_A h₁
         · simp only [le_of_lt (half_pos hr), mem_closedBall, dist_self]
         · simp only [dist_eq_norm, add_sub_cancel', mem_closedBall, ylt.le]
     _ = 2 * ε * r := by ring
     _ ≤ 2 * ε * (2 * ‖c‖ * ‖y‖) := (mul_le_mul_of_nonneg_left ley (mul_nonneg (by norm_num) hε.le))
     _ = 4 * ‖c‖ * ε * ‖y‖ := by ring
-#align fderiv_measurable_aux.norm_sub_le_of_mem_A FDerivMeasurableAux.norm_sub_le_of_mem_a
+#align fderiv_measurable_aux.norm_sub_le_of_mem_A FDerivMeasurableAux.norm_sub_le_of_mem_A
 
 /-- Easy inclusion: a differentiability point with derivative in `K` belongs to `D f K`. -/
-theorem differentiable_set_subset_d :
+theorem differentiable_set_subset_D :
     { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } ⊆ D f K := by
   intro x hx
   rw [D, mem_iInter]
   intro e
   have : (0 : ℝ) < (1 / 2) ^ e := pow_pos (by norm_num) _
-  rcases mem_a_of_differentiable this hx.1 with ⟨R, R_pos, hR⟩
+  rcases mem_A_of_differentiable this hx.1 with ⟨R, R_pos, hR⟩
   obtain ⟨n, hn⟩ : ∃ n : ℕ, (1 / 2) ^ n < R :=
     exists_pow_lt_of_lt_one R_pos (by norm_num : (1 : ℝ) / 2 < 1)
   simp only [mem_iUnion, mem_iInter, B, mem_inter_iff]
   refine' ⟨n, fun p hp q hq => ⟨fderiv 𝕜 f x, hx.2, ⟨_, _⟩⟩⟩ <;>
     · refine' hR _ ⟨pow_pos (by norm_num) _, lt_of_le_of_lt _ hn⟩
       exact pow_le_pow_of_le_one (by norm_num) (by norm_num) (by assumption)
-#align fderiv_measurable_aux.differentiable_set_subset_D FDerivMeasurableAux.differentiable_set_subset_d
+#align fderiv_measurable_aux.differentiable_set_subset_D FDerivMeasurableAux.differentiable_set_subset_D
 
 /-- Harder inclusion: at a point in `D f K`, the function `f` has a derivative, in `K`. -/
-theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete K) :
+theorem D_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete K) :
     D f K ⊆ { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } := by
   have P : ∀ {n : ℕ}, (0 : ℝ) < (1 / 2) ^ n := fun {n} => pow_pos (by norm_num) n
   rcases NormedField.exists_one_lt_norm 𝕜 with ⟨c, hc⟩
@@ -258,26 +264,24 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     have J1 : ‖L e p q - L e p r‖ ≤ 4 * ‖c‖ * (1 / 2) ^ e := by
       have I1 : x ∈ A f (L e p q) ((1 / 2) ^ p) ((1 / 2) ^ e) := (hn e p q hp hq).2.1
       have I2 : x ∈ A f (L e p r) ((1 / 2) ^ p) ((1 / 2) ^ e) := (hn e p r hp (le_max_left _ _)).2.1
-      exact norm_sub_le_of_mem_a hc P P I1 I2
+      exact norm_sub_le_of_mem_A hc P P I1 I2
     have J2 : ‖L e p r - L e' p' r‖ ≤ 4 * ‖c‖ * (1 / 2) ^ e := by
       have I1 : x ∈ A f (L e p r) ((1 / 2) ^ r) ((1 / 2) ^ e) := (hn e p r hp (le_max_left _ _)).2.2
       have I2 : x ∈ A f (L e' p' r) ((1 / 2) ^ r) ((1 / 2) ^ e') :=
         (hn e' p' r hp' (le_max_right _ _)).2.2
-      exact norm_sub_le_of_mem_a hc P P I1 (a_mono _ _ I I2)
+      exact norm_sub_le_of_mem_A hc P P I1 (A_mono _ _ I I2)
     have J3 : ‖L e' p' r - L e' p' q'‖ ≤ 4 * ‖c‖ * (1 / 2) ^ e := by
       have I1 : x ∈ A f (L e' p' r) ((1 / 2) ^ p') ((1 / 2) ^ e') :=
         (hn e' p' r hp' (le_max_right _ _)).2.1
       have I2 : x ∈ A f (L e' p' q') ((1 / 2) ^ p') ((1 / 2) ^ e') := (hn e' p' q' hp' hq').2.1
-      exact norm_sub_le_of_mem_a hc P P (a_mono _ _ I I1) (a_mono _ _ I I2)
+      exact norm_sub_le_of_mem_A hc P P (A_mono _ _ I I1) (A_mono _ _ I I2)
     calc
       ‖L e p q - L e' p' q'‖ =
           ‖L e p q - L e p r + (L e p r - L e' p' r) + (L e' p' r - L e' p' q')‖ :=
         by congr 1; abel
       _ ≤ ‖L e p q - L e p r‖ + ‖L e p r - L e' p' r‖ + ‖L e' p' r - L e' p' q'‖ :=
-        (le_trans (norm_add_le _ _) (add_le_add_right (norm_add_le _ _) _))
-      _ ≤ 4 * ‖c‖ * (1 / 2) ^ e + 4 * ‖c‖ * (1 / 2) ^ e + 4 * ‖c‖ * (1 / 2) ^ e :=
-        add_le_add (add_le_add J1 J2) J3
-        -- Porting note: proof was `by apply_rules [add_le_add]`
+        norm_add₃_le _ _ _
+      _ ≤ 4 * ‖c‖ * (1 / 2) ^ e + 4 * ‖c‖ * (1 / 2) ^ e + 4 * ‖c‖ * (1 / 2) ^ e := by gcongr
       _ = 12 * ‖c‖ * (1 / 2) ^ e := by ring
   /- For definiteness, use `L0 e = L e (n e) (n e)`, to have a single sequence. We claim that this
     is a Cauchy sequence. -/
@@ -337,7 +341,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     -- `f` is well approximated by `L e (n e) k` at the relevant scale
     -- (in fact, we use `m = k - 1` instead of `k` because of the precise definition of `A`).
     have J1 : ‖f (x + y) - f x - L e (n e) m (x + y - x)‖ ≤ (1 / 2) ^ e * (1 / 2) ^ m := by
-      apply le_of_mem_a (hn e (n e) m le_rfl m_ge).2.2
+      apply le_of_mem_A (hn e (n e) m le_rfl m_ge).2.2
       · simp only [mem_closedBall, dist_self]
         exact div_nonneg (le_of_lt P) zero_le_two
       · simpa only [dist_eq_norm, add_sub_cancel', mem_closedBall, pow_succ', mul_one_div] using
@@ -361,12 +365,12 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       _ = ε * ‖y‖ := by field_simp [ne_of_gt pos]; ring
   rw [← this.fderiv] at f'K
   exact ⟨this.differentiableAt, f'K⟩
-#align fderiv_measurable_aux.D_subset_differentiable_set FDerivMeasurableAux.d_subset_differentiable_set
+#align fderiv_measurable_aux.D_subset_differentiable_set FDerivMeasurableAux.D_subset_differentiable_set
 
