analysis.normed_space.pointwise ⟷ Mathlib.Analysis.NormedSpace.Pointwise

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

@@ -168,7 +168,7 @@ theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bounded s
       _ = ε := by field_simp [Rpos.ne']
   have : y = x + r • z := by simp only [hz, add_neg_cancel_left]
   apply hε
-  simpa only [this, dist_eq_norm, add_sub_cancel', mem_closed_ball] using I
+  simpa only [this, dist_eq_norm, add_sub_cancel_left, mem_closed_ball] using I
 #align eventually_singleton_add_smul_subset eventually_singleton_add_smul_subset
 -/
 
@@ -323,7 +323,7 @@ theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
     have := hs.trans_lt ((inf_edist_le_edist_of_mem hz).trans_lt h)
     rw [of_real_eq_coe_nnreal hδ.le, some_eq_coe] at this
     exact_mod_cast this
-  rw [some_eq_coe, edist_lt_coe, ← dist_lt_coe, ← add_sub_cancel'_right δ ↑r] at h
+  rw [some_eq_coe, edist_lt_coe, ← dist_lt_coe, ← add_sub_cancel δ ↑r] at h
   obtain ⟨y, hxy, hyz⟩ := exists_dist_lt_lt hr hδ h
   refine'
     (ENNReal.add_lt_add_right of_real_ne_top <|

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

@@ -57,7 +57,7 @@ theorem ediam_smul₀ (c : 𝕜) (s : Set E) : EMetric.diam (c • s) = ‖c‖
     simp [zero_smul_set hs, ← Set.singleton_zero]
   · have := (lipschitzWith_smul c⁻¹).ediam_image_le (c • s)
     rwa [← smul_eq_mul, ← ENNReal.smul_def, Set.image_smul, inv_smul_smul₀ hc s, nnnorm_inv,
-      ENNReal.le_inv_smul_iff (nnnorm_ne_zero_iff.mpr hc)] at this 
+      ENNReal.le_inv_smul_iff (nnnorm_ne_zero_iff.mpr hc)] at this
 #align ediam_smul₀ ediam_smul₀
 -/
 
@@ -199,14 +199,14 @@ theorem exists_dist_le_le (hδ : 0 ≤ δ) (hε : 0 ≤ ε) (h : dist x z ≤ ε
     ∃ y, dist x y ≤ δ ∧ dist y z ≤ ε :=
   by
   obtain rfl | hε' := hε.eq_or_lt
-  · exact ⟨z, by rwa [zero_add] at h , (dist_self _).le⟩
+  · exact ⟨z, by rwa [zero_add] at h, (dist_self _).le⟩
   have hεδ := add_pos_of_pos_of_nonneg hε' hδ
   refine'
     (exists_dist_eq x z (div_nonneg hε <| add_nonneg hε hδ) (div_nonneg hδ <| add_nonneg hε hδ) <|
           by rw [← add_div, div_self hεδ.ne']).imp
       fun y hy => _
   rw [hy.1, hy.2, div_mul_comm, div_mul_comm ε]
-  rw [← div_le_one hεδ] at h 
+  rw [← div_le_one hεδ] at h
   exact ⟨mul_le_of_le_one_left hδ h, mul_le_of_le_one_left hε h⟩
 #align exists_dist_le_le exists_dist_le_le
 -/
@@ -222,7 +222,7 @@ theorem exists_dist_le_lt (hδ : 0 ≤ δ) (hε : 0 < ε) (h : dist x z < ε + 
           by rw [← add_div, div_self (add_pos_of_pos_of_nonneg hε hδ).ne']).imp
       fun y hy => _
   rw [hy.1, hy.2, div_mul_comm, div_mul_comm ε]
-  rw [← div_lt_one (add_pos_of_pos_of_nonneg hε hδ)] at h 
+  rw [← div_lt_one (add_pos_of_pos_of_nonneg hε hδ)] at h
   exact ⟨mul_le_of_le_one_left hδ h.le, mul_lt_of_lt_one_left hε h⟩
 #align exists_dist_le_lt exists_dist_le_lt
 -/
@@ -249,7 +249,7 @@ theorem exists_dist_lt_lt (hδ : 0 < δ) (hε : 0 < ε) (h : dist x z < ε + δ)
           by rw [← add_div, div_self (add_pos hε hδ).ne']).imp
       fun y hy => _
   rw [hy.1, hy.2, div_mul_comm, div_mul_comm ε]
-  rw [← div_lt_one (add_pos hε hδ)] at h 
+  rw [← div_lt_one (add_pos hε hδ)] at h
   exact ⟨mul_lt_of_lt_one_left hδ h, mul_lt_of_lt_one_left hε h⟩
 #align exists_dist_lt_lt exists_dist_lt_lt
 -/
@@ -260,9 +260,9 @@ theorem disjoint_ball_ball_iff (hδ : 0 < δ) (hε : 0 < ε) :
     Disjoint (ball x δ) (ball y ε) ↔ δ + ε ≤ dist x y :=
   by
   refine' ⟨fun h => le_of_not_lt fun hxy => _, ball_disjoint_ball⟩
-  rw [add_comm] at hxy 
+  rw [add_comm] at hxy
   obtain ⟨z, hxz, hzy⟩ := exists_dist_lt_lt hδ hε hxy
-  rw [dist_comm] at hxz 
+  rw [dist_comm] at hxz
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_ball_ball_iff disjoint_ball_ball_iff
 -/
@@ -273,9 +273,9 @@ theorem disjoint_ball_closedBall_iff (hδ : 0 < δ) (hε : 0 ≤ ε) :
     Disjoint (ball x δ) (closedBall y ε) ↔ δ + ε ≤ dist x y :=
   by
   refine' ⟨fun h => le_of_not_lt fun hxy => _, ball_disjoint_closed_ball⟩
-  rw [add_comm] at hxy 
+  rw [add_comm] at hxy
   obtain ⟨z, hxz, hzy⟩ := exists_dist_lt_le hδ hε hxy
-  rw [dist_comm] at hxz 
+  rw [dist_comm] at hxz
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_ball_closed_ball_iff disjoint_ball_closedBall_iff
 -/
@@ -293,9 +293,9 @@ theorem disjoint_closedBall_closedBall_iff (hδ : 0 ≤ δ) (hε : 0 ≤ ε) :
     Disjoint (closedBall x δ) (closedBall y ε) ↔ δ + ε < dist x y :=
   by
   refine' ⟨fun h => lt_of_not_ge fun hxy => _, closed_ball_disjoint_closed_ball⟩
-  rw [add_comm] at hxy 
+  rw [add_comm] at hxy
   obtain ⟨z, hxz, hzy⟩ := exists_dist_le_le hδ hε hxy
-  rw [dist_comm] at hxz 
+  rw [dist_comm] at hxz
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_closed_ball_closed_ball_iff disjoint_closedBall_closedBall_iff
 -/
@@ -321,9 +321,9 @@ theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
   have hr : 0 < ↑r - δ := by
     refine' sub_pos_of_lt _
     have := hs.trans_lt ((inf_edist_le_edist_of_mem hz).trans_lt h)
-    rw [of_real_eq_coe_nnreal hδ.le, some_eq_coe] at this 
+    rw [of_real_eq_coe_nnreal hδ.le, some_eq_coe] at this
     exact_mod_cast this
-  rw [some_eq_coe, edist_lt_coe, ← dist_lt_coe, ← add_sub_cancel'_right δ ↑r] at h 
+  rw [some_eq_coe, edist_lt_coe, ← dist_lt_coe, ← add_sub_cancel'_right δ ↑r] at h
   obtain ⟨y, hxy, hyz⟩ := exists_dist_lt_lt hr hδ h
   refine'
     (ENNReal.add_lt_add_right of_real_ne_top <|
@@ -342,7 +342,7 @@ theorem thickening_thickening (hε : 0 < ε) (hδ : 0 < δ) (s : Set E) :
     by
     simp_rw [mem_thickening_iff]
     rintro ⟨z, hz, hxz⟩
-    rw [add_comm] at hxz 
+    rw [add_comm] at hxz
     obtain ⟨y, hxy, hyz⟩ := exists_dist_lt_lt hε hδ hxz
     exact ⟨y, ⟨_, hz, hyz⟩, hxy⟩
 #align thickening_thickening thickening_thickening

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

@@ -3,9 +3,9 @@ Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yaël Dillies
 -/
-import Mathbin.Analysis.Normed.Group.AddTorsor
-import Mathbin.Analysis.Normed.Group.Pointwise
-import Mathbin.Analysis.NormedSpace.Basic
+import Analysis.Normed.Group.AddTorsor
+import Analysis.Normed.Group.Pointwise
+import Analysis.NormedSpace.Basic
 
 #align_import analysis.normed_space.pointwise from "leanprover-community/mathlib"@"bc91ed7093bf098d253401e69df601fc33dde156"
 

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

@@ -133,16 +133,16 @@ theorem smul_closedBall' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
 #align smul_closed_ball' smul_closedBall'
 -/
 
-#print Metric.Bounded.smul₀ /-
-theorem Metric.Bounded.smul₀ {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c • s) :=
+#print Bornology.IsBounded.smul₀ /-
+theorem Bornology.IsBounded.smul₀ {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c • s) :=
   by
   obtain ⟨R, hR⟩ : ∃ R : ℝ, ∀ x ∈ s, ‖x‖ ≤ R := hs.exists_norm_le
-  refine' bounded_iff_forall_norm_le.2 ⟨‖c‖ * R, fun z hz => _⟩
+  refine' isBounded_iff_forall_norm_le.2 ⟨‖c‖ * R, fun z hz => _⟩
   obtain ⟨y, ys, rfl⟩ : ∃ y : E, y ∈ s ∧ c • y = z := mem_smul_set.1 hz
   calc
     ‖c • y‖ = ‖c‖ * ‖y‖ := norm_smul _ _
     _ ≤ ‖c‖ * R := mul_le_mul_of_nonneg_left (hR y ys) (norm_nonneg _)
-#align metric.bounded.smul Metric.Bounded.smul₀
+#align metric.bounded.smul Bornology.IsBounded.smul₀
 -/
 
 #print eventually_singleton_add_smul_subset /-

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yaël Dillies
-
-! This file was ported from Lean 3 source module analysis.normed_space.pointwise
-! leanprover-community/mathlib commit bc91ed7093bf098d253401e69df601fc33dde156
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Normed.Group.AddTorsor
 import Mathbin.Analysis.Normed.Group.Pointwise
 import Mathbin.Analysis.NormedSpace.Basic
 
+#align_import analysis.normed_space.pointwise from "leanprover-community/mathlib"@"bc91ed7093bf098d253401e69df601fc33dde156"
+
 /-!
 # Properties of pointwise scalar multiplication of sets in normed spaces.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

@@ -136,8 +136,8 @@ theorem smul_closedBall' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
 #align smul_closed_ball' smul_closedBall'
 -/
 
-#print Metric.Bounded.smul /-
-theorem Metric.Bounded.smul {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c • s) :=
+#print Metric.Bounded.smul₀ /-
+theorem Metric.Bounded.smul₀ {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c • s) :=
   by
   obtain ⟨R, hR⟩ : ∃ R : ℝ, ∀ x ∈ s, ‖x‖ ≤ R := hs.exists_norm_le
   refine' bounded_iff_forall_norm_le.2 ⟨‖c‖ * R, fun z hz => _⟩
@@ -145,7 +145,7 @@ theorem Metric.Bounded.smul {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c
   calc
     ‖c • y‖ = ‖c‖ * ‖y‖ := norm_smul _ _
     _ ≤ ‖c‖ * R := mul_le_mul_of_nonneg_left (hR y ys) (norm_nonneg _)
-#align metric.bounded.smul Metric.Bounded.smul
+#align metric.bounded.smul Metric.Bounded.smul₀
 -/
 
 #print eventually_singleton_add_smul_subset /-

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

@@ -36,9 +36,11 @@ variable [SeminormedAddCommGroup 𝕜] [SeminormedAddCommGroup E]
 
 variable [SMulZeroClass 𝕜 E] [BoundedSMul 𝕜 E]
 
+#print ediam_smul_le /-
 theorem ediam_smul_le (c : 𝕜) (s : Set E) : EMetric.diam (c • s) ≤ ‖c‖₊ • EMetric.diam s :=
   (lipschitzWith_smul c).ediam_image_le s
 #align ediam_smul_le ediam_smul_le
+-/
 
 end SMulZeroClass
 
@@ -48,6 +50,7 @@ variable [NormedDivisionRing 𝕜] [SeminormedAddCommGroup E]
 
 variable [Module 𝕜 E] [BoundedSMul 𝕜 E]
 
+#print ediam_smul₀ /-
 theorem ediam_smul₀ (c : 𝕜) (s : Set E) : EMetric.diam (c • s) = ‖c‖₊ • EMetric.diam s :=
   by
   refine' le_antisymm (ediam_smul_le c s) _
@@ -59,11 +62,15 @@ theorem ediam_smul₀ (c : 𝕜) (s : Set E) : EMetric.diam (c • s) = ‖c‖
     rwa [← smul_eq_mul, ← ENNReal.smul_def, Set.image_smul, inv_smul_smul₀ hc s, nnnorm_inv,
       ENNReal.le_inv_smul_iff (nnnorm_ne_zero_iff.mpr hc)] at this 
 #align ediam_smul₀ ediam_smul₀
+-/
 
+#print diam_smul₀ /-
 theorem diam_smul₀ (c : 𝕜) (x : Set E) : diam (c • x) = ‖c‖ * diam x := by
   simp_rw [diam, ediam_smul₀, ENNReal.toReal_smul, NNReal.smul_def, coe_nnnorm, smul_eq_mul]
 #align diam_smul₀ diam_smul₀
+-/
 