-theorem differentiable_set_eq_d (hK : IsComplete K) :
+theorem differentiable_set_eq_D (hK : IsComplete K) :
     { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } = D f K :=
-  Subset.antisymm (differentiable_set_subset_d _) (d_subset_differentiable_set hK)
-#align fderiv_measurable_aux.differentiable_set_eq_D FDerivMeasurableAux.differentiable_set_eq_d
+  Subset.antisymm (differentiable_set_subset_D _) (D_subset_differentiable_set hK)
+#align fderiv_measurable_aux.differentiable_set_eq_D FDerivMeasurableAux.differentiable_set_eq_D
 
 end FDerivMeasurableAux
 
@@ -381,16 +385,16 @@ is Borel-measurable. -/
 theorem measurableSet_of_differentiableAt_of_isComplete {K : Set (E →L[𝕜] F)} (hK : IsComplete K) :
     MeasurableSet { x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K } := by
   -- Porting note: was
-  -- simp [differentiable_set_eq_d K hK, D, isOpen_b.measurableSet, MeasurableSet.iInter,
+  -- simp [differentiable_set_eq_D K hK, D, isOpen_B.measurableSet, MeasurableSet.iInter,
   --   MeasurableSet.iUnion]
-  simp only [D, differentiable_set_eq_d K hK]
+  simp only [D, differentiable_set_eq_D K hK]
   refine MeasurableSet.iInter fun _ => ?_
   refine MeasurableSet.iUnion fun _ => ?_
   refine MeasurableSet.iInter fun _ => ?_
   refine MeasurableSet.iInter fun _ => ?_
   refine MeasurableSet.iInter fun _ => ?_
   refine MeasurableSet.iInter fun _ => ?_
-  refine isOpen_b.measurableSet
+  exact isOpen_B.measurableSet
 #align measurable_set_of_differentiable_at_of_is_complete measurableSet_of_differentiableAt_of_isComplete
 
 variable [CompleteSpace F]
@@ -481,7 +485,7 @@ def D (f : ℝ → F) (K : Set F) : Set ℝ :=
   ⋂ e : ℕ, ⋃ n : ℕ, ⋂ (p ≥ n) (q ≥ n), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ e)
 #align right_deriv_measurable_aux.D RightDerivMeasurableAux.D
 
-theorem a_mem_nhdsWithin_Ioi {L : F} {r ε x : ℝ} (hx : x ∈ A f L r ε) : A f L r ε ∈ 𝓝[>] x := by
+theorem A_mem_nhdsWithin_Ioi {L : F} {r ε x : ℝ} (hx : x ∈ A f L r ε) : A f L r ε ∈ 𝓝[>] x := by
   rcases hx with ⟨r', rr', hr'⟩
   rw [mem_nhdsWithin_Ioi_iff_exists_Ioo_subset]
   obtain ⟨s, s_gt, s_lt⟩ : ∃ s : ℝ, r / 2 < s ∧ s < r' := exists_between rr'.1
@@ -492,36 +496,36 @@ theorem a_mem_nhdsWithin_Ioi {L : F} {r ε x : ℝ} (hx : x ∈ A f L r ε) : A
     linarith [hx'.2]
   intro y hy z hz
   exact hr' y (A hy) z (A hz)
-#align right_deriv_measurable_aux.A_mem_nhds_within_Ioi RightDerivMeasurableAux.a_mem_nhdsWithin_Ioi
+#align right_deriv_measurable_aux.A_mem_nhds_within_Ioi RightDerivMeasurableAux.A_mem_nhdsWithin_Ioi
 
-theorem b_mem_nhdsWithin_Ioi {K : Set F} {r s ε x : ℝ} (hx : x ∈ B f K r s ε) :
+theorem B_mem_nhdsWithin_Ioi {K : Set F} {r s ε x : ℝ} (hx : x ∈ B f K r s ε) :
     B f K r s ε ∈ 𝓝[>] x := by
   obtain ⟨L, LK, hL₁, hL₂⟩ : ∃ L : F, L ∈ K ∧ x ∈ A f L r ε ∧ x ∈ A f L s ε := by
     simpa only [B, mem_iUnion, mem_inter_iff, exists_prop] using hx
-  filter_upwards [a_mem_nhdsWithin_Ioi hL₁, a_mem_nhdsWithin_Ioi hL₂]with y hy₁ hy₂
+  filter_upwards [A_mem_nhdsWithin_Ioi hL₁, A_mem_nhdsWithin_Ioi hL₂]with y hy₁ hy₂
   simp only [B, mem_iUnion, mem_inter_iff, exists_prop]
   exact ⟨L, LK, hy₁, hy₂⟩
-#align right_deriv_measurable_aux.B_mem_nhds_within_Ioi RightDerivMeasurableAux.b_mem_nhdsWithin_Ioi
+#align right_deriv_measurable_aux.B_mem_nhds_within_Ioi RightDerivMeasurableAux.B_mem_nhdsWithin_Ioi
 
-theorem measurableSet_b {K : Set F} {r s ε : ℝ} : MeasurableSet (B f K r s ε) :=
-  measurableSet_of_mem_nhdsWithin_Ioi fun _ hx => b_mem_nhdsWithin_Ioi hx
-#align right_deriv_measurable_aux.measurable_set_B RightDerivMeasurableAux.measurableSet_b
+theorem measurableSet_B {K : Set F} {r s ε : ℝ} : MeasurableSet (B f K r s ε) :=
+  measurableSet_of_mem_nhdsWithin_Ioi fun _ hx => B_mem_nhdsWithin_Ioi hx
+#align right_deriv_measurable_aux.measurable_set_B RightDerivMeasurableAux.measurableSet_B
 
-theorem a_mono (L : F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : A f L r ε ⊆ A f L r δ := by
+theorem A_mono (L : F) (r : ℝ) {ε δ : ℝ} (h : ε ≤ δ) : A f L r ε ⊆ A f L r δ := by
   rintro x ⟨r', r'r, hr'⟩
   refine' ⟨r', r'r, fun y hy z hz => (hr' y hy z hz).trans (mul_le_mul_of_nonneg_right h _)⟩
   linarith [hy.1, hy.2, r'r.2]
-#align right_deriv_measurable_aux.A_mono RightDerivMeasurableAux.a_mono
+#align right_deriv_measurable_aux.A_mono RightDerivMeasurableAux.A_mono
 
-theorem le_of_mem_a {r ε : ℝ} {L : F} {x : ℝ} (hx : x ∈ A f L r ε) {y z : ℝ}
+theorem le_of_mem_A {r ε : ℝ} {L : F} {x : ℝ} (hx : x ∈ A f L r ε) {y z : ℝ}
     (hy : y ∈ Icc x (x + r / 2)) (hz : z ∈ Icc x (x + r / 2)) :
   ‖f z - f y - (z - y) • L‖ ≤ ε * r := by
   rcases hx with ⟨r', r'mem, hr'⟩
   have A : x + r / 2 ≤ x + r' := by linarith [r'mem.1]
   exact hr' _ ((Icc_subset_Icc le_rfl A) hy) _ ((Icc_subset_Icc le_rfl A) hz)
-#align right_deriv_measurable_aux.le_of_mem_A RightDerivMeasurableAux.le_of_mem_a
+#align right_deriv_measurable_aux.le_of_mem_A RightDerivMeasurableAux.le_of_mem_A
 
-theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
+theorem mem_A_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
     (hx : DifferentiableWithinAt ℝ f (Ici x) x) :
     ∃ R > 0, ∀ r ∈ Ioo (0 : ℝ) R, x ∈ A f (derivWithin f (Ici x) x) r ε := by
   have := hx.hasDerivWithinAt
@@ -547,9 +551,9 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
       · rw [Real.norm_of_nonneg] <;> linarith [hz.1, hz.2]
       · rw [Real.norm_of_nonneg] <;> linarith [hy.1, hy.2]
     _ = ε * r := by ring
-#align right_deriv_measurable_aux.mem_A_of_differentiable RightDerivMeasurableAux.mem_a_of_differentiable
+#align right_deriv_measurable_aux.mem_A_of_differentiable RightDerivMeasurableAux.mem_A_of_differentiable
 
-theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F} (h₁ : x ∈ A f L₁ r ε)
+theorem norm_sub_le_of_mem_A {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F} (h₁ : x ∈ A f L₁ r ε)
     (h₂ : x ∈ A f L₂ r ε) : ‖L₁ - L₂‖ ≤ 4 * ε := by
   suffices H : ‖(r / 2) • (L₁ - L₂)‖ ≤ r / 2 * (4 * ε)
   · rwa [norm_smul, Real.norm_of_nonneg (half_pos hr).le, mul_le_mul_left (half_pos hr)] at H
@@ -564,29 +568,29 @@ theorem norm_sub_le_of_mem_a {r x : ℝ} (hr : 0 < r) (ε : ℝ) {L₁ L₂ : F}
       (norm_sub_le _ _)
     _ ≤ ε * r + ε * r := by
       apply add_le_add
-      · apply le_of_mem_a h₂ <;> simp [(half_pos hr).le]
-      · apply le_of_mem_a h₁ <;> simp [(half_pos hr).le]
+      · apply le_of_mem_A h₂ <;> simp [(half_pos hr).le]
+      · apply le_of_mem_A h₁ <;> simp [(half_pos hr).le]
     _ = r / 2 * (4 * ε) := by ring
-#align right_deriv_measurable_aux.norm_sub_le_of_mem_A RightDerivMeasurableAux.norm_sub_le_of_mem_a
+#align right_deriv_measurable_aux.norm_sub_le_of_mem_A RightDerivMeasurableAux.norm_sub_le_of_mem_A
 
 /-- Easy inclusion: a differentiability point with derivative in `K` belongs to `D f K`. -/
-theorem differentiable_set_subset_d :
+theorem differentiable_set_subset_D :
     { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } ⊆ D f K := by
   intro x hx
   rw [D, mem_iInter]
   intro e
   have : (0 : ℝ) < (1 / 2) ^ e := pow_pos (by norm_num) _
-  rcases mem_a_of_differentiable this hx.1 with ⟨R, R_pos, hR⟩
+  rcases mem_A_of_differentiable this hx.1 with ⟨R, R_pos, hR⟩
   obtain ⟨n, hn⟩ : ∃ n : ℕ, (1 / 2) ^ n < R :=
     exists_pow_lt_of_lt_one R_pos (by norm_num : (1 : ℝ) / 2 < 1)
   simp only [mem_iUnion, mem_iInter, B, mem_inter_iff]
   refine' ⟨n, fun p hp q hq => ⟨derivWithin f (Ici x) x, hx.2, ⟨_, _⟩⟩⟩ <;>
     · refine' hR _ ⟨pow_pos (by norm_num) _, lt_of_le_of_lt _ hn⟩
       exact pow_le_pow_of_le_one (by norm_num) (by norm_num) (by assumption)
-#align right_deriv_measurable_aux.differentiable_set_subset_D RightDerivMeasurableAux.differentiable_set_subset_d
+#align right_deriv_measurable_aux.differentiable_set_subset_D RightDerivMeasurableAux.differentiable_set_subset_D
 