+#print infEdist_smul₀ /-
 theorem infEdist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
     EMetric.infEdist (c • x) (c • s) = ‖c‖₊ • EMetric.infEdist x s :=
   by
@@ -76,12 +83,15 @@ theorem infEdist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
   · have : (‖c‖₊ : ENNReal) ≠ 0 := by simp [hc]
     simp_rw [ENNReal.smul_def, smul_eq_mul, ENNReal.mul_iInf_of_ne this ENNReal.coe_ne_top]
 #align inf_edist_smul₀ infEdist_smul₀
+-/
 
+#print infDist_smul₀ /-
 theorem infDist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
     Metric.infDist (c • x) (c • s) = ‖c‖ * Metric.infDist x s := by
   simp_rw [Metric.infDist, infEdist_smul₀ hc, ENNReal.toReal_smul, NNReal.smul_def, coe_nnnorm,
     smul_eq_mul]
 #align inf_dist_smul₀ infDist_smul₀
+-/
 
 end DivisionRing
 
@@ -91,6 +101,7 @@ section SeminormedAddCommGroup
 
 variable [SeminormedAddCommGroup E] [NormedSpace 𝕜 E]
 
+#print smul_ball /-
 theorem smul_ball {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) : c • ball x r = ball (c • x) (‖c‖ * r) :=
   by
   ext y
@@ -98,11 +109,15 @@ theorem smul_ball {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) : c • ball x r =
   conv_lhs => rw [← inv_smul_smul₀ hc x]
   simp [← div_eq_inv_mul, div_lt_iff (norm_pos_iff.2 hc), mul_comm _ r, dist_smul₀]
 #align smul_ball smul_ball
+-/
 
+#print smul_unitBall /-
 theorem smul_unitBall {c : 𝕜} (hc : c ≠ 0) : c • ball (0 : E) (1 : ℝ) = ball (0 : E) ‖c‖ := by
   rw [smul_ball hc, smul_zero, mul_one]
 #align smul_unit_ball smul_unitBall
+-/
 
+#print smul_sphere' /-
 theorem smul_sphere' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
     c • sphere x r = sphere (c • x) (‖c‖ * r) :=
   by
@@ -112,11 +127,14 @@ theorem smul_sphere' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
   simp only [mem_sphere, dist_smul₀, norm_inv, ← div_eq_inv_mul, div_eq_iff (norm_pos_iff.2 hc).ne',
     mul_comm r]
 #align smul_sphere' smul_sphere'
+-/
 
+#print smul_closedBall' /-
 theorem smul_closedBall' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
     c • closedBall x r = closedBall (c • x) (‖c‖ * r) := by
   simp only [← ball_union_sphere, Set.smul_set_union, smul_ball hc, smul_sphere' hc]
 #align smul_closed_ball' smul_closedBall'
+-/
 
 #print Metric.Bounded.smul /-
 theorem Metric.Bounded.smul {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c • s) :=
@@ -130,6 +148,7 @@ theorem Metric.Bounded.smul {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c
 #align metric.bounded.smul Metric.Bounded.smul
 -/
 
+#print eventually_singleton_add_smul_subset /-
 /-- If `s` is a bounded set, then for small enough `r`, the set `{x} + r • s` is contained in any
 fixed neighborhood of `x`. -/
 theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bounded s) {u : Set E}
@@ -154,15 +173,19 @@ theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bounded s
   apply hε
   simpa only [this, dist_eq_norm, add_sub_cancel', mem_closed_ball] using I
 #align eventually_singleton_add_smul_subset eventually_singleton_add_smul_subset
+-/
 
 variable [NormedSpace ℝ E] {x y z : E} {δ ε : ℝ}
 
+#print smul_unitBall_of_pos /-
 /-- In a real normed space, the image of the unit ball under scalar multiplication by a positive
 constant `r` is the ball of radius `r`. -/
 theorem smul_unitBall_of_pos {r : ℝ} (hr : 0 < r) : r • ball 0 1 = ball (0 : E) r := by
   rw [smul_unitBall hr.ne', Real.norm_of_nonneg hr.le]
 #align smul_unit_ball_of_pos smul_unitBall_of_pos
+-/
 
+#print exists_dist_eq /-
 -- This is also true for `ℚ`-normed spaces
 theorem exists_dist_eq (x z : E) {a b : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1) :
     ∃ y, dist x y = b * dist x z ∧ dist y z = a * dist x z :=
@@ -172,7 +195,9 @@ theorem exists_dist_eq (x z : E) {a b : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) (hab
   nth_rw 4 [← one_smul ℝ z]
   simp [dist_eq_norm, ← hab, add_smul, ← smul_sub, norm_smul_of_nonneg, ha, hb]
 #align exists_dist_eq exists_dist_eq
+-/
 
+#print exists_dist_le_le /-
 theorem exists_dist_le_le (hδ : 0 ≤ δ) (hε : 0 ≤ ε) (h : dist x z ≤ ε + δ) :
     ∃ y, dist x y ≤ δ ∧ dist y z ≤ ε :=
   by
@@ -187,7 +212,9 @@ theorem exists_dist_le_le (hδ : 0 ≤ δ) (hε : 0 ≤ ε) (h : dist x z ≤ ε
   rw [← div_le_one hεδ] at h 
   exact ⟨mul_le_of_le_one_left hδ h, mul_le_of_le_one_left hε h⟩
 #align exists_dist_le_le exists_dist_le_le
+-/
 
+#print exists_dist_le_lt /-
 -- This is also true for `ℚ`-normed spaces
 theorem exists_dist_le_lt (hδ : 0 ≤ δ) (hε : 0 < ε) (h : dist x z < ε + δ) :
     ∃ y, dist x y ≤ δ ∧ dist y z < ε :=
@@ -201,7 +228,9 @@ theorem exists_dist_le_lt (hδ : 0 ≤ δ) (hε : 0 < ε) (h : dist x z < ε + 
   rw [← div_lt_one (add_pos_of_pos_of_nonneg hε hδ)] at h 
   exact ⟨mul_le_of_le_one_left hδ h.le, mul_lt_of_lt_one_left hε h⟩
 #align exists_dist_le_lt exists_dist_le_lt
+-/
 
+#print exists_dist_lt_le /-
 -- This is also true for `ℚ`-normed spaces
 theorem exists_dist_lt_le (hδ : 0 < δ) (hε : 0 ≤ ε) (h : dist x z < ε + δ) :
     ∃ y, dist x y < δ ∧ dist y z ≤ ε :=
@@ -210,7 +239,9 @@ theorem exists_dist_lt_le (hδ : 0 < δ) (hε : 0 ≤ ε) (h : dist x z < ε + 
     exists_dist_le_lt hε hδ (show dist z x < δ + ε by simpa only [dist_comm, add_comm] using h)
   exact ⟨y, by simp [dist_comm x y, dist_comm y z, *]⟩
 #align exists_dist_lt_le exists_dist_lt_le
+-/
 
+#print exists_dist_lt_lt /-
 -- This is also true for `ℚ`-normed spaces
 theorem exists_dist_lt_lt (hδ : 0 < δ) (hε : 0 < ε) (h : dist x z < ε + δ) :
     ∃ y, dist x y < δ ∧ dist y z < ε :=
@@ -224,7 +255,9 @@ theorem exists_dist_lt_lt (hδ : 0 < δ) (hε : 0 < ε) (h : dist x z < ε + δ)
   rw [← div_lt_one (add_pos hε hδ)] at h 
   exact ⟨mul_lt_of_lt_one_left hδ h, mul_lt_of_lt_one_left hε h⟩
 #align exists_dist_lt_lt exists_dist_lt_lt
+-/
 
+#print disjoint_ball_ball_iff /-
 -- This is also true for `ℚ`-normed spaces
 theorem disjoint_ball_ball_iff (hδ : 0 < δ) (hε : 0 < ε) :
     Disjoint (ball x δ) (ball y ε) ↔ δ + ε ≤ dist x y :=
@@ -235,7 +268,9 @@ theorem disjoint_ball_ball_iff (hδ : 0 < δ) (hε : 0 < ε) :
   rw [dist_comm] at hxz 
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_ball_ball_iff disjoint_ball_ball_iff
+-/
 
+#print disjoint_ball_closedBall_iff /-
 -- This is also true for `ℚ`-normed spaces
 theorem disjoint_ball_closedBall_iff (hδ : 0 < δ) (hε : 0 ≤ ε) :
     Disjoint (ball x δ) (closedBall y ε) ↔ δ + ε ≤ dist x y :=
@@ -246,13 +281,17 @@ theorem disjoint_ball_closedBall_iff (hδ : 0 < δ) (hε : 0 ≤ ε) :
   rw [dist_comm] at hxz 
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_ball_closed_ball_iff disjoint_ball_closedBall_iff
+-/
 
+#print disjoint_closedBall_ball_iff /-
 -- This is also true for `ℚ`-normed spaces
 theorem disjoint_closedBall_ball_iff (hδ : 0 ≤ δ) (hε : 0 < ε) :
     Disjoint (closedBall x δ) (ball y ε) ↔ δ + ε ≤ dist x y := by
   rw [disjoint_comm, disjoint_ball_closedBall_iff hε hδ, add_comm, dist_comm] <;> infer_instance
 #align disjoint_closed_ball_ball_iff disjoint_closedBall_ball_iff
+-/
 
+#print disjoint_closedBall_closedBall_iff /-
 theorem disjoint_closedBall_closedBall_iff (hδ : 0 ≤ δ) (hε : 0 ≤ ε) :
     Disjoint (closedBall x δ) (closedBall y ε) ↔ δ + ε < dist x y :=
   by
@@ -262,9 +301,11 @@ theorem disjoint_closedBall_closedBall_iff (hδ : 0 ≤ δ) (hε : 0 ≤ ε) :
   rw [dist_comm] at hxz 
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_closed_ball_closed_ball_iff disjoint_closedBall_closedBall_iff
+-/
 
 open Emetric ENNReal
 
+#print infEdist_thickening /-
 @[simp]
 theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
     infEdist x (thickening δ s) = infEdist x s - ENNReal.ofReal δ :=
@@ -294,7 +335,9 @@ theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
   rw [← of_real_add hr.le hδ.le, sub_add_cancel, of_real_coe_nnreal]
   exact le_rfl
 #align inf_edist_thickening infEdist_thickening
+-/
 
+#print thickening_thickening /-
 @[simp]
 theorem thickening_thickening (hε : 0 < ε) (hδ : 0 < δ) (s : Set E) :
     thickening ε (thickening δ s) = thickening (ε + δ) s :=
@@ -306,7 +349,9 @@ theorem thickening_thickening (hε : 0 < ε) (hδ : 0 < δ) (s : Set E) :
     obtain ⟨y, hxy, hyz⟩ := exists_dist_lt_lt hε hδ hxz
     exact ⟨y, ⟨_, hz, hyz⟩, hxy⟩
 #align thickening_thickening thickening_thickening
+-/
 
+#print cthickening_thickening /-
 @[simp]
 theorem cthickening_thickening (hε : 0 ≤ ε) (hδ : 0 < δ) (s : Set E) :
     cthickening ε (thickening δ s) = cthickening (ε + δ) s :=
@@ -315,13 +360,17 @@ theorem cthickening_thickening (hε : 0 ≤ ε) (hδ : 0 < δ) (s : Set E) :
     simp_rw [mem_cthickening_iff, ENNReal.ofReal_add hε hδ.le, infEdist_thickening hδ]
     exact tsub_le_iff_right.2
 #align cthickening_thickening cthickening_thickening
+-/
 
+#print closure_thickening /-
 -- Note: `interior (cthickening δ s) ≠ thickening δ s` in general
 @[simp]
 theorem closure_thickening (hδ : 0 < δ) (s : Set E) : closure (thickening δ s) = cthickening δ s :=
   by rw [← cthickening_zero, cthickening_thickening le_rfl hδ, zero_add]; infer_instance
 #align closure_thickening closure_thickening
+-/
 
+#print infEdist_cthickening /-
 @[simp]
 theorem infEdist_cthickening (δ : ℝ) (s : Set E) (x : E) :
     infEdist x (cthickening δ s) = infEdist x s - ENNReal.ofReal δ :=
@@ -330,7 +379,9 @@ theorem infEdist_cthickening (δ : ℝ) (s : Set E) (x : E) :
   · rw [cthickening_of_nonpos hδ, inf_edist_closure, of_real_of_nonpos hδ, tsub_zero]
   · rw [← closure_thickening hδ, inf_edist_closure, infEdist_thickening hδ] <;> infer_instance
 #align inf_edist_cthickening infEdist_cthickening
+-/
 
+#print thickening_cthickening /-
 @[simp]
 theorem thickening_cthickening (hε : 0 < ε) (hδ : 0 ≤ δ) (s : Set E) :
     thickening ε (cthickening δ s) = thickening (ε + δ) s :=
@@ -339,7 +390,9 @@ theorem thickening_cthickening (hε : 0 < ε) (hδ : 0 ≤ δ) (s : Set E) :
   · rw [cthickening_zero, thickening_closure, add_zero]
   · rw [← closure_thickening hδ, thickening_closure, thickening_thickening hε hδ] <;> infer_instance
 #align thickening_cthickening thickening_cthickening
+-/
 
+#print cthickening_cthickening /-
 @[simp]
 theorem cthickening_cthickening (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (s : Set E) :
     cthickening ε (cthickening δ s) = cthickening (ε + δ) s :=
@@ -348,20 +401,26 @@ theorem cthickening_cthickening (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (s : Set E) :
     simp_rw [mem_cthickening_iff, ENNReal.ofReal_add hε hδ, infEdist_cthickening]
     exact tsub_le_iff_right.2
 #align cthickening_cthickening cthickening_cthickening
+-/
 
+#print thickening_ball /-
 @[simp]
 theorem thickening_ball (hε : 0 < ε) (hδ : 0 < δ) (x : E) :
     thickening ε (ball x δ) = ball x (ε + δ) := by
   rw [← thickening_singleton, thickening_thickening hε hδ, thickening_singleton] <;> infer_instance
 #align thickening_ball thickening_ball
+-/
 