 /-- Harder inclusion: at a point in `D f K`, the function `f` has a derivative, in `K`. -/
-theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
+theorem D_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     D f K ⊆ { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } := by
   have P : ∀ {n : ℕ}, (0 : ℝ) < (1 / 2) ^ n := fun {n} => pow_pos (by norm_num) n
   intro x hx
@@ -620,17 +624,17 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     have J1 : ‖L e p q - L e p r‖ ≤ 4 * (1 / 2) ^ e := by
       have I1 : x ∈ A f (L e p q) ((1 / 2) ^ p) ((1 / 2) ^ e) := (hn e p q hp hq).2.1
       have I2 : x ∈ A f (L e p r) ((1 / 2) ^ p) ((1 / 2) ^ e) := (hn e p r hp (le_max_left _ _)).2.1
-      exact norm_sub_le_of_mem_a P _ I1 I2
+      exact norm_sub_le_of_mem_A P _ I1 I2
     have J2 : ‖L e p r - L e' p' r‖ ≤ 4 * (1 / 2) ^ e := by
       have I1 : x ∈ A f (L e p r) ((1 / 2) ^ r) ((1 / 2) ^ e) := (hn e p r hp (le_max_left _ _)).2.2
       have I2 : x ∈ A f (L e' p' r) ((1 / 2) ^ r) ((1 / 2) ^ e') :=
         (hn e' p' r hp' (le_max_right _ _)).2.2
-      exact norm_sub_le_of_mem_a P _ I1 (a_mono _ _ I I2)
+      exact norm_sub_le_of_mem_A P _ I1 (A_mono _ _ I I2)
     have J3 : ‖L e' p' r - L e' p' q'‖ ≤ 4 * (1 / 2) ^ e := by
       have I1 : x ∈ A f (L e' p' r) ((1 / 2) ^ p') ((1 / 2) ^ e') :=
         (hn e' p' r hp' (le_max_right _ _)).2.1
       have I2 : x ∈ A f (L e' p' q') ((1 / 2) ^ p') ((1 / 2) ^ e') := (hn e' p' q' hp' hq').2.1
-      exact norm_sub_le_of_mem_a P _ (a_mono _ _ I I1) (a_mono _ _ I I2)
+      exact norm_sub_le_of_mem_A P _ (A_mono _ _ I I1) (A_mono _ _ I I2)
     calc
       ‖L e p q - L e' p' q'‖ =
           ‖L e p q - L e p r + (L e p r - L e' p' r) + (L e' p' r - L e' p' q')‖ :=
@@ -703,7 +707,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     have J : ‖f y - f x - (y - x) • L e (n e) m‖ ≤ 4 * (1 / 2) ^ e * ‖y - x‖ :=
       calc
         ‖f y - f x - (y - x) • L e (n e) m‖ ≤ (1 / 2) ^ e * (1 / 2) ^ m := by
-          apply le_of_mem_a (hn e (n e) m le_rfl m_ge).2.2
+          apply le_of_mem_A (hn e (n e) m le_rfl m_ge).2.2
           · simp only [one_div, inv_pow, left_mem_Icc, le_add_iff_nonneg_right]
             exact div_nonneg (inv_nonneg.2 (pow_nonneg zero_le_two _)) zero_le_two
           · simp only [pow_add, tsub_le_iff_left] at h'k
@@ -727,12 +731,12 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
 
   rw [← this.derivWithin (uniqueDiffOn_Ici x x Set.left_mem_Ici)] at f'K
   exact ⟨this.differentiableWithinAt, f'K⟩
-#align right_deriv_measurable_aux.D_subset_differentiable_set RightDerivMeasurableAux.d_subset_differentiable_set
+#align right_deriv_measurable_aux.D_subset_differentiable_set RightDerivMeasurableAux.D_subset_differentiable_set
 
-theorem differentiable_set_eq_d (hK : IsComplete K) :
+theorem differentiable_set_eq_D (hK : IsComplete K) :
     { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } = D f K :=
-  Subset.antisymm (differentiable_set_subset_d _) (d_subset_differentiable_set hK)
-#align right_deriv_measurable_aux.differentiable_set_eq_D RightDerivMeasurableAux.differentiable_set_eq_d
+  Subset.antisymm (differentiable_set_subset_D _) (D_subset_differentiable_set hK)
+#align right_deriv_measurable_aux.differentiable_set_eq_D RightDerivMeasurableAux.differentiable_set_eq_D
 
 end RightDerivMeasurableAux
 
@@ -746,14 +750,14 @@ theorem measurableSet_of_differentiableWithinAt_Ici_of_isComplete {K : Set F} (h
     MeasurableSet { x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K } := by
   -- simp [differentiable_set_eq_d K hK, D, measurableSet_b, MeasurableSet.iInter,
   --   MeasurableSet.iUnion]
-  simp only [differentiable_set_eq_d K hK, D]
+  simp only [differentiable_set_eq_D K hK, D]
   refine MeasurableSet.iInter fun _ => ?_
   refine MeasurableSet.iUnion fun _ => ?_
   refine MeasurableSet.iInter fun _ => ?_
   refine MeasurableSet.iInter fun _ => ?_
   refine MeasurableSet.iInter fun _ => ?_
   refine MeasurableSet.iInter fun _ => ?_
-  exact measurableSet_b
+  exact measurableSet_B
 #align measurable_set_of_differentiable_within_at_Ici_of_is_complete measurableSet_of_differentiableWithinAt_Ici_of_isComplete
 
 variable [CompleteSpace F]
@@ -828,3 +832,176 @@ theorem aestronglyMeasurable_derivWithin_Ioi [SecondCountableTopology F] (μ : M
 #align ae_strongly_measurable_deriv_within_Ioi aestronglyMeasurable_derivWithin_Ioi
 