+#print thickening_closedBall /-
 @[simp]
 theorem thickening_closedBall (hε : 0 < ε) (hδ : 0 ≤ δ) (x : E) :
     thickening ε (closedBall x δ) = ball x (ε + δ) := by
   rw [← cthickening_singleton _ hδ, thickening_cthickening hε hδ, thickening_singleton] <;>
     infer_instance
 #align thickening_closed_ball thickening_closedBall
+-/
 
+#print cthickening_ball /-
 @[simp]
 theorem cthickening_ball (hε : 0 ≤ ε) (hδ : 0 < δ) (x : E) :
     cthickening ε (ball x δ) = closedBall x (ε + δ) := by
@@ -369,7 +428,9 @@ theorem cthickening_ball (hε : 0 ≤ ε) (hδ : 0 < δ) (x : E) :
       cthickening_singleton _ (add_nonneg hε hδ.le)] <;>
     infer_instance
 #align cthickening_ball cthickening_ball
+-/
 
+#print cthickening_closedBall /-
 @[simp]
 theorem cthickening_closedBall (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (x : E) :
     cthickening ε (closedBall x δ) = closedBall x (ε + δ) := by
@@ -377,47 +438,64 @@ theorem cthickening_closedBall (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (x : E) :
       cthickening_singleton _ (add_nonneg hε hδ)] <;>
     infer_instance
 #align cthickening_closed_ball cthickening_closedBall
+-/
 
+#print ball_add_ball /-
 theorem ball_add_ball (hε : 0 < ε) (hδ : 0 < δ) (a b : E) :
     ball a ε + ball b δ = ball (a + b) (ε + δ) := by
   rw [ball_add, thickening_ball hε hδ b, Metric.vadd_ball, vadd_eq_add]
 #align ball_add_ball ball_add_ball
+-/
 
+#print ball_sub_ball /-
 theorem ball_sub_ball (hε : 0 < ε) (hδ : 0 < δ) (a b : E) :
     ball a ε - ball b δ = ball (a - b) (ε + δ) := by
   simp_rw [sub_eq_add_neg, neg_ball, ball_add_ball hε hδ]
 #align ball_sub_ball ball_sub_ball
+-/
 
+#print ball_add_closedBall /-
 theorem ball_add_closedBall (hε : 0 < ε) (hδ : 0 ≤ δ) (a b : E) :
     ball a ε + closedBall b δ = ball (a + b) (ε + δ) := by
   rw [ball_add, thickening_closedBall hε hδ b, Metric.vadd_ball, vadd_eq_add]
 #align ball_add_closed_ball ball_add_closedBall
+-/
 
+#print ball_sub_closedBall /-
 theorem ball_sub_closedBall (hε : 0 < ε) (hδ : 0 ≤ δ) (a b : E) :
     ball a ε - closedBall b δ = ball (a - b) (ε + δ) := by
   simp_rw [sub_eq_add_neg, neg_closedBall, ball_add_closedBall hε hδ]
 #align ball_sub_closed_ball ball_sub_closedBall
+-/
 
+#print closedBall_add_ball /-
 theorem closedBall_add_ball (hε : 0 ≤ ε) (hδ : 0 < δ) (a b : E) :
     closedBall a ε + ball b δ = ball (a + b) (ε + δ) := by
   rw [add_comm, ball_add_closedBall hδ hε b, add_comm, add_comm δ]
 #align closed_ball_add_ball closedBall_add_ball
+-/
 
+#print closedBall_sub_ball /-
 theorem closedBall_sub_ball (hε : 0 ≤ ε) (hδ : 0 < δ) (a b : E) :
     closedBall a ε - ball b δ = ball (a - b) (ε + δ) := by
   simp_rw [sub_eq_add_neg, neg_ball, closedBall_add_ball hε hδ]
 #align closed_ball_sub_ball closedBall_sub_ball
+-/
 
+#print closedBall_add_closedBall /-
 theorem closedBall_add_closedBall [ProperSpace E] (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (a b : E) :
     closedBall a ε + closedBall b δ = closedBall (a + b) (ε + δ) := by
   rw [(is_compact_closed_ball _ _).add_closedBall hδ b, cthickening_closedBall hδ hε a,
     Metric.vadd_closedBall, vadd_eq_add, add_comm, add_comm δ]
 #align closed_ball_add_closed_ball closedBall_add_closedBall
+-/
 
+#print closedBall_sub_closedBall /-
 theorem closedBall_sub_closedBall [ProperSpace E] (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (a b : E) :
     closedBall a ε - closedBall b δ = closedBall (a - b) (ε + δ) := by
   simp_rw [sub_eq_add_neg, neg_closedBall, closedBall_add_closedBall hε hδ]
 #align closed_ball_sub_closed_ball closedBall_sub_closedBall
+-/
 
 end SeminormedAddCommGroup
 
@@ -425,6 +503,7 @@ section NormedAddCommGroup
 
 variable [NormedAddCommGroup E] [NormedSpace 𝕜 E]
 
+#print smul_closedBall /-
 theorem smul_closedBall (c : 𝕜) (x : E) {r : ℝ} (hr : 0 ≤ r) :
     c • closedBall x r = closedBall (c • x) (‖c‖ * r) :=
   by
@@ -432,19 +511,25 @@ theorem smul_closedBall (c : 𝕜) (x : E) {r : ℝ} (hr : 0 ≤ r) :
   · simp [hr, zero_smul_set, Set.singleton_zero, ← nonempty_closed_ball]
   · exact smul_closedBall' hc x r
 #align smul_closed_ball smul_closedBall
+-/
 
+#print smul_closedUnitBall /-
 theorem smul_closedUnitBall (c : 𝕜) : c • closedBall (0 : E) (1 : ℝ) = closedBall (0 : E) ‖c‖ := by
   rw [smul_closedBall _ _ zero_le_one, smul_zero, mul_one]
 #align smul_closed_unit_ball smul_closedUnitBall
+-/
 
 variable [NormedSpace ℝ E]
 
+#print smul_closedUnitBall_of_nonneg /-
 /-- In a real normed space, the image of the unit closed ball under multiplication by a nonnegative
 number `r` is the closed ball of radius `r` with center at the origin. -/
 theorem smul_closedUnitBall_of_nonneg {r : ℝ} (hr : 0 ≤ r) :
     r • closedBall 0 1 = closedBall (0 : E) r := by rw [smul_closedUnitBall, Real.norm_of_nonneg hr]
 #align smul_closed_unit_ball_of_nonneg smul_closedUnitBall_of_nonneg
+-/
 
+#print NormedSpace.sphere_nonempty /-
 /-- In a nontrivial real normed space, a sphere is nonempty if and only if its radius is
 nonnegative. -/
 @[simp]
@@ -458,7 +543,9 @@ theorem NormedSpace.sphere_nonempty [Nontrivial E] {x : E} {r : ℝ} :
   have : ‖y - x‖ ≠ 0 := by simpa [sub_eq_zero]
   simp [norm_smul, this, Real.norm_of_nonneg hr]
 #align normed_space.sphere_nonempty NormedSpace.sphere_nonempty
+-/
 
+#print smul_sphere /-
 theorem smul_sphere [Nontrivial E] (c : 𝕜) (x : E) {r : ℝ} (hr : 0 ≤ r) :
     c • sphere x r = sphere (c • x) (‖c‖ * r) :=
   by
@@ -466,18 +553,23 @@ theorem smul_sphere [Nontrivial E] (c : 𝕜) (x : E) {r : ℝ} (hr : 0 ≤ r) :
   · simp [zero_smul_set, Set.singleton_zero, hr]
   · exact smul_sphere' hc x r
 #align smul_sphere smul_sphere
+-/
 
+#print affinity_unitBall /-
 /-- Any ball `metric.ball x r`, `0 < r` is the image of the unit ball under `λ y, x + r • y`. -/
 theorem affinity_unitBall {r : ℝ} (hr : 0 < r) (x : E) : x +ᵥ r • ball 0 1 = ball x r := by
   rw [smul_unitBall_of_pos hr, vadd_ball_zero]
 #align affinity_unit_ball affinity_unitBall
+-/
 
+#print affinity_unitClosedBall /-
 /-- Any closed ball `metric.closed_ball x r`, `0 ≤ r` is the image of the unit closed ball under
 `λ y, x + r • y`. -/
 theorem affinity_unitClosedBall {r : ℝ} (hr : 0 ≤ r) (x : E) :
     x +ᵥ r • closedBall 0 1 = closedBall x r := by
   rw [smul_closedUnitBall, Real.norm_of_nonneg hr, vadd_closedBall_zero]
 #align affinity_unit_closed_ball affinity_unitClosedBall
+-/
 
 end NormedAddCommGroup
 

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

@@ -127,7 +127,6 @@ theorem Metric.Bounded.smul {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c
   calc
     ‖c • y‖ = ‖c‖ * ‖y‖ := norm_smul _ _
     _ ≤ ‖c‖ * R := mul_le_mul_of_nonneg_left (hR y ys) (norm_nonneg _)
-    
 #align metric.bounded.smul Metric.Bounded.smul
 -/
 
@@ -151,7 +150,6 @@ theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bounded s
         (mul_le_mul (mem_closedBall_zero_iff.1 hr) (mem_closedBall_zero_iff.1 (hR zs))
           (norm_nonneg _) (div_pos εpos Rpos).le)
       _ = ε := by field_simp [Rpos.ne']
-      
   have : y = x + r • z := by simp only [hz, add_neg_cancel_left]
   apply hε
   simpa only [this, dist_eq_norm, add_sub_cancel', mem_closed_ball] using I

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

@@ -140,7 +140,7 @@ theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bounded s
     nhds_basis_closed_ball.mem_iff.1 hu
   obtain ⟨R, Rpos, hR⟩ : ∃ R : ℝ, 0 < R ∧ s ⊆ closed_ball 0 R := hs.subset_ball_lt 0 0
   have : Metric.closedBall (0 : 𝕜) (ε / R) ∈ 𝓝 (0 : 𝕜) := closed_ball_mem_nhds _ (div_pos εpos Rpos)
-  filter_upwards [this]with r hr
+  filter_upwards [this] with r hr
   simp only [image_add_left, singleton_add]
   intro y hy
   obtain ⟨z, zs, hz⟩ : ∃ z : E, z ∈ s ∧ r • z = -x + y := by simpa [mem_smul_set] using hy

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

@@ -57,7 +57,7 @@ theorem ediam_smul₀ (c : 𝕜) (s : Set E) : EMetric.diam (c • s) = ‖c‖
     simp [zero_smul_set hs, ← Set.singleton_zero]
   · have := (lipschitzWith_smul c⁻¹).ediam_image_le (c • s)
     rwa [← smul_eq_mul, ← ENNReal.smul_def, Set.image_smul, inv_smul_smul₀ hc s, nnnorm_inv,
-      ENNReal.le_inv_smul_iff (nnnorm_ne_zero_iff.mpr hc)] at this
+      ENNReal.le_inv_smul_iff (nnnorm_ne_zero_iff.mpr hc)] at this 
 #align ediam_smul₀ ediam_smul₀
 
 theorem diam_smul₀ (c : 𝕜) (x : Set E) : diam (c • x) = ‖c‖ * diam x := by
@@ -136,7 +136,7 @@ fixed neighborhood of `x`. -/
 theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bounded s) {u : Set E}
     (hu : u ∈ 𝓝 x) : ∀ᶠ r in 𝓝 (0 : 𝕜), {x} + r • s ⊆ u :=
   by
-  obtain ⟨ε, εpos, hε⟩ : ∃ (ε : _)(hε : 0 < ε), closed_ball x ε ⊆ u :=
+  obtain ⟨ε, εpos, hε⟩ : ∃ (ε : _) (hε : 0 < ε), closed_ball x ε ⊆ u :=
     nhds_basis_closed_ball.mem_iff.1 hu
   obtain ⟨R, Rpos, hR⟩ : ∃ R : ℝ, 0 < R ∧ s ⊆ closed_ball 0 R := hs.subset_ball_lt 0 0
   have : Metric.closedBall (0 : 𝕜) (ε / R) ∈ 𝓝 (0 : 𝕜) := closed_ball_mem_nhds _ (div_pos εpos Rpos)
@@ -179,14 +179,14 @@ theorem exists_dist_le_le (hδ : 0 ≤ δ) (hε : 0 ≤ ε) (h : dist x z ≤ ε
     ∃ y, dist x y ≤ δ ∧ dist y z ≤ ε :=
   by
   obtain rfl | hε' := hε.eq_or_lt
-  · exact ⟨z, by rwa [zero_add] at h, (dist_self _).le⟩
+  · exact ⟨z, by rwa [zero_add] at h , (dist_self _).le⟩
   have hεδ := add_pos_of_pos_of_nonneg hε' hδ
   refine'
     (exists_dist_eq x z (div_nonneg hε <| add_nonneg hε hδ) (div_nonneg hδ <| add_nonneg hε hδ) <|
           by rw [← add_div, div_self hεδ.ne']).imp
       fun y hy => _
   rw [hy.1, hy.2, div_mul_comm, div_mul_comm ε]
-  rw [← div_le_one hεδ] at h
+  rw [← div_le_one hεδ] at h 
   exact ⟨mul_le_of_le_one_left hδ h, mul_le_of_le_one_left hε h⟩
 #align exists_dist_le_le exists_dist_le_le
 
@@ -200,7 +200,7 @@ theorem exists_dist_le_lt (hδ : 0 ≤ δ) (hε : 0 < ε) (h : dist x z < ε + 
           by rw [← add_div, div_self (add_pos_of_pos_of_nonneg hε hδ).ne']).imp
       fun y hy => _
   rw [hy.1, hy.2, div_mul_comm, div_mul_comm ε]
-  rw [← div_lt_one (add_pos_of_pos_of_nonneg hε hδ)] at h
+  rw [← div_lt_one (add_pos_of_pos_of_nonneg hε hδ)] at h 
   exact ⟨mul_le_of_le_one_left hδ h.le, mul_lt_of_lt_one_left hε h⟩
 #align exists_dist_le_lt exists_dist_le_lt
 