 end RightDeriv
+
+section WithParam
+
+/- In this section, we prove the measurability of the derivative in a context with parameters:
+given `f : α → E → F`, we want to show that `p ↦ fderiv 𝕜 (f p.1) p.2` is measurable. Contrary
+to the previous sections, some assumptions are needed for this: if `f p.1` depends arbitrarily on
+`p.1`, this is obviously false. We require that `f` is continuous and `E` is locally compact --
+then the proofs in the previous sections adapt readily, as the set `A` defined above is open, so
+that the differentiability set `D` is measurable. -/
+
+variable {𝕜 : Type*} [NontriviallyNormedField 𝕜]
+  {E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E] [LocallyCompactSpace E]
+  {F : Type*} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
+  {α : Type*} [TopologicalSpace α] [MeasurableSpace α] [MeasurableSpace E]
+  [OpensMeasurableSpace α] [OpensMeasurableSpace E]
+  {f : α → E → F} (K : Set (E →L[𝕜] F))
+
+namespace FDerivMeasurableAux
+
+open Uniformity
+
+lemma isOpen_A_with_param {r s : ℝ} (hf : Continuous f.uncurry) (L : E →L[𝕜] F) :
+    IsOpen {p : α × E | p.2 ∈ A (f p.1) L r s} := by
+  have : ProperSpace E := properSpace_of_locallyCompactSpace 𝕜
+  simp only [A, half_lt_self_iff, not_lt, mem_Ioc, mem_ball, map_sub, mem_setOf_eq]
+  apply isOpen_iff_mem_nhds.2
+  rintro ⟨a, x⟩ ⟨r', ⟨Irr', Ir'r⟩, hr⟩
+  have ha : Continuous (f a) := continuous_uncurry_left a hf
+  rcases exists_between Irr' with ⟨t, hrt, htr'⟩
+  rcases exists_between hrt with ⟨t', hrt', ht't⟩
+  obtain ⟨b, b_lt, hb⟩ : ∃ b, b < s * r ∧ ∀ y ∈ closedBall x t, ∀ z ∈ closedBall x t,
+      ‖f a z - f a y - (L z - L y)‖ ≤ b := by
+    have B : Continuous (fun (p : E × E) ↦ ‖f a p.2 - f a p.1 - (L p.2 - L p.1)‖) := by
+      continuity
+    have C : (closedBall x t ×ˢ closedBall x t).Nonempty := by simp; linarith
+    rcases ((isCompact_closedBall x t).prod (isCompact_closedBall x t)).exists_isMaxOn
+      C B.continuousOn with ⟨p, pt, hp⟩
+    simp only [mem_prod, mem_closedBall] at pt
+    refine ⟨‖f a p.2 - f a p.1 - (L p.2 - L p.1)‖,
+      hr p.1 (pt.1.trans_lt htr') p.2 (pt.2.trans_lt htr'), fun y hy z hz ↦ ?_⟩
+    have D : (y, z) ∈ closedBall x t ×ˢ closedBall x t := mem_prod.2 ⟨hy, hz⟩
+    exact hp D
+  obtain ⟨ε, εpos, hε⟩ : ∃ ε, 0 < ε ∧ b + 2 * ε < s * r := ⟨(s * r - b)/3, by linarith, by linarith⟩
+  obtain ⟨u, u_open, au, hu⟩ : ∃ u, IsOpen u ∧ a ∈ u ∧ ∀ (p : α × E),
+      p.1 ∈ u → p.2 ∈ closedBall x t → dist (f.uncurry p) (f.uncurry (a, p.2)) < ε := by
+    have C : Continuous (fun (p : α × E) ↦ f a p.2) := by continuity
+    have D : ({a} ×ˢ closedBall x t).EqOn f.uncurry (fun p ↦ f a p.2) := by
+      rintro ⟨b, y⟩ ⟨hb, -⟩
+      simp at hb
+      simp [hb]
+    obtain ⟨v, v_open, sub_v, hv⟩ : ∃ v, IsOpen v ∧ {a} ×ˢ closedBall x t ⊆ v ∧
+        ∀ p ∈ v, dist (Function.uncurry f p) (f a p.2) < ε :=
+      Uniform.exists_is_open_mem_uniformity_of_forall_mem_eq (s := {a} ×ˢ closedBall x t)
+        (fun p _ ↦ hf.continuousAt) (fun p _ ↦ C.continuousAt) D (dist_mem_uniformity εpos)
+    obtain ⟨w, w', w_open, -, sub_w, sub_w', hww'⟩ : ∃ (w : Set α) (w' : Set E),
+        IsOpen w ∧ IsOpen w' ∧ {a} ⊆ w ∧ closedBall x t ⊆ w' ∧ w ×ˢ w' ⊆ v :=
+      generalized_tube_lemma isCompact_singleton (isCompact_closedBall x t) v_open sub_v
+    refine ⟨w, w_open, sub_w rfl, ?_⟩
+    rintro ⟨b, y⟩ h hby
+    exact hv _ (hww' ⟨h, sub_w' hby⟩)
+  have : u ×ˢ ball x (t - t') ∈ 𝓝 (a, x) :=
+    prod_mem_nhds (u_open.mem_nhds au) (ball_mem_nhds _ (sub_pos.2 ht't))
+  filter_upwards [this]
+  rintro ⟨a', x'⟩ ha'x'
+  simp only [mem_prod, mem_ball] at ha'x'
+  refine ⟨t', ⟨hrt', ht't.le.trans (htr'.le.trans Ir'r)⟩, fun y hy z hz ↦ ?_⟩
+  have dyx : dist y x ≤ t := by linarith [dist_triangle y x' x]
+  have dzx : dist z x ≤ t := by linarith [dist_triangle z x' x]
+  calc
+  ‖f a' z - f a' y - (L z - L y)‖ =
+    ‖(f a' z - f a z) + (f a y - f a' y) + (f a z - f a y - (L z - L y))‖ := by congr; abel
+  _ ≤ ‖f a' z - f a z‖ + ‖f a y - f a' y‖ + ‖f a z - f a y - (L z - L y)‖ := norm_add₃_le _ _ _
+  _ ≤ ε + ε + b := by
+      gcongr
+      · rw [← dist_eq_norm]
+        change dist (f.uncurry (a', z)) (f.uncurry (a, z)) ≤ ε
+        apply (hu _ _ _).le
+        · exact ha'x'.1
+        · simp [dzx]
+      · rw [← dist_eq_norm']
+        change dist (f.uncurry (a', y)) (f.uncurry (a, y)) ≤ ε
+        apply (hu _ _ _).le
+        · exact ha'x'.1
+        · simp [dyx]
+      · simp [hb, dyx, dzx]
+  _ < s * r := by linarith
+
+lemma isOpen_B_with_param {r s t : ℝ} (hf : Continuous f.uncurry) (K : Set (E →L[𝕜] F)) :
+    IsOpen {p : α × E | p.2 ∈ B (f p.1) K r s t} := by
+  suffices H : IsOpen (⋃ L ∈ K,
+      {p : α × E | p.2 ∈ A (f p.1) L r t ∧ p.2 ∈ A (f p.1) L s t}) by
+    convert H; ext p; simp [B]
+  refine isOpen_biUnion (fun L _ ↦ ?_)
+  exact (isOpen_A_with_param hf L).inter (isOpen_A_with_param hf L)
+
+end FDerivMeasurableAux
+
+open FDerivMeasurableAux
+
+theorem measurableSet_of_differentiableAt_of_isComplete_with_param
+    (hf : Continuous f.uncurry) {K : Set (E →L[𝕜] F)} (hK : IsComplete K) :
+    MeasurableSet {p : α × E | DifferentiableAt 𝕜 (f p.1) p.2 ∧ fderiv 𝕜 (f p.1) p.2 ∈ K} := by
+  have : {p : α × E | DifferentiableAt 𝕜 (f p.1) p.2 ∧ fderiv 𝕜 (f p.1) p.2 ∈ K}
+          = {p : α × E | p.2 ∈ D (f p.1) K} := by simp [← differentiable_set_eq_D K hK]
+  rw [this]
+  simp only [D, mem_iInter, mem_iUnion]
+  simp only [setOf_forall, setOf_exists]
+  refine MeasurableSet.iInter (fun _ ↦ ?_)
+  refine MeasurableSet.iUnion (fun _ ↦ ?_)
+  refine MeasurableSet.iInter (fun _ ↦ ?_)
+  refine MeasurableSet.iInter (fun _ ↦ ?_)
+  refine MeasurableSet.iInter (fun _ ↦ ?_)
+  refine MeasurableSet.iInter (fun _ ↦ ?_)
+  have : ProperSpace E := properSpace_of_locallyCompactSpace 𝕜
+  exact (isOpen_B_with_param hf K).measurableSet
+
+variable (𝕜)
+variable [CompleteSpace F]
+
+/-- The set of differentiability points of a continuous function depending on a parameter taking
+values in a complete space is Borel-measurable. -/
+theorem measurableSet_of_differentiableAt_with_param (hf : Continuous f.uncurry) :
+    MeasurableSet {p : α × E | DifferentiableAt 𝕜 (f p.1) p.2} := by
+  have : IsComplete (univ : Set (E →L[𝕜] F)) := complete_univ
+  convert measurableSet_of_differentiableAt_of_isComplete_with_param hf this
+  simp
+
+theorem measurable_fderiv_with_param (hf : Continuous f.uncurry) :
+    Measurable (fun (p : α × E) ↦ fderiv 𝕜 (f p.1) p.2) := by
+  refine measurable_of_isClosed (fun s hs ↦ ?_)
+  have :
+    (fun (p : α × E) ↦ fderiv 𝕜 (f p.1) p.2) ⁻¹' s =
+      {p | DifferentiableAt 𝕜 (f p.1) p.2 ∧ fderiv 𝕜 (f p.1) p.2 ∈ s } ∪
+        { p | ¬DifferentiableAt 𝕜 (f p.1) p.2} ∩ { _p | (0 : E →L[𝕜] F) ∈ s} :=
+    Set.ext (fun x ↦ mem_preimage.trans fderiv_mem_iff)
+  rw [this]
+  exact
+    (measurableSet_of_differentiableAt_of_isComplete_with_param hf hs.isComplete).union
+      ((measurableSet_of_differentiableAt_with_param _ hf).compl.inter (MeasurableSet.const _))
+
+theorem measurable_fderiv_apply_const_with_param [MeasurableSpace F] [BorelSpace F]
+    (hf : Continuous f.uncurry) (y : E) :
+    Measurable (fun (p : α × E) ↦ fderiv 𝕜 (f p.1) p.2 y) :=
+  (ContinuousLinearMap.measurable_apply y).comp (measurable_fderiv_with_param 𝕜 hf)
+
+variable {𝕜}
+
+theorem measurable_deriv_with_param [LocallyCompactSpace 𝕜] [MeasurableSpace 𝕜]
+    [OpensMeasurableSpace 𝕜] [MeasurableSpace F]
+    [BorelSpace F] {f : α → 𝕜 → F} (hf : Continuous f.uncurry) :
+    Measurable (fun (p : α × 𝕜) ↦ deriv (f p.1) p.2) := by
+  simpa only [fderiv_deriv] using measurable_fderiv_apply_const_with_param 𝕜 hf 1
+
+theorem stronglyMeasurable_deriv_with_param [LocallyCompactSpace 𝕜] [MeasurableSpace 𝕜]
+    [OpensMeasurableSpace 𝕜] [SecondCountableTopology F]
+    {f : α → 𝕜 → F} (hf : Continuous f.uncurry) :
+    StronglyMeasurable (fun (p : α × 𝕜) ↦ deriv (f p.1) p.2) := by
+  borelize F
+  exact (measurable_deriv_with_param hf).stronglyMeasurable
+
+theorem aemeasurable_deriv_with_param [LocallyCompactSpace 𝕜] [MeasurableSpace 𝕜]
+    [OpensMeasurableSpace 𝕜] [MeasurableSpace F]
+    [BorelSpace F] {f : α → 𝕜 → F} (hf : Continuous f.uncurry) (μ : Measure (α × 𝕜)) :
+    AEMeasurable (fun (p : α × 𝕜) ↦ deriv (f p.1) p.2) μ :=
+  (measurable_deriv_with_param hf).aemeasurable
+
+theorem aestronglyMeasurable_deriv_with_param [LocallyCompactSpace 𝕜] [MeasurableSpace 𝕜]
+    [OpensMeasurableSpace 𝕜] [SecondCountableTopology F]
+    {f : α → 𝕜 → F} (hf : Continuous f.uncurry) (μ : Measure (α × 𝕜)) :
+    AEStronglyMeasurable (fun (p : α × 𝕜) ↦ deriv (f p.1) p.2) μ :=
+  (stronglyMeasurable_deriv_with_param hf).aestronglyMeasurable
+
+end WithParam