@@ -223,7 +223,7 @@ theorem exists_dist_lt_lt (hδ : 0 < δ) (hε : 0 < ε) (h : dist x z < ε + δ)
           by rw [← add_div, div_self (add_pos hε hδ).ne']).imp
       fun y hy => _
   rw [hy.1, hy.2, div_mul_comm, div_mul_comm ε]
-  rw [← div_lt_one (add_pos hε hδ)] at h
+  rw [← div_lt_one (add_pos hε hδ)] at h 
   exact ⟨mul_lt_of_lt_one_left hδ h, mul_lt_of_lt_one_left hε h⟩
 #align exists_dist_lt_lt exists_dist_lt_lt
 
@@ -232,9 +232,9 @@ theorem disjoint_ball_ball_iff (hδ : 0 < δ) (hε : 0 < ε) :
     Disjoint (ball x δ) (ball y ε) ↔ δ + ε ≤ dist x y :=
   by
   refine' ⟨fun h => le_of_not_lt fun hxy => _, ball_disjoint_ball⟩
-  rw [add_comm] at hxy
+  rw [add_comm] at hxy 
   obtain ⟨z, hxz, hzy⟩ := exists_dist_lt_lt hδ hε hxy
-  rw [dist_comm] at hxz
+  rw [dist_comm] at hxz 
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_ball_ball_iff disjoint_ball_ball_iff
 
@@ -243,9 +243,9 @@ theorem disjoint_ball_closedBall_iff (hδ : 0 < δ) (hε : 0 ≤ ε) :
     Disjoint (ball x δ) (closedBall y ε) ↔ δ + ε ≤ dist x y :=
   by
   refine' ⟨fun h => le_of_not_lt fun hxy => _, ball_disjoint_closed_ball⟩
-  rw [add_comm] at hxy
+  rw [add_comm] at hxy 
   obtain ⟨z, hxz, hzy⟩ := exists_dist_lt_le hδ hε hxy
-  rw [dist_comm] at hxz
+  rw [dist_comm] at hxz 
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_ball_closed_ball_iff disjoint_ball_closedBall_iff
 
@@ -259,9 +259,9 @@ theorem disjoint_closedBall_closedBall_iff (hδ : 0 ≤ δ) (hε : 0 ≤ ε) :
     Disjoint (closedBall x δ) (closedBall y ε) ↔ δ + ε < dist x y :=
   by
   refine' ⟨fun h => lt_of_not_ge fun hxy => _, closed_ball_disjoint_closed_ball⟩
-  rw [add_comm] at hxy
+  rw [add_comm] at hxy 
   obtain ⟨z, hxz, hzy⟩ := exists_dist_le_le hδ hε hxy
-  rw [dist_comm] at hxz
+  rw [dist_comm] at hxz 
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_closed_ball_closed_ball_iff disjoint_closedBall_closedBall_iff
 
@@ -285,9 +285,9 @@ theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
   have hr : 0 < ↑r - δ := by
     refine' sub_pos_of_lt _
     have := hs.trans_lt ((inf_edist_le_edist_of_mem hz).trans_lt h)
-    rw [of_real_eq_coe_nnreal hδ.le, some_eq_coe] at this
+    rw [of_real_eq_coe_nnreal hδ.le, some_eq_coe] at this 
     exact_mod_cast this
-  rw [some_eq_coe, edist_lt_coe, ← dist_lt_coe, ← add_sub_cancel'_right δ ↑r] at h
+  rw [some_eq_coe, edist_lt_coe, ← dist_lt_coe, ← add_sub_cancel'_right δ ↑r] at h 
   obtain ⟨y, hxy, hyz⟩ := exists_dist_lt_lt hr hδ h
   refine'
     (ENNReal.add_lt_add_right of_real_ne_top <|
@@ -304,7 +304,7 @@ theorem thickening_thickening (hε : 0 < ε) (hδ : 0 < δ) (s : Set E) :
     by
     simp_rw [mem_thickening_iff]
     rintro ⟨z, hz, hxz⟩
-    rw [add_comm] at hxz
+    rw [add_comm] at hxz 
     obtain ⟨y, hxy, hyz⟩ := exists_dist_lt_lt hε hδ hxz
     exact ⟨y, ⟨_, hz, hyz⟩, hxy⟩
 #align thickening_thickening thickening_thickening

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

@@ -26,7 +26,7 @@ multiplication of bounded sets remain bounded.
 
 open Metric Set
 
-open Pointwise Topology
+open scoped Pointwise Topology
 
 variable {𝕜 E : Type _}
 

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

@@ -36,12 +36,6 @@ variable [SeminormedAddCommGroup 𝕜] [SeminormedAddCommGroup E]
 
 variable [SMulZeroClass 𝕜 E] [BoundedSMul 𝕜 E]
 
-/- warning: ediam_smul_le -> ediam_smul_le is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : SMulZeroClass.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2))))))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} 𝕜 _inst_1) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (SubNegMonoid.toAddMonoid.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (SeminormedAddGroup.toAddGroup.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) _inst_3)] (c : 𝕜) (s : Set.{u2} E), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) _inst_3)) c s)) (SMul.smul.{0, 0} NNReal ENNReal (SMulZeroClass.toHasSmul.{0, 0} NNReal ENNReal (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (SMulWithZero.toSmulZeroClass.{0, 0} NNReal ENNReal (MulZeroClass.toHasZero.{0} NNReal (MulZeroOneClass.toMulZeroClass.{0} NNReal (MonoidWithZero.toMulZeroOneClass.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} NNReal ENNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (Module.toMulActionWithZero.{0, 0} NNReal ENNReal NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (ENNReal.module.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (Semiring.toModule.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (NNNorm.nnnorm.{u1} 𝕜 (SeminormedAddGroup.toNNNorm.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 _inst_1)) c) (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : SMulZeroClass.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} 𝕜 _inst_1) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (NegZeroClass.toZero.{u1} 𝕜 (SubNegZeroMonoid.toNegZeroClass.{u1} 𝕜 (SubtractionMonoid.toSubNegZeroMonoid.{u1} 𝕜 (SubtractionCommMonoid.toSubtractionMonoid.{u1} 𝕜 (AddCommGroup.toDivisionAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) _inst_3)] (c : 𝕜) (s : Set.{u2} E), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) _inst_3))) c s)) (HSMul.hSMul.{0, 0, 0} NNReal ENNReal ENNReal (instHSMul.{0, 0} NNReal ENNReal (Algebra.toSMul.{0, 0} NNReal ENNReal instNNRealCommSemiring (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.instAlgebraNNRealInstNNRealCommSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))) (NNNorm.nnnorm.{u1} 𝕜 (SeminormedAddGroup.toNNNorm.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 _inst_1)) c) (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s))
-Case conversion may be inaccurate. Consider using '#align ediam_smul_le ediam_smul_leₓ'. -/
 theorem ediam_smul_le (c : 𝕜) (s : Set E) : EMetric.diam (c • s) ≤ ‖c‖₊ • EMetric.diam s :=
   (lipschitzWith_smul c).ediam_image_le s
 #align ediam_smul_le ediam_smul_le
@@ -54,9 +48,6 @@ variable [NormedDivisionRing 𝕜] [SeminormedAddCommGroup E]
 
 variable [Module 𝕜 E] [BoundedSMul 𝕜 E]
 
-/- warning: ediam_smul₀ -> ediam_smul₀ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ediam_smul₀ ediam_smul₀ₓ'. -/
 theorem ediam_smul₀ (c : 𝕜) (s : Set E) : EMetric.diam (c • s) = ‖c‖₊ • EMetric.diam s :=
   by
   refine' le_antisymm (ediam_smul_le c s) _
@@ -69,19 +60,10 @@ theorem ediam_smul₀ (c : 𝕜) (s : Set E) : EMetric.diam (c • s) = ‖c‖
       ENNReal.le_inv_smul_iff (nnnorm_ne_zero_iff.mpr hc)] at this
 #align ediam_smul₀ ediam_smul₀
 
-/- warning: diam_smul₀ -> diam_smul₀ is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (NormedRing.toSeminormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))] (c : 𝕜) (x : Set.{u2} E), Eq.{1} Real (Metric.diam.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))) c x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} 𝕜 (NormedDivisionRing.toHasNorm.{u1} 𝕜 _inst_1) c) (Metric.diam.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) x))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (NormedRing.toSeminormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))] (c : 𝕜) (x : Set.{u2} E), Eq.{1} Real (Metric.diam.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3)))))) c x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} 𝕜 (NormedDivisionRing.toNorm.{u1} 𝕜 _inst_1) c) (Metric.diam.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) x))
-Case conversion may be inaccurate. Consider using '#align diam_smul₀ diam_smul₀ₓ'. -/
 theorem diam_smul₀ (c : 𝕜) (x : Set E) : diam (c • x) = ‖c‖ * diam x := by
   simp_rw [diam, ediam_smul₀, ENNReal.toReal_smul, NNReal.smul_def, coe_nnnorm, smul_eq_mul]
 #align diam_smul₀ diam_smul₀
 
-/- warning: inf_edist_smul₀ -> infEdist_smul₀ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inf_edist_smul₀ infEdist_smul₀ₓ'. -/
 theorem infEdist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
     EMetric.infEdist (c • x) (c • s) = ‖c‖₊ • EMetric.infEdist x s :=
   by
@@ -95,9 +77,6 @@ theorem infEdist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
     simp_rw [ENNReal.smul_def, smul_eq_mul, ENNReal.mul_iInf_of_ne this ENNReal.coe_ne_top]
 #align inf_edist_smul₀ infEdist_smul₀
 
-/- warning: inf_dist_smul₀ -> infDist_smul₀ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inf_dist_smul₀ infDist_smul₀ₓ'. -/
 theorem infDist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
     Metric.infDist (c • x) (c • s) = ‖c‖ * Metric.infDist x s := by
   simp_rw [Metric.infDist, infEdist_smul₀ hc, ENNReal.toReal_smul, NNReal.smul_def, coe_nnnorm,
@@ -112,12 +91,6 @@ section SeminormedAddCommGroup
 
 variable [SeminormedAddCommGroup E] [NormedSpace 𝕜 E]
 
-/- warning: smul_ball -> smul_ball is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align smul_ball smul_ballₓ'. -/
 theorem smul_ball {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) : c • ball x r = ball (c • x) (‖c‖ * r) :=
   by
   ext y
@@ -126,22 +99,10 @@ theorem smul_ball {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) : c • ball x r =
   simp [← div_eq_inv_mul, div_lt_iff (norm_pos_iff.2 hc), mul_comm _ r, dist_smul₀]
 #align smul_ball smul_ball
 
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-Case conversion may be inaccurate. Consider using '#align smul_unit_ball smul_unitBallₓ'. -/
 theorem smul_unitBall {c : 𝕜} (hc : c ≠ 0) : c • ball (0 : E) (1 : ℝ) = ball (0 : E) ‖c‖ := by
   rw [smul_ball hc, smul_zero, mul_one]
 #align smul_unit_ball smul_unitBall
 
-/- warning: smul_sphere' -> smul_sphere' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align smul_sphere' smul_sphere'ₓ'. -/
 theorem smul_sphere' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
     c • sphere x r = sphere (c • x) (‖c‖ * r) :=
   by
@@ -152,12 +113,6 @@ theorem smul_sphere' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
     mul_comm r]
 #align smul_sphere' smul_sphere'
 
-/- warning: smul_closed_ball' -> smul_closedBall' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align smul_closed_ball' smul_closedBall'ₓ'. -/
 theorem smul_closedBall' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
     c • closedBall x r = closedBall (c • x) (‖c‖ * r) := by
   simp only [← ball_union_sphere, Set.smul_set_union, smul_ball hc, smul_sphere' hc]
@@ -176,9 +131,6 @@ theorem Metric.Bounded.smul {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c
 #align metric.bounded.smul Metric.Bounded.smul
 -/
 
-/- warning: eventually_singleton_add_smul_subset -> eventually_singleton_add_smul_subset is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align eventually_singleton_add_smul_subset eventually_singleton_add_smul_subsetₓ'. -/
 /-- If `s` is a bounded set, then for small enough `r`, the set `{x} + r • s` is contained in any
 fixed neighborhood of `x`. -/
 theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bounded s) {u : Set E}
@@ -207,24 +159,12 @@ theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bounded s
 
 variable [NormedSpace ℝ E] {x y z : E} {δ ε : ℝ}
 
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-Case conversion may be inaccurate. Consider using '#align smul_unit_ball_of_pos smul_unitBall_of_posₓ'. -/
 /-- In a real normed space, the image of the unit ball under scalar multiplication by a positive
 constant `r` is the ball of radius `r`. -/
 theorem smul_unitBall_of_pos {r : ℝ} (hr : 0 < r) : r • ball 0 1 = ball (0 : E) r := by
   rw [smul_unitBall hr.ne', Real.norm_of_nonneg hr.le]
 #align smul_unit_ball_of_pos smul_unitBall_of_pos
 
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 -- This is also true for `ℚ`-normed spaces
 theorem exists_dist_eq (x z : E) {a b : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1) :
     ∃ y, dist x y = b * dist x z ∧ dist y z = a * dist x z :=
@@ -235,12 +175,6 @@ theorem exists_dist_eq (x z : E) {a b : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) (hab
   simp [dist_eq_norm, ← hab, add_smul, ← smul_sub, norm_smul_of_nonneg, ha, hb]
 #align exists_dist_eq exists_dist_eq
 
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 theorem exists_dist_le_le (hδ : 0 ≤ δ) (hε : 0 ≤ ε) (h : dist x z ≤ ε + δ) :
     ∃ y, dist x y ≤ δ ∧ dist y z ≤ ε :=
   by
@@ -256,12 +190,6 @@ theorem exists_dist_le_le (hδ : 0 ≤ δ) (hε : 0 ≤ ε) (h : dist x z ≤ ε
   exact ⟨mul_le_of_le_one_left hδ h, mul_le_of_le_one_left hε h⟩
 #align exists_dist_le_le exists_dist_le_le
 
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 -- This is also true for `ℚ`-normed spaces
 theorem exists_dist_le_lt (hδ : 0 ≤ δ) (hε : 0 < ε) (h : dist x z < ε + δ) :
     ∃ y, dist x y ≤ δ ∧ dist y z < ε :=
@@ -276,12 +204,6 @@ theorem exists_dist_le_lt (hδ : 0 ≤ δ) (hε : 0 < ε) (h : dist x z < ε + 
   exact ⟨mul_le_of_le_one_left hδ h.le, mul_lt_of_lt_one_left hε h⟩
 #align exists_dist_le_lt exists_dist_le_lt
 
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-Case conversion may be inaccurate. Consider using '#align exists_dist_lt_le exists_dist_lt_leₓ'. -/
 -- This is also true for `ℚ`-normed spaces
 theorem exists_dist_lt_le (hδ : 0 < δ) (hε : 0 ≤ ε) (h : dist x z < ε + δ) :
     ∃ y, dist x y < δ ∧ dist y z ≤ ε :=
@@ -291,12 +213,6 @@ theorem exists_dist_lt_le (hδ : 0 < δ) (hε : 0 ≤ ε) (h : dist x z < ε + 
   exact ⟨y, by simp [dist_comm x y, dist_comm y z, *]⟩
 #align exists_dist_lt_le exists_dist_lt_le
 
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-Case conversion may be inaccurate. Consider using '#align exists_dist_lt_lt exists_dist_lt_ltₓ'. -/
 -- This is also true for `ℚ`-normed spaces
 theorem exists_dist_lt_lt (hδ : 0 < δ) (hε : 0 < ε) (h : dist x z < ε + δ) :
     ∃ y, dist x y < δ ∧ dist y z < ε :=
@@ -311,12 +227,6 @@ theorem exists_dist_lt_lt (hδ : 0 < δ) (hε : 0 < ε) (h : dist x z < ε + δ)
   exact ⟨mul_lt_of_lt_one_left hδ h, mul_lt_of_lt_one_left hε h⟩
 #align exists_dist_lt_lt exists_dist_lt_lt
 
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-Case conversion may be inaccurate. Consider using '#align disjoint_ball_ball_iff disjoint_ball_ball_iffₓ'. -/
 -- This is also true for `ℚ`-normed spaces
 theorem disjoint_ball_ball_iff (hδ : 0 < δ) (hε : 0 < ε) :
     Disjoint (ball x δ) (ball y ε) ↔ δ + ε ≤ dist x y :=
@@ -328,12 +238,6 @@ theorem disjoint_ball_ball_iff (hδ : 0 < δ) (hε : 0 < ε) :
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_ball_ball_iff disjoint_ball_ball_iff
 
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-Case conversion may be inaccurate. Consider using '#align disjoint_ball_closed_ball_iff disjoint_ball_closedBall_iffₓ'. -/
 -- This is also true for `ℚ`-normed spaces
 theorem disjoint_ball_closedBall_iff (hδ : 0 < δ) (hε : 0 ≤ ε) :
     Disjoint (ball x δ) (closedBall y ε) ↔ δ + ε ≤ dist x y :=
@@ -345,24 +249,12 @@ theorem disjoint_ball_closedBall_iff (hδ : 0 < δ) (hε : 0 ≤ ε) :
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_ball_closed_ball_iff disjoint_ball_closedBall_iff
 
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 -- This is also true for `ℚ`-normed spaces
 theorem disjoint_closedBall_ball_iff (hδ : 0 ≤ δ) (hε : 0 < ε) :
     Disjoint (closedBall x δ) (ball y ε) ↔ δ + ε ≤ dist x y := by
   rw [disjoint_comm, disjoint_ball_closedBall_iff hε hδ, add_comm, dist_comm] <;> infer_instance
 #align disjoint_closed_ball_ball_iff disjoint_closedBall_ball_iff
 
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 theorem disjoint_closedBall_closedBall_iff (hδ : 0 ≤ δ) (hε : 0 ≤ ε) :
     Disjoint (closedBall x δ) (closedBall y ε) ↔ δ + ε < dist x y :=
   by
@@ -375,12 +267,6 @@ theorem disjoint_closedBall_closedBall_iff (hδ : 0 ≤ δ) (hε : 0 ≤ ε) :
 
 open Emetric ENNReal
 
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 @[simp]
 theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
     infEdist x (thickening δ s) = infEdist x s - ENNReal.ofReal δ :=
@@ -411,12 +297,6 @@ theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
   exact le_rfl
 #align inf_edist_thickening infEdist_thickening
 
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 @[simp]
 theorem thickening_thickening (hε : 0 < ε) (hδ : 0 < δ) (s : Set E) :
     thickening ε (thickening δ s) = thickening (ε + δ) s :=
@@ -429,12 +309,6 @@ theorem thickening_thickening (hε : 0 < ε) (hδ : 0 < δ) (s : Set E) :
     exact ⟨y, ⟨_, hz, hyz⟩, hxy⟩
 #align thickening_thickening thickening_thickening
 
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 @[simp]
 theorem cthickening_thickening (hε : 0 ≤ ε) (hδ : 0 < δ) (s : Set E) :
     cthickening ε (thickening δ s) = cthickening (ε + δ) s :=
@@ -444,24 +318,12 @@ theorem cthickening_thickening (hε : 0 ≤ ε) (hδ : 0 < δ) (s : Set E) :
     exact tsub_le_iff_right.2
 #align cthickening_thickening cthickening_thickening
 
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-Case conversion may be inaccurate. Consider using '#align closure_thickening closure_thickeningₓ'. -/
 -- Note: `interior (cthickening δ s) ≠ thickening δ s` in general
 @[simp]
 theorem closure_thickening (hδ : 0 < δ) (s : Set E) : closure (thickening δ s) = cthickening δ s :=
   by rw [← cthickening_zero, cthickening_thickening le_rfl hδ, zero_add]; infer_instance
 #align closure_thickening closure_thickening
 
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 @[simp]
 theorem infEdist_cthickening (δ : ℝ) (s : Set E) (x : E) :
     infEdist x (cthickening δ s) = infEdist x s - ENNReal.ofReal δ :=
@@ -471,12 +333,6 @@ theorem infEdist_cthickening (δ : ℝ) (s : Set E) (x : E) :
   · rw [← closure_thickening hδ, inf_edist_closure, infEdist_thickening hδ] <;> infer_instance
 #align inf_edist_cthickening infEdist_cthickening
 
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 @[simp]
 theorem thickening_cthickening (hε : 0 < ε) (hδ : 0 ≤ δ) (s : Set E) :
     thickening ε (cthickening δ s) = thickening (ε + δ) s :=
@@ -486,12 +342,6 @@ theorem thickening_cthickening (hε : 0 < ε) (hδ : 0 ≤ δ) (s : Set E) :
   · rw [← closure_thickening hδ, thickening_closure, thickening_thickening hε hδ] <;> infer_instance
 #align thickening_cthickening thickening_cthickening
 
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 @[simp]
 theorem cthickening_cthickening (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (s : Set E) :
     cthickening ε (cthickening δ s) = cthickening (ε + δ) s :=
@@ -501,24 +351,12 @@ theorem cthickening_cthickening (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (s : Set E) :
     exact tsub_le_iff_right.2
 #align cthickening_cthickening cthickening_cthickening
 
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 @[simp]
 theorem thickening_ball (hε : 0 < ε) (hδ : 0 < δ) (x : E) :
     thickening ε (ball x δ) = ball x (ε + δ) := by
   rw [← thickening_singleton, thickening_thickening hε hδ, thickening_singleton] <;> infer_instance
 #align thickening_ball thickening_ball
 
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 @[simp]
 theorem thickening_closedBall (hε : 0 < ε) (hδ : 0 ≤ δ) (x : E) :
     thickening ε (closedBall x δ) = ball x (ε + δ) := by
@@ -526,12 +364,6 @@ theorem thickening_closedBall (hε : 0 < ε) (hδ : 0 ≤ δ) (x : E) :
     infer_instance
 #align thickening_closed_ball thickening_closedBall
 
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 @[simp]
 theorem cthickening_ball (hε : 0 ≤ ε) (hδ : 0 < δ) (x : E) :
     cthickening ε (ball x δ) = closedBall x (ε + δ) := by
@@ -540,12 +372,6 @@ theorem cthickening_ball (hε : 0 ≤ ε) (hδ : 0 < δ) (x : E) :
     infer_instance
 #align cthickening_ball cthickening_ball
 
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 @[simp]
 theorem cthickening_closedBall (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (x : E) :
     cthickening ε (closedBall x δ) = closedBall x (ε + δ) := by
@@ -554,90 +380,42 @@ theorem cthickening_closedBall (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (x : E) :
     infer_instance
 #align cthickening_closed_ball cthickening_closedBall
 
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 theorem ball_add_ball (hε : 0 < ε) (hδ : 0 < δ) (a b : E) :
     ball a ε + ball b δ = ball (a + b) (ε + δ) := by
   rw [ball_add, thickening_ball hε hδ b, Metric.vadd_ball, vadd_eq_add]
 #align ball_add_ball ball_add_ball
 
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 theorem ball_sub_ball (hε : 0 < ε) (hδ : 0 < δ) (a b : E) :
     ball a ε - ball b δ = ball (a - b) (ε + δ) := by
   simp_rw [sub_eq_add_neg, neg_ball, ball_add_ball hε hδ]
 #align ball_sub_ball ball_sub_ball
 
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 theorem ball_add_closedBall (hε : 0 < ε) (hδ : 0 ≤ δ) (a b : E) :
     ball a ε + closedBall b δ = ball (a + b) (ε + δ) := by
   rw [ball_add, thickening_closedBall hε hδ b, Metric.vadd_ball, vadd_eq_add]
 #align ball_add_closed_ball ball_add_closedBall
 
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 theorem ball_sub_closedBall (hε : 0 < ε) (hδ : 0 ≤ δ) (a b : E) :
     ball a ε - closedBall b δ = ball (a - b) (ε + δ) := by
   simp_rw [sub_eq_add_neg, neg_closedBall, ball_add_closedBall hε hδ]
 #align ball_sub_closed_ball ball_sub_closedBall
 
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 theorem closedBall_add_ball (hε : 0 ≤ ε) (hδ : 0 < δ) (a b : E) :
     closedBall a ε + ball b δ = ball (a + b) (ε + δ) := by
   rw [add_comm, ball_add_closedBall hδ hε b, add_comm, add_comm δ]
 #align closed_ball_add_ball closedBall_add_ball
 
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 theorem closedBall_sub_ball (hε : 0 ≤ ε) (hδ : 0 < δ) (a b : E) :
     closedBall a ε - ball b δ = ball (a - b) (ε + δ) := by
   simp_rw [sub_eq_add_neg, neg_ball, closedBall_add_ball hε hδ]
 #align closed_ball_sub_ball closedBall_sub_ball
 
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 theorem closedBall_add_closedBall [ProperSpace E] (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (a b : E) :
     closedBall a ε + closedBall b δ = closedBall (a + b) (ε + δ) := by
   rw [(is_compact_closed_ball _ _).add_closedBall hδ b, cthickening_closedBall hδ hε a,
     Metric.vadd_closedBall, vadd_eq_add, add_comm, add_comm δ]
 #align closed_ball_add_closed_ball closedBall_add_closedBall
 
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 theorem closedBall_sub_closedBall [ProperSpace E] (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (a b : E) :
     closedBall a ε - closedBall b δ = closedBall (a - b) (ε + δ) := by
   simp_rw [sub_eq_add_neg, neg_closedBall, closedBall_add_closedBall hε hδ]
@@ -649,12 +427,6 @@ section NormedAddCommGroup
 
 variable [NormedAddCommGroup E] [NormedSpace 𝕜 E]
 
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-Case conversion may be inaccurate. Consider using '#align smul_closed_ball smul_closedBallₓ'. -/
 theorem smul_closedBall (c : 𝕜) (x : E) {r : ℝ} (hr : 0 ≤ r) :
     c • closedBall x r = closedBall (c • x) (‖c‖ * r) :=
   by
@@ -663,36 +435,18 @@ theorem smul_closedBall (c : 𝕜) (x : E) {r : ℝ} (hr : 0 ≤ r) :
   · exact smul_closedBall' hc x r
 #align smul_closed_ball smul_closedBall
 
-/- warning: smul_closed_unit_ball -> smul_closedUnitBall is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align smul_closed_unit_ball smul_closedUnitBallₓ'. -/
 theorem smul_closedUnitBall (c : 𝕜) : c • closedBall (0 : E) (1 : ℝ) = closedBall (0 : E) ‖c‖ := by
   rw [smul_closedBall _ _ zero_le_one, smul_zero, mul_one]
 #align smul_closed_unit_ball smul_closedUnitBall
 
 variable [NormedSpace ℝ E]
 
-/- warning: smul_closed_unit_ball_of_nonneg -> smul_closedUnitBall_of_nonneg is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align smul_closed_unit_ball_of_nonneg smul_closedUnitBall_of_nonnegₓ'. -/
 /-- In a real normed space, the image of the unit closed ball under multiplication by a nonnegative
 number `r` is the closed ball of radius `r` with center at the origin. -/
 theorem smul_closedUnitBall_of_nonneg {r : ℝ} (hr : 0 ≤ r) :
     r • closedBall 0 1 = closedBall (0 : E) r := by rw [smul_closedUnitBall, Real.norm_of_nonneg hr]
 #align smul_closed_unit_ball_of_nonneg smul_closedUnitBall_of_nonneg
 
-/- warning: normed_space.sphere_nonempty -> NormedSpace.sphere_nonempty is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align normed_space.sphere_nonempty NormedSpace.sphere_nonemptyₓ'. -/
 /-- In a nontrivial real normed space, a sphere is nonempty if and only if its radius is
 nonnegative. -/
 @[simp]
@@ -707,12 +461,6 @@ theorem NormedSpace.sphere_nonempty [Nontrivial E] {x : E} {r : ℝ} :
   simp [norm_smul, this, Real.norm_of_nonneg hr]
 #align normed_space.sphere_nonempty NormedSpace.sphere_nonempty
 