@@ -89,7 +89,7 @@ variable {𝕜 E F : Type*} [NontriviallyNormedField 𝕜] [NormedAddCommGroup E
 theorem measurable_apply₂ [MeasurableSpace E] [OpensMeasurableSpace E]
     [SecondCountableTopologyEither (E →L[𝕜] F) E]
     [MeasurableSpace F] [BorelSpace F] : Measurable fun p : (E →L[𝕜] F) × E => p.1 p.2 :=
-  isBoundedBilinearMapApply.continuous.measurable
+  isBoundedBilinearMap_apply.continuous.measurable
 #align continuous_linear_map.measurable_apply₂ ContinuousLinearMap.measurable_apply₂
 
 end ContinuousLinearMap

We have currently that the product of two Borel spaces is Borel when both of them are second-countable. It is in fact sufficient to assume that only one of them is second-countable. We prove this in this PR.

Also move the definition of SecondCountableEither from Function.StronglyMeasurable to BorelSpace.Basic to be able to use it in the statement of the above theorem.

@@ -86,9 +86,9 @@ namespace ContinuousLinearMap
 variable {𝕜 E F : Type*} [NontriviallyNormedField 𝕜] [NormedAddCommGroup E] [NormedSpace 𝕜 E]
   [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
-theorem measurable_apply₂ [MeasurableSpace E] [OpensMeasurableSpace E] [SecondCountableTopology E]
-    [SecondCountableTopology (E →L[𝕜] F)] [MeasurableSpace F] [BorelSpace F] :
-    Measurable fun p : (E →L[𝕜] F) × E => p.1 p.2 :=
+theorem measurable_apply₂ [MeasurableSpace E] [OpensMeasurableSpace E]
+    [SecondCountableTopologyEither (E →L[𝕜] F) E]
+    [MeasurableSpace F] [BorelSpace F] : Measurable fun p : (E →L[𝕜] F) × E => p.1 p.2 :=
   isBoundedBilinearMapApply.continuous.measurable
 #align continuous_linear_map.measurable_apply₂ ContinuousLinearMap.measurable_apply₂
 

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

This has nice performance benefits.

@@ -83,7 +83,7 @@ open scoped Topology
 
 namespace ContinuousLinearMap
 
-variable {𝕜 E F : Type _} [NontriviallyNormedField 𝕜] [NormedAddCommGroup E] [NormedSpace 𝕜 E]
+variable {𝕜 E F : Type*} [NontriviallyNormedField 𝕜] [NormedAddCommGroup E] [NormedSpace 𝕜 E]
   [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
 theorem measurable_apply₂ [MeasurableSpace E] [OpensMeasurableSpace E] [SecondCountableTopology E]
@@ -96,11 +96,11 @@ end ContinuousLinearMap
 
 section fderiv
 
-variable {𝕜 : Type _} [NontriviallyNormedField 𝕜]
+variable {𝕜 : Type*} [NontriviallyNormedField 𝕜]
 
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
 
-variable {F : Type _} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
+variable {F : Type*} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
 variable {f : E → F} (K : Set (E →L[𝕜] F))
 
@@ -451,7 +451,7 @@ end fderiv
 
 section RightDeriv
 
-variable {F : Type _} [NormedAddCommGroup F] [NormedSpace ℝ F]
+variable {F : Type*} [NormedAddCommGroup F] [NormedSpace ℝ F]
 
 variable {f : ℝ → F} (K : Set F)
 

• 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) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.calculus.fderiv_measurable
-! 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.Deriv.Basic
 import Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap
 import Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic
 
+#align_import analysis.calculus.fderiv_measurable from "leanprover-community/mathlib"@"3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe"
+
 /-!
 # Derivative is measurable
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -295,7 +295,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     calc
       ‖L0 e - L0 e'‖ ≤ 12 * ‖c‖ * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
       _ < 12 * ‖c‖ * (ε / (12 * ‖c‖)) := by gcongr
-      _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0), ne_of_gt cpos] ; ring
+      _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0), ne_of_gt cpos]; ring
   -- As it is Cauchy, the sequence `L0` converges, to a limit `f'` in `K`.
   obtain ⟨f', f'K, hf'⟩ : ∃ f' ∈ K, Tendsto L0 atTop (𝓝 f') :=
     cauchySeq_tendsto_of_isComplete hK (fun e => (hn e (n e) (n e) le_rfl le_rfl).1) this
@@ -657,7 +657,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
     calc
       ‖L0 e - L0 e'‖ ≤ 12 * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
       _ < 12 * (ε / 12) := (mul_lt_mul' le_rfl he (le_of_lt P) (by norm_num))
-      _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0)] ; ring
+      _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0)]; ring
 
   -- As it is Cauchy, the sequence `L0` converges, to a limit `f'` in `K`.
   obtain ⟨f', f'K, hf'⟩ : ∃ f' ∈ K, Tendsto L0 atTop (𝓝 f') :=

I wrote a script to find lines that contain an odd number of backticks

@@ -18,14 +18,14 @@ import Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic
 In this file we prove that the derivative of any function with complete codomain is a measurable
 function. Namely, we prove:
 
-* `measurable_set_of_differentiable_at`: the set `{x | differentiable_at 𝕜 f x}` is measurable;
+* `measurableSet_of_differentiableAt`: the set `{x | DifferentiableAt 𝕜 f x}` is measurable;
 * `measurable_fderiv`: the function `fderiv 𝕜 f` is measurable;
 * `measurable_fderiv_apply_const`: for a fixed vector `y`, the function `fun x ↦ fderiv 𝕜 f x y`
   is measurable;
 * `measurable_deriv`: the function `deriv f` is measurable (for `f : 𝕜 → F`).
 
 We also show the same results for the right derivative on the real line
-(see `measurable_deriv_within_Ici` and ``measurable_deriv_within_Ioi`), following the same
+(see `measurable_derivWithin_Ici` and `measurable_derivWithin_Ioi`), following the same
 proof strategy.
 
 ## Implementation

Found with git grep -n "λ [a-zA-Z_ ]*,"

@@ -20,7 +20,7 @@ function. Namely, we prove:
 
 * `measurable_set_of_differentiable_at`: the set `{x | differentiable_at 𝕜 f x}` is measurable;
 * `measurable_fderiv`: the function `fderiv 𝕜 f` is measurable;
-* `measurable_fderiv_apply_const`: for a fixed vector `y`, the function `λ x, fderiv 𝕜 f x y`
+* `measurable_fderiv_apply_const`: for a fixed vector `y`, the function `fun x ↦ fderiv 𝕜 f x y`
   is measurable;
 * `measurable_deriv`: the function `deriv f` is measurable (for `f : 𝕜 → F`).
 