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-Case conversion may be inaccurate. Consider using '#align smul_sphere smul_sphereₓ'. -/
 theorem smul_sphere [Nontrivial E] (c : 𝕜) (x : E) {r : ℝ} (hr : 0 ≤ r) :
     c • sphere x r = sphere (c • x) (‖c‖ * r) :=
   by
@@ -721,23 +469,11 @@ theorem smul_sphere [Nontrivial E] (c : 𝕜) (x : E) {r : ℝ} (hr : 0 ≤ r) :
   · exact smul_sphere' hc x r
 #align smul_sphere smul_sphere
 
-/- warning: affinity_unit_ball -> affinity_unitBall is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align affinity_unit_ball affinity_unitBallₓ'. -/
 /-- Any ball `metric.ball x r`, `0 < r` is the image of the unit ball under `λ y, x + r • y`. -/
 theorem affinity_unitBall {r : ℝ} (hr : 0 < r) (x : E) : x +ᵥ r • ball 0 1 = ball x r := by
   rw [smul_unitBall_of_pos hr, vadd_ball_zero]
 #align affinity_unit_ball affinity_unitBall
 
-/- warning: affinity_unit_closed_ball -> affinity_unitClosedBall is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align affinity_unit_closed_ball affinity_unitClosedBallₓ'. -/
 /-- Any closed ball `metric.closed_ball x r`, `0 ≤ r` is the image of the unit closed ball under
 `λ y, x + r • y`. -/
 theorem affinity_unitClosedBall {r : ℝ} (hr : 0 ≤ r) (x : E) :

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

@@ -386,8 +386,7 @@ theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
     infEdist x (thickening δ s) = infEdist x s - ENNReal.ofReal δ :=
   by
   obtain hs | hs := lt_or_le (inf_edist x s) (ENNReal.ofReal δ)
-  · rw [inf_edist_zero_of_mem, tsub_eq_zero_of_le hs.le]
-    exact hs
+  · rw [inf_edist_zero_of_mem, tsub_eq_zero_of_le hs.le]; exact hs
   refine' (tsub_le_iff_right.2 inf_edist_le_inf_edist_thickening_add).antisymm' _
   refine' le_sub_of_add_le_right of_real_ne_top _
   refine' le_inf_edist.2 fun z hz => le_of_forall_lt' fun r h => _
@@ -454,9 +453,7 @@ Case conversion may be inaccurate. Consider using '#align closure_thickening clo
 -- Note: `interior (cthickening δ s) ≠ thickening δ s` in general
 @[simp]
 theorem closure_thickening (hδ : 0 < δ) (s : Set E) : closure (thickening δ s) = cthickening δ s :=
-  by
-  rw [← cthickening_zero, cthickening_thickening le_rfl hδ, zero_add]
-  infer_instance
+  by rw [← cthickening_zero, cthickening_thickening le_rfl hδ, zero_add]; infer_instance
 #align closure_thickening closure_thickening
 
 /- warning: inf_edist_cthickening -> infEdist_cthickening is a dubious translation:

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

@@ -55,10 +55,7 @@ variable [NormedDivisionRing 𝕜] [SeminormedAddCommGroup E]
 variable [Module 𝕜 E] [BoundedSMul 𝕜 E]
 
 /- warning: ediam_smul₀ -> ediam_smul₀ is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (NormedRing.toSeminormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))] (c : 𝕜) (s : Set.{u2} E), Eq.{1} ENNReal (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))) c s)) (SMul.smul.{0, 0} NNReal ENNReal (SMulZeroClass.toHasSmul.{0, 0} NNReal ENNReal (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (SMulWithZero.toSmulZeroClass.{0, 0} NNReal ENNReal (MulZeroClass.toHasZero.{0} NNReal (MulZeroOneClass.toMulZeroClass.{0} NNReal (MonoidWithZero.toMulZeroOneClass.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} NNReal ENNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (Module.toMulActionWithZero.{0, 0} NNReal ENNReal NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (ENNReal.module.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (Semiring.toModule.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (NNNorm.nnnorm.{u1} 𝕜 (SeminormedAddGroup.toNNNorm.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))))) c) (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (NormedRing.toSeminormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))] (c : 𝕜) (s : Set.{u2} E), Eq.{1} ENNReal (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3)))))) c s)) (HSMul.hSMul.{0, 0, 0} NNReal ENNReal ENNReal (instHSMul.{0, 0} NNReal ENNReal (Algebra.toSMul.{0, 0} NNReal ENNReal instNNRealCommSemiring (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.instAlgebraNNRealInstNNRealCommSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))) (NNNorm.nnnorm.{u1} 𝕜 (SeminormedAddGroup.toNNNorm.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))))) c) (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ediam_smul₀ ediam_smul₀ₓ'. -/
 theorem ediam_smul₀ (c : 𝕜) (s : Set E) : EMetric.diam (c • s) = ‖c‖₊ • EMetric.diam s :=
   by
@@ -83,10 +80,7 @@ theorem diam_smul₀ (c : 𝕜) (x : Set E) : diam (c • x) = ‖c‖ * diam x
 #align diam_smul₀ diam_smul₀
 
 /- warning: inf_edist_smul₀ -> infEdist_smul₀ is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (NormedRing.toSeminormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))] {c : 𝕜}, (Ne.{succ u1} 𝕜 c (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))))))) -> (forall (s : Set.{u2} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3)))) c x) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))) c s)) (SMul.smul.{0, 0} NNReal ENNReal (SMulZeroClass.toHasSmul.{0, 0} NNReal ENNReal (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (SMulWithZero.toSmulZeroClass.{0, 0} NNReal ENNReal (MulZeroClass.toHasZero.{0} NNReal (MulZeroOneClass.toMulZeroClass.{0} NNReal (MonoidWithZero.toMulZeroOneClass.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} NNReal ENNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (Module.toMulActionWithZero.{0, 0} NNReal ENNReal NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (ENNReal.module.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (Semiring.toModule.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (NNNorm.nnnorm.{u1} 𝕜 (SeminormedAddGroup.toNNNorm.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))))) c) (EMetric.infEdist.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) x s)))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedDivisionRing.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2))] [_inst_4 : BoundedSMul.{u2, u1} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (NormedRing.toSeminormedRing.{u2} 𝕜 (NormedDivisionRing.toNormedRing.{u2} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) _inst_3))))] {c : 𝕜}, (Ne.{succ u2} 𝕜 c (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))))))) -> (forall (s : Set.{u1} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) _inst_3))))) c x) (HSMul.hSMul.{u2, u1, u1} 𝕜 (Set.{u1} E) (Set.{u1} E) (instHSMul.{u2, u1} 𝕜 (Set.{u1} E) (Set.smulSet.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) _inst_3)))))) c s)) (HSMul.hSMul.{0, 0, 0} NNReal ENNReal ENNReal (instHSMul.{0, 0} NNReal ENNReal (Algebra.toSMul.{0, 0} NNReal ENNReal instNNRealCommSemiring (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.instAlgebraNNRealInstNNRealCommSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))) (NNNorm.nnnorm.{u2} 𝕜 (SeminormedAddGroup.toNNNorm.{u2} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedDivisionRing.toNormedRing.{u2} 𝕜 _inst_1)))))) c) (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x s)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align inf_edist_smul₀ infEdist_smul₀ₓ'. -/
 theorem infEdist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
     EMetric.infEdist (c • x) (c • s) = ‖c‖₊ • EMetric.infEdist x s :=
@@ -102,10 +96,7 @@ theorem infEdist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
 #align inf_edist_smul₀ infEdist_smul₀
 
 /- warning: inf_dist_smul₀ -> infDist_smul₀ is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (NormedRing.toSeminormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))] {c : 𝕜}, (Ne.{succ u1} 𝕜 c (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))))))) -> (forall (s : Set.{u2} E) (x : E), Eq.{1} Real (Metric.infDist.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3)))) c x) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))) c s)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} 𝕜 (NormedDivisionRing.toHasNorm.{u1} 𝕜 _inst_1) c) (Metric.infDist.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) x s)))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedDivisionRing.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2))] [_inst_4 : BoundedSMul.{u2, u1} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (NormedRing.toSeminormedRing.{u2} 𝕜 (NormedDivisionRing.toNormedRing.{u2} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) _inst_3))))] {c : 𝕜}, (Ne.{succ u2} 𝕜 c (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))))))) -> (forall (s : Set.{u1} E) (x : E), Eq.{1} Real (Metric.infDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) _inst_3))))) c x) (HSMul.hSMul.{u2, u1, u1} 𝕜 (Set.{u1} E) (Set.{u1} E) (instHSMul.{u2, u1} 𝕜 (Set.{u1} E) (Set.smulSet.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) _inst_3)))))) c s)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u2} 𝕜 (NormedDivisionRing.toNorm.{u2} 𝕜 _inst_1) c) (Metric.infDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x s)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align inf_dist_smul₀ infDist_smul₀ₓ'. -/
 theorem infDist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
     Metric.infDist (c • x) (c • s) = ‖c‖ * Metric.infDist x s := by
@@ -186,10 +177,7 @@ theorem Metric.Bounded.smul {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c
 -/
 
 /- warning: eventually_singleton_add_smul_subset -> eventually_singleton_add_smul_subset is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {x : E} {s : Set.{u2} E}, (Metric.Bounded.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) s) -> (forall {u : Set.{u2} E}, (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) u (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2))) x)) -> (Filter.Eventually.{u1} 𝕜 (fun (r : 𝕜) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} E) (Set.{u2} E) (Set.{u2} E) (instHAdd.{u2} (Set.{u2} E) (Set.add.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))))) (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) r s)) u) (nhds.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))))))))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {x : E} {s : Set.{u2} E}, (Metric.Bounded.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) s) -> (forall {u : Set.{u2} E}, (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) u (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2))) x)) -> (Filter.Eventually.{u1} 𝕜 (fun (r : 𝕜) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} E) (Set.{u2} E) (Set.{u2} E) (instHAdd.{u2} (Set.{u2} E) (Set.add.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))))) (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.instSingletonSet.{u2} E) x) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))))))) r s)) u) (nhds.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align eventually_singleton_add_smul_subset eventually_singleton_add_smul_subsetₓ'. -/
 /-- If `s` is a bounded set, then for small enough `r`, the set `{x} + r • s` is contained in any
 fixed neighborhood of `x`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -36,6 +36,12 @@ variable [SeminormedAddCommGroup 𝕜] [SeminormedAddCommGroup E]
 
 variable [SMulZeroClass 𝕜 E] [BoundedSMul 𝕜 E]
 
+/- warning: ediam_smul_le -> ediam_smul_le is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : SMulZeroClass.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2))))))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} 𝕜 _inst_1) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (SubNegMonoid.toAddMonoid.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (SeminormedAddGroup.toAddGroup.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) _inst_3)] (c : 𝕜) (s : Set.{u2} E), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) _inst_3)) c s)) (SMul.smul.{0, 0} NNReal ENNReal (SMulZeroClass.toHasSmul.{0, 0} NNReal ENNReal (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (SMulWithZero.toSmulZeroClass.{0, 0} NNReal ENNReal (MulZeroClass.toHasZero.{0} NNReal (MulZeroOneClass.toMulZeroClass.{0} NNReal (MonoidWithZero.toMulZeroOneClass.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} NNReal ENNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (Module.toMulActionWithZero.{0, 0} NNReal ENNReal NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (ENNReal.module.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (Semiring.toModule.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (NNNorm.nnnorm.{u1} 𝕜 (SeminormedAddGroup.toNNNorm.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 _inst_1)) c) (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : SMulZeroClass.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} 𝕜 _inst_1) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (NegZeroClass.toZero.{u1} 𝕜 (SubNegZeroMonoid.toNegZeroClass.{u1} 𝕜 (SubtractionMonoid.toSubNegZeroMonoid.{u1} 𝕜 (SubtractionCommMonoid.toSubtractionMonoid.{u1} 𝕜 (AddCommGroup.toDivisionAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) _inst_3)] (c : 𝕜) (s : Set.{u2} E), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) _inst_3))) c s)) (HSMul.hSMul.{0, 0, 0} NNReal ENNReal ENNReal (instHSMul.{0, 0} NNReal ENNReal (Algebra.toSMul.{0, 0} NNReal ENNReal instNNRealCommSemiring (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.instAlgebraNNRealInstNNRealCommSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))) (NNNorm.nnnorm.{u1} 𝕜 (SeminormedAddGroup.toNNNorm.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 _inst_1)) c) (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s))
+Case conversion may be inaccurate. Consider using '#align ediam_smul_le ediam_smul_leₓ'. -/
 theorem ediam_smul_le (c : 𝕜) (s : Set E) : EMetric.diam (c • s) ≤ ‖c‖₊ • EMetric.diam s :=
   (lipschitzWith_smul c).ediam_image_le s
 #align ediam_smul_le ediam_smul_le
@@ -48,6 +54,12 @@ variable [NormedDivisionRing 𝕜] [SeminormedAddCommGroup E]
 
 variable [Module 𝕜 E] [BoundedSMul 𝕜 E]
 
+/- warning: ediam_smul₀ -> ediam_smul₀ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (NormedRing.toSeminormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))] (c : 𝕜) (s : Set.{u2} E), Eq.{1} ENNReal (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))) c s)) (SMul.smul.{0, 0} NNReal ENNReal (SMulZeroClass.toHasSmul.{0, 0} NNReal ENNReal (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (SMulWithZero.toSmulZeroClass.{0, 0} NNReal ENNReal (MulZeroClass.toHasZero.{0} NNReal (MulZeroOneClass.toMulZeroClass.{0} NNReal (MonoidWithZero.toMulZeroOneClass.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} NNReal ENNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (Module.toMulActionWithZero.{0, 0} NNReal ENNReal NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (ENNReal.module.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (Semiring.toModule.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (NNNorm.nnnorm.{u1} 𝕜 (SeminormedAddGroup.toNNNorm.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))))) c) (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (NormedRing.toSeminormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))] (c : 𝕜) (s : Set.{u2} E), Eq.{1} ENNReal (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3)))))) c s)) (HSMul.hSMul.{0, 0, 0} NNReal ENNReal ENNReal (instHSMul.{0, 0} NNReal ENNReal (Algebra.toSMul.{0, 0} NNReal ENNReal instNNRealCommSemiring (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.instAlgebraNNRealInstNNRealCommSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))) (NNNorm.nnnorm.{u1} 𝕜 (SeminormedAddGroup.toNNNorm.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))))) c) (EMetric.diam.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s))
+Case conversion may be inaccurate. Consider using '#align ediam_smul₀ ediam_smul₀ₓ'. -/
 theorem ediam_smul₀ (c : 𝕜) (s : Set E) : EMetric.diam (c • s) = ‖c‖₊ • EMetric.diam s :=
   by
   refine' le_antisymm (ediam_smul_le c s) _
@@ -60,10 +72,22 @@ theorem ediam_smul₀ (c : 𝕜) (s : Set E) : EMetric.diam (c • s) = ‖c‖
       ENNReal.le_inv_smul_iff (nnnorm_ne_zero_iff.mpr hc)] at this
 #align ediam_smul₀ ediam_smul₀
 
+/- warning: diam_smul₀ -> diam_smul₀ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (NormedRing.toSeminormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))] (c : 𝕜) (x : Set.{u2} E), Eq.{1} Real (Metric.diam.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))) c x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} 𝕜 (NormedDivisionRing.toHasNorm.{u1} 𝕜 _inst_1) c) (Metric.diam.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) x))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (NormedRing.toSeminormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))] (c : 𝕜) (x : Set.{u2} E), Eq.{1} Real (Metric.diam.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3)))))) c x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} 𝕜 (NormedDivisionRing.toNorm.{u1} 𝕜 _inst_1) c) (Metric.diam.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) x))
+Case conversion may be inaccurate. Consider using '#align diam_smul₀ diam_smul₀ₓ'. -/
 theorem diam_smul₀ (c : 𝕜) (x : Set E) : diam (c • x) = ‖c‖ * diam x := by
   simp_rw [diam, ediam_smul₀, ENNReal.toReal_smul, NNReal.smul_def, coe_nnnorm, smul_eq_mul]
 #align diam_smul₀ diam_smul₀
 
+/- warning: inf_edist_smul₀ -> infEdist_smul₀ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (NormedRing.toSeminormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))] {c : 𝕜}, (Ne.{succ u1} 𝕜 c (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))))))) -> (forall (s : Set.{u2} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3)))) c x) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))) c s)) (SMul.smul.{0, 0} NNReal ENNReal (SMulZeroClass.toHasSmul.{0, 0} NNReal ENNReal (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (SMulWithZero.toSmulZeroClass.{0, 0} NNReal ENNReal (MulZeroClass.toHasZero.{0} NNReal (MulZeroOneClass.toMulZeroClass.{0} NNReal (MonoidWithZero.toMulZeroOneClass.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} NNReal ENNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (Module.toMulActionWithZero.{0, 0} NNReal ENNReal NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (ENNReal.module.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (Semiring.toModule.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (NNNorm.nnnorm.{u1} 𝕜 (SeminormedAddGroup.toNNNorm.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))))) c) (EMetric.infEdist.{u2} E (PseudoMetricSpace.toPseudoEMetricSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) x s)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedDivisionRing.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2))] [_inst_4 : BoundedSMul.{u2, u1} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (NormedRing.toSeminormedRing.{u2} 𝕜 (NormedDivisionRing.toNormedRing.{u2} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) _inst_3))))] {c : 𝕜}, (Ne.{succ u2} 𝕜 c (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))))))) -> (forall (s : Set.{u1} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) _inst_3))))) c x) (HSMul.hSMul.{u2, u1, u1} 𝕜 (Set.{u1} E) (Set.{u1} E) (instHSMul.{u2, u1} 𝕜 (Set.{u1} E) (Set.smulSet.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) _inst_3)))))) c s)) (HSMul.hSMul.{0, 0, 0} NNReal ENNReal ENNReal (instHSMul.{0, 0} NNReal ENNReal (Algebra.toSMul.{0, 0} NNReal ENNReal instNNRealCommSemiring (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.instAlgebraNNRealInstNNRealCommSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))) (NNNorm.nnnorm.{u2} 𝕜 (SeminormedAddGroup.toNNNorm.{u2} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedDivisionRing.toNormedRing.{u2} 𝕜 _inst_1)))))) c) (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x s)))
+Case conversion may be inaccurate. Consider using '#align inf_edist_smul₀ infEdist_smul₀ₓ'. -/
 theorem infEdist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
     EMetric.infEdist (c • x) (c • s) = ‖c‖₊ • EMetric.infEdist x s :=
   by
@@ -77,6 +101,12 @@ theorem infEdist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
     simp_rw [ENNReal.smul_def, smul_eq_mul, ENNReal.mul_iInf_of_ne this ENNReal.coe_ne_top]
 #align inf_edist_smul₀ infEdist_smul₀
 
+/- warning: inf_dist_smul₀ -> infDist_smul₀ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (NormedRing.toSeminormedRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))] {c : 𝕜}, (Ne.{succ u1} 𝕜 c (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))))))) -> (forall (s : Set.{u2} E) (x : E), Eq.{1} Real (Metric.infDist.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3)))) c x) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedDivisionRing.toNormedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))))) c s)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} 𝕜 (NormedDivisionRing.toHasNorm.{u1} 𝕜 _inst_1) c) (Metric.infDist.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) x s)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedDivisionRing.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2))] [_inst_4 : BoundedSMul.{u2, u1} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (NormedRing.toSeminormedRing.{u2} 𝕜 (NormedDivisionRing.toNormedRing.{u2} 𝕜 _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) _inst_3))))] {c : 𝕜}, (Ne.{succ u2} 𝕜 c (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))))))) -> (forall (s : Set.{u1} E) (x : E), Eq.{1} Real (Metric.infDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) _inst_3))))) c x) (HSMul.hSMul.{u2, u1, u1} 𝕜 (Set.{u1} E) (Set.{u1} E) (instHSMul.{u2, u1} 𝕜 (Set.{u1} E) (Set.smulSet.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (DivisionRing.toDivisionSemiring.{u2} 𝕜 (NormedDivisionRing.toDivisionRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) _inst_3)))))) c s)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u2} 𝕜 (NormedDivisionRing.toNorm.{u2} 𝕜 _inst_1) c) (Metric.infDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x s)))
+Case conversion may be inaccurate. Consider using '#align inf_dist_smul₀ infDist_smul₀ₓ'. -/
 theorem infDist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
     Metric.infDist (c • x) (c • s) = ‖c‖ * Metric.infDist x s := by
   simp_rw [Metric.infDist, infEdist_smul₀ hc, ENNReal.toReal_smul, NNReal.smul_def, coe_nnnorm,

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yaël Dillies
 
 ! This file was ported from Lean 3 source module analysis.normed_space.pointwise
-! leanprover-community/mathlib commit ce38d86c0b2d427ce208c3cee3159cb421d2b3c4
+! leanprover-community/mathlib commit bc91ed7093bf098d253401e69df601fc33dde156
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -28,7 +28,64 @@ open Metric Set
 
 open Pointwise Topology
 
-variable {𝕜 E : Type _} [NormedField 𝕜]
+variable {𝕜 E : Type _}
+
+section SMulZeroClass
+
+variable [SeminormedAddCommGroup 𝕜] [SeminormedAddCommGroup E]
+
+variable [SMulZeroClass 𝕜 E] [BoundedSMul 𝕜 E]
+
+theorem ediam_smul_le (c : 𝕜) (s : Set E) : EMetric.diam (c • s) ≤ ‖c‖₊ • EMetric.diam s :=
+  (lipschitzWith_smul c).ediam_image_le s
+#align ediam_smul_le ediam_smul_le
+
+end SMulZeroClass
+
+section DivisionRing
+
+variable [NormedDivisionRing 𝕜] [SeminormedAddCommGroup E]
+
+variable [Module 𝕜 E] [BoundedSMul 𝕜 E]
+
+theorem ediam_smul₀ (c : 𝕜) (s : Set E) : EMetric.diam (c • s) = ‖c‖₊ • EMetric.diam s :=
+  by
+  refine' le_antisymm (ediam_smul_le c s) _
+  obtain rfl | hc := eq_or_ne c 0
+  · obtain rfl | hs := s.eq_empty_or_nonempty
+    · simp
+    simp [zero_smul_set hs, ← Set.singleton_zero]
+  · have := (lipschitzWith_smul c⁻¹).ediam_image_le (c • s)
+    rwa [← smul_eq_mul, ← ENNReal.smul_def, Set.image_smul, inv_smul_smul₀ hc s, nnnorm_inv,
+      ENNReal.le_inv_smul_iff (nnnorm_ne_zero_iff.mpr hc)] at this
+#align ediam_smul₀ ediam_smul₀
+
+theorem diam_smul₀ (c : 𝕜) (x : Set E) : diam (c • x) = ‖c‖ * diam x := by
+  simp_rw [diam, ediam_smul₀, ENNReal.toReal_smul, NNReal.smul_def, coe_nnnorm, smul_eq_mul]
+#align diam_smul₀ diam_smul₀
+
+theorem infEdist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
+    EMetric.infEdist (c • x) (c • s) = ‖c‖₊ • EMetric.infEdist x s :=
+  by
+  simp_rw [EMetric.infEdist]
+  have : Function.Surjective ((· • ·) c : E → E) :=
+    Function.RightInverse.surjective (smul_inv_smul₀ hc)
+  trans ⨅ (y) (H : y ∈ s), ‖c‖₊ • edist x y
+  · refine' (this.infi_congr _ fun y => _).symm
+    simp_rw [smul_mem_smul_set_iff₀ hc, edist_smul₀]
+  · have : (‖c‖₊ : ENNReal) ≠ 0 := by simp [hc]
+    simp_rw [ENNReal.smul_def, smul_eq_mul, ENNReal.mul_iInf_of_ne this ENNReal.coe_ne_top]
+#align inf_edist_smul₀ infEdist_smul₀
+
+theorem infDist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
+    Metric.infDist (c • x) (c • s) = ‖c‖ * Metric.infDist x s := by
+  simp_rw [Metric.infDist, infEdist_smul₀ hc, ENNReal.toReal_smul, NNReal.smul_def, coe_nnnorm,
+    smul_eq_mul]
+#align inf_dist_smul₀ infDist_smul₀
+
+end DivisionRing
+
+variable [NormedField 𝕜]
 
 section SeminormedAddCommGroup
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ad820c4997738e2f542f8a20f32911f52020e26

@@ -304,7 +304,7 @@ open Emetric ENNReal
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (s : Set.{u1} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x s) (ENNReal.ofReal δ)))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (s : Set.{u1} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x s) (ENNReal.ofReal δ)))
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (s : Set.{u1} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x s) (ENNReal.ofReal δ)))
 Case conversion may be inaccurate. Consider using '#align inf_edist_thickening infEdist_thickeningₓ'. -/
 @[simp]
 theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
@@ -388,7 +388,7 @@ theorem closure_thickening (hδ : 0 < δ) (s : Set E) : closure (thickening δ s
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] (δ : Real) (s : Set.{u1} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x s) (ENNReal.ofReal δ))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] (δ : Real) (s : Set.{u1} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x s) (ENNReal.ofReal δ))
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] (δ : Real) (s : Set.{u1} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x s) (ENNReal.ofReal δ))
 Case conversion may be inaccurate. Consider using '#align inf_edist_cthickening infEdist_cthickeningₓ'. -/
 @[simp]
 theorem infEdist_cthickening (δ : ℝ) (s : Set E) (x : E) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yaël Dillies
 
 ! This file was ported from Lean 3 source module analysis.normed_space.pointwise
-! leanprover-community/mathlib commit 832a8ba8f10f11fea99367c469ff802e69a5b8ec
+! leanprover-community/mathlib commit ce38d86c0b2d427ce208c3cee3159cb421d2b3c4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.NormedSpace.Basic
 /-!
 # Properties of pointwise scalar multiplication of sets in normed spaces.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We explore the relationships between scalar multiplication of sets in vector spaces, and the norm.
 Notably, we express arbitrary balls as rescaling of other balls, and we show that the
 multiplication of bounded sets remain bounded.

mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0

@@ -31,6 +31,12 @@ section SeminormedAddCommGroup
 
 variable [SeminormedAddCommGroup E] [NormedSpace 𝕜 E]
 
+/- warning: smul_ball -> smul_ball is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {c : 𝕜}, (Ne.{succ u1} 𝕜 c (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (forall (x : E) (r : Real), Eq.{succ u2} (Set.{u2} E) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) c (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) x r)) (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))))) c x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) c) r)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {c : 𝕜}, (Ne.{succ u2} 𝕜 c (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))))) -> (forall (x : E) (r : Real), Eq.{succ u1} (Set.{u1} E) (HSMul.hSMul.{u2, u1, u1} 𝕜 (Set.{u1} E) (Set.{u1} E) (instHSMul.{u2, u1} 𝕜 (Set.{u1} E) (Set.smulSet.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) c (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x r)) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))))) c x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u2} 𝕜 (NormedField.toNorm.{u2} 𝕜 _inst_1) c) r)))
+Case conversion may be inaccurate. Consider using '#align smul_ball smul_ballₓ'. -/
 theorem smul_ball {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) : c • ball x r = ball (c • x) (‖c‖ * r) :=
   by
   ext y
@@ -39,10 +45,22 @@ theorem smul_ball {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) : c • ball x r =
   simp [← div_eq_inv_mul, div_lt_iff (norm_pos_iff.2 hc), mul_comm _ r, dist_smul₀]
 #align smul_ball smul_ball
 