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

@@ -179,10 +179,7 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : E} (hx : Differen
       (norm_sub_le _ _)
     _ ≤ ε / 2 * ‖z - x‖ + ε / 2 * ‖y - x‖ :=
       (add_le_add (hR _ (lt_trans (mem_ball.1 hz) hr.2)) (hR _ (lt_trans (mem_ball.1 hy) hr.2)))
-    _ ≤ ε / 2 * r + ε / 2 * r :=
-      (add_le_add
-        (mul_le_mul_of_nonneg_left (le_of_lt (mem_ball_iff_norm.1 hz)) (le_of_lt (half_pos hε)))
-        (mul_le_mul_of_nonneg_left (le_of_lt (mem_ball_iff_norm.1 hy)) (le_of_lt (half_pos hε))))
+    _ ≤ ε / 2 * r + ε / 2 * r := by rw [mem_ball_iff_norm] at hz hy; gcongr
     _ = ε * r := by ring
 #align fderiv_measurable_aux.mem_A_of_differentiable FDerivMeasurableAux.mem_a_of_differentiable
 
@@ -297,8 +294,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
     rw [dist_comm, dist_eq_norm]
     calc
       ‖L0 e - L0 e'‖ ≤ 12 * ‖c‖ * (1 / 2) ^ e := M _ _ _ _ _ _ le_rfl le_rfl le_rfl le_rfl he'
-      _ < 12 * ‖c‖ * (ε / (12 * ‖c‖)) :=
-        (mul_lt_mul' le_rfl he (le_of_lt P) (mul_pos (by norm_num) cpos))
+      _ < 12 * ‖c‖ * (ε / (12 * ‖c‖)) := by gcongr
       _ = ε := by field_simp [(by norm_num : (12 : ℝ) ≠ 0), ne_of_gt cpos] ; ring
   -- As it is Cauchy, the sequence `L0` converges, to a limit `f'` in `K`.
   obtain ⟨f', f'K, hf'⟩ : ∃ f' ∈ K, Tendsto L0 atTop (𝓝 f') :=
@@ -316,8 +312,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
       this makes it possible to cover all scales, and thus to obtain a good linear approximation in
       the whole ball of radius `(1/2)^(n e)`. -/
     intro ε εpos
-    have pos : 0 < 4 + 12 * ‖c‖ :=
-      add_pos_of_pos_of_nonneg (by norm_num) (mul_nonneg (by norm_num) (norm_nonneg _))
+    have pos : 0 < 4 + 12 * ‖c‖ := by positivity
     obtain ⟨e, he⟩ : ∃ e : ℕ, (1 / 2) ^ e < ε / (4 + 12 * ‖c‖) :=
       exists_pow_lt_of_lt_one (div_pos εpos pos) (by norm_num)
     rw [eventually_nhds_iff_ball]
@@ -365,10 +360,7 @@ theorem d_subset_differentiable_set {K : Set (E →L[𝕜] F)} (hK : IsComplete
         (norm_add_le_of_le J2
           ((le_op_norm _ _).trans (mul_le_mul_of_nonneg_right (Lf' _ _ m_ge) (norm_nonneg _))))
       _ = (4 + 12 * ‖c‖) * ‖y‖ * (1 / 2) ^ e := by ring
-      _ ≤ (4 + 12 * ‖c‖) * ‖y‖ * (ε / (4 + 12 * ‖c‖)) :=
-        (mul_le_mul_of_nonneg_left he.le
-          (mul_nonneg (add_nonneg (by norm_num) (mul_nonneg (by norm_num) (norm_nonneg _)))
-            (norm_nonneg _)))
+      _ ≤ (4 + 12 * ‖c‖) * ‖y‖ * (ε / (4 + 12 * ‖c‖)) := by gcongr
       _ = ε * ‖y‖ := by field_simp [ne_of_gt pos]; ring
   rw [← this.fderiv] at f'K
   exact ⟨this.differentiableAt, f'K⟩
@@ -554,11 +546,9 @@ theorem mem_a_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
       (add_le_add (hm ⟨hz.1, hz.2.trans_lt (by linarith [hr.2])⟩)
         (hm ⟨hy.1, hy.2.trans_lt (by linarith [hr.2])⟩))
     _ ≤ ε / 2 * r + ε / 2 * r := by
-      apply add_le_add
-      · apply mul_le_mul_of_nonneg_left _ (le_of_lt (half_pos hε))
-        rw [Real.norm_of_nonneg] <;> linarith [hz.1, hz.2]
-      · apply mul_le_mul_of_nonneg_left _ (le_of_lt (half_pos hε))
-        rw [Real.norm_of_nonneg] <;> linarith [hy.1, hy.2]
+      gcongr
+      · rw [Real.norm_of_nonneg] <;> linarith [hz.1, hz.2]
+      · rw [Real.norm_of_nonneg] <;> linarith [hy.1, hy.2]
     _ = ε * r := by ring
 #align right_deriv_measurable_aux.mem_A_of_differentiable RightDerivMeasurableAux.mem_a_of_differentiable
 
@@ -650,7 +640,7 @@ theorem d_subset_differentiable_set {K : Set F} (hK : IsComplete K) :
         by congr 1; abel
       _ ≤ ‖L e p q - L e p r‖ + ‖L e p r - L e' p' r‖ + ‖L e' p' r - L e' p' q'‖ :=
         (le_trans (norm_add_le _ _) (add_le_add_right (norm_add_le _ _) _))
-      _ ≤ 4 * (1 / 2) ^ e + 4 * (1 / 2) ^ e + 4 * (1 / 2) ^ e := add_le_add (add_le_add J1 J2) J3
+      _ ≤ 4 * (1 / 2) ^ e + 4 * (1 / 2) ^ e + 4 * (1 / 2) ^ e := by gcongr
         -- Porting note: proof was `by apply_rules [add_le_add]`
       _ = 12 * (1 / 2) ^ e := by ring