-theorem smul_unit_ball {c : 𝕜} (hc : c ≠ 0) : c • ball (0 : E) (1 : ℝ) = ball (0 : E) ‖c‖ := by
+/- warning: smul_unit_ball -> smul_unitBall is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {c : 𝕜}, (Ne.{succ u1} 𝕜 c (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (Eq.{succ u2} (Set.{u2} E) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) c (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2))))))))) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) c)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {c : 𝕜}, (Ne.{succ u2} 𝕜 c (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} E) (HSMul.hSMul.{u2, u1, u1} 𝕜 (Set.{u1} E) (Set.{u1} E) (instHSMul.{u2, u1} 𝕜 (Set.{u1} E) (Set.smulSet.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) c (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))))) (Norm.norm.{u2} 𝕜 (NormedField.toNorm.{u2} 𝕜 _inst_1) c)))
+Case conversion may be inaccurate. Consider using '#align smul_unit_ball smul_unitBallₓ'. -/
+theorem smul_unitBall {c : 𝕜} (hc : c ≠ 0) : c • ball (0 : E) (1 : ℝ) = ball (0 : E) ‖c‖ := by
   rw [smul_ball hc, smul_zero, mul_one]
-#align smul_unit_ball smul_unit_ball
-
+#align smul_unit_ball smul_unitBall
+
+/- warning: smul_sphere' -> smul_sphere' is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {c : 𝕜}, (Ne.{succ u1} 𝕜 c (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (forall (x : E) (r : Real), Eq.{succ u2} (Set.{u2} E) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) c (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) x r)) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))))) c x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) c) r)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {c : 𝕜}, (Ne.{succ u2} 𝕜 c (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))))) -> (forall (x : E) (r : Real), Eq.{succ u1} (Set.{u1} E) (HSMul.hSMul.{u2, u1, u1} 𝕜 (Set.{u1} E) (Set.{u1} E) (instHSMul.{u2, u1} 𝕜 (Set.{u1} E) (Set.smulSet.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) c (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x r)) (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))))) c x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u2} 𝕜 (NormedField.toNorm.{u2} 𝕜 _inst_1) c) r)))
+Case conversion may be inaccurate. Consider using '#align smul_sphere' smul_sphere'ₓ'. -/
 theorem smul_sphere' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
     c • sphere x r = sphere (c • x) (‖c‖ * r) :=
   by
@@ -53,11 +71,18 @@ theorem smul_sphere' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
     mul_comm r]
 #align smul_sphere' smul_sphere'
 
-theorem smul_closed_ball' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
+/- warning: smul_closed_ball' -> smul_closedBall' is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {c : 𝕜}, (Ne.{succ u1} 𝕜 c (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (forall (x : E) (r : Real), Eq.{succ u2} (Set.{u2} E) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) c (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) x r)) (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))))) c x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) c) r)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {c : 𝕜}, (Ne.{succ u2} 𝕜 c (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))))) -> (forall (x : E) (r : Real), Eq.{succ u1} (Set.{u1} E) (HSMul.hSMul.{u2, u1, u1} 𝕜 (Set.{u1} E) (Set.{u1} E) (instHSMul.{u2, u1} 𝕜 (Set.{u1} E) (Set.smulSet.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) c (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x r)) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))))) c x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u2} 𝕜 (NormedField.toNorm.{u2} 𝕜 _inst_1) c) r)))
+Case conversion may be inaccurate. Consider using '#align smul_closed_ball' smul_closedBall'ₓ'. -/
+theorem smul_closedBall' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
     c • closedBall x r = closedBall (c • x) (‖c‖ * r) := by
   simp only [← ball_union_sphere, Set.smul_set_union, smul_ball hc, smul_sphere' hc]
-#align smul_closed_ball' smul_closed_ball'
+#align smul_closed_ball' smul_closedBall'
 
+#print Metric.Bounded.smul /-
 theorem Metric.Bounded.smul {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c • s) :=
   by
   obtain ⟨R, hR⟩ : ∃ R : ℝ, ∀ x ∈ s, ‖x‖ ≤ R := hs.exists_norm_le
@@ -68,7 +93,14 @@ theorem Metric.Bounded.smul {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c
     _ ≤ ‖c‖ * R := mul_le_mul_of_nonneg_left (hR y ys) (norm_nonneg _)
     
 #align metric.bounded.smul Metric.Bounded.smul
+-/
 
+/- warning: eventually_singleton_add_smul_subset -> eventually_singleton_add_smul_subset is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {x : E} {s : Set.{u2} E}, (Metric.Bounded.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) s) -> (forall {u : Set.{u2} E}, (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) u (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2))) x)) -> (Filter.Eventually.{u1} 𝕜 (fun (r : 𝕜) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} E) (Set.{u2} E) (Set.{u2} E) (instHAdd.{u2} (Set.{u2} E) (Set.add.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))))) (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) r s)) u) (nhds.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {x : E} {s : Set.{u2} E}, (Metric.Bounded.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) s) -> (forall {u : Set.{u2} E}, (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) u (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2))) x)) -> (Filter.Eventually.{u1} 𝕜 (fun (r : 𝕜) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} E) (Set.{u2} E) (Set.{u2} E) (instHAdd.{u2} (Set.{u2} E) (Set.add.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))))) (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.instSingletonSet.{u2} E) x) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))))))) r s)) u) (nhds.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))))))))
+Case conversion may be inaccurate. Consider using '#align eventually_singleton_add_smul_subset eventually_singleton_add_smul_subsetₓ'. -/
 /-- If `s` is a bounded set, then for small enough `r`, the set `{x} + r • s` is contained in any
 fixed neighborhood of `x`. -/
 theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bounded s) {u : Set E}
@@ -97,12 +129,24 @@ theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bounded s
 
 variable [NormedSpace ℝ E] {x y z : E} {δ ε : ℝ}
 
+/- warning: smul_unit_ball_of_pos -> smul_unitBall_of_pos is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Eq.{succ u1} (Set.{u1} E) (SMul.smul.{0, u1} Real (Set.{u1} E) (Set.smulSet.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{0, u1} Real E Real.normedField _inst_2 _inst_4)))))) r (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_2))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_2))))))))) r))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Eq.{succ u1} (Set.{u1} E) (HSMul.hSMul.{0, u1, u1} Real (Set.{u1} E) (Set.{u1} E) (instHSMul.{0, u1} Real (Set.{u1} E) (Set.smulSet.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{0, u1} Real E Real.normedField _inst_2 _inst_4))))))) r (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))))) r))
+Case conversion may be inaccurate. Consider using '#align smul_unit_ball_of_pos smul_unitBall_of_posₓ'. -/
 /-- In a real normed space, the image of the unit ball under scalar multiplication by a positive
 constant `r` is the ball of radius `r`. -/
-theorem smul_unit_ball_of_pos {r : ℝ} (hr : 0 < r) : r • ball 0 1 = ball (0 : E) r := by
-  rw [smul_unit_ball hr.ne', Real.norm_of_nonneg hr.le]
-#align smul_unit_ball_of_pos smul_unit_ball_of_pos
-
+theorem smul_unitBall_of_pos {r : ℝ} (hr : 0 < r) : r • ball 0 1 = ball (0 : E) r := by
+  rw [smul_unitBall hr.ne', Real.norm_of_nonneg hr.le]
+#align smul_unit_ball_of_pos smul_unitBall_of_pos
+
+/- warning: exists_dist_eq -> exists_dist_eq is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] (x : E) (z : E) {a : Real} {b : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) a) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) b) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) a b) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Exists.{succ u1} E (fun (y : E) => And (Eq.{1} Real (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) b (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x z))) (Eq.{1} Real (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) y z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) a (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x z)))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] (x : E) (z : E) {a : Real} {b : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) a) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) b) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) a b) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Exists.{succ u1} E (fun (y : E) => And (Eq.{1} Real (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) b (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x z))) (Eq.{1} Real (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) y z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) a (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x z)))))
+Case conversion may be inaccurate. Consider using '#align exists_dist_eq exists_dist_eqₓ'. -/
 -- This is also true for `ℚ`-normed spaces
 theorem exists_dist_eq (x z : E) {a b : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1) :
     ∃ y, dist x y = b * dist x z ∧ dist y z = a * dist x z :=
@@ -113,6 +157,12 @@ theorem exists_dist_eq (x z : E) {a b : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) (hab
   simp [dist_eq_norm, ← hab, add_smul, ← smul_sub, norm_smul_of_nonneg, ha, hb]
 #align exists_dist_eq exists_dist_eq
 
+/- warning: exists_dist_le_le -> exists_dist_le_le is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {z : E} {δ : Real} {ε : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ)) -> (Exists.{succ u1} E (fun (y : E) => And (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y) δ) (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) y z) ε)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {z : E} {δ : Real} {ε : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ)) -> (Exists.{succ u1} E (fun (y : E) => And (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y) δ) (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) y z) ε)))
+Case conversion may be inaccurate. Consider using '#align exists_dist_le_le exists_dist_le_leₓ'. -/
 theorem exists_dist_le_le (hδ : 0 ≤ δ) (hε : 0 ≤ ε) (h : dist x z ≤ ε + δ) :
     ∃ y, dist x y ≤ δ ∧ dist y z ≤ ε :=
   by
@@ -128,6 +178,12 @@ theorem exists_dist_le_le (hδ : 0 ≤ δ) (hε : 0 ≤ ε) (h : dist x z ≤ ε
   exact ⟨mul_le_of_le_one_left hδ h, mul_le_of_le_one_left hε h⟩
 #align exists_dist_le_le exists_dist_le_le
 
+/- warning: exists_dist_le_lt -> exists_dist_le_lt is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {z : E} {δ : Real} {ε : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ)) -> (Exists.{succ u1} E (fun (y : E) => And (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y) δ) (LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) y z) ε)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {z : E} {δ : Real} {ε : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ)) -> (Exists.{succ u1} E (fun (y : E) => And (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y) δ) (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) y z) ε)))
+Case conversion may be inaccurate. Consider using '#align exists_dist_le_lt exists_dist_le_ltₓ'. -/
 -- This is also true for `ℚ`-normed spaces
 theorem exists_dist_le_lt (hδ : 0 ≤ δ) (hε : 0 < ε) (h : dist x z < ε + δ) :
     ∃ y, dist x y ≤ δ ∧ dist y z < ε :=
@@ -142,6 +198,12 @@ theorem exists_dist_le_lt (hδ : 0 ≤ δ) (hε : 0 < ε) (h : dist x z < ε + 
   exact ⟨mul_le_of_le_one_left hδ h.le, mul_lt_of_lt_one_left hε h⟩
 #align exists_dist_le_lt exists_dist_le_lt
 
+/- warning: exists_dist_lt_le -> exists_dist_lt_le is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {z : E} {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ)) -> (Exists.{succ u1} E (fun (y : E) => And (LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y) δ) (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) y z) ε)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {z : E} {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ)) -> (Exists.{succ u1} E (fun (y : E) => And (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y) δ) (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) y z) ε)))
+Case conversion may be inaccurate. Consider using '#align exists_dist_lt_le exists_dist_lt_leₓ'. -/
 -- This is also true for `ℚ`-normed spaces
 theorem exists_dist_lt_le (hδ : 0 < δ) (hε : 0 ≤ ε) (h : dist x z < ε + δ) :
     ∃ y, dist x y < δ ∧ dist y z ≤ ε :=
@@ -151,6 +213,12 @@ theorem exists_dist_lt_le (hδ : 0 < δ) (hε : 0 ≤ ε) (h : dist x z < ε + 
   exact ⟨y, by simp [dist_comm x y, dist_comm y z, *]⟩
 #align exists_dist_lt_le exists_dist_lt_le
 
+/- warning: exists_dist_lt_lt -> exists_dist_lt_lt is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {z : E} {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ)) -> (Exists.{succ u1} E (fun (y : E) => And (LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y) δ) (LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) y z) ε)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {z : E} {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ)) -> (Exists.{succ u1} E (fun (y : E) => And (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y) δ) (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) y z) ε)))
+Case conversion may be inaccurate. Consider using '#align exists_dist_lt_lt exists_dist_lt_ltₓ'. -/
 -- This is also true for `ℚ`-normed spaces
 theorem exists_dist_lt_lt (hδ : 0 < δ) (hε : 0 < ε) (h : dist x z < ε + δ) :
     ∃ y, dist x y < δ ∧ dist y z < ε :=
@@ -165,6 +233,12 @@ theorem exists_dist_lt_lt (hδ : 0 < δ) (hε : 0 < ε) (h : dist x z < ε + δ)
   exact ⟨mul_lt_of_lt_one_left hδ h, mul_lt_of_lt_one_left hε h⟩
 #align exists_dist_lt_lt exists_dist_lt_lt
 
+/- warning: disjoint_ball_ball_iff -> disjoint_ball_ball_iff is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {y : E} {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Iff (Disjoint.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} E) (Set.booleanAlgebra.{u1} E))) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) y ε)) (LE.le.{0} Real Real.hasLe (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) δ ε) (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {y : E} {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Iff (Disjoint.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} E) (Preorder.toLE.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) y ε)) (LE.le.{0} Real Real.instLEReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) δ ε) (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y)))
+Case conversion may be inaccurate. Consider using '#align disjoint_ball_ball_iff disjoint_ball_ball_iffₓ'. -/
 -- This is also true for `ℚ`-normed spaces
 theorem disjoint_ball_ball_iff (hδ : 0 < δ) (hε : 0 < ε) :
     Disjoint (ball x δ) (ball y ε) ↔ δ + ε ≤ dist x y :=
@@ -176,6 +250,12 @@ theorem disjoint_ball_ball_iff (hδ : 0 < δ) (hε : 0 < ε) :
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_ball_ball_iff disjoint_ball_ball_iff
 
+/- warning: disjoint_ball_closed_ball_iff -> disjoint_ball_closedBall_iff is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {y : E} {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Iff (Disjoint.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} E) (Set.booleanAlgebra.{u1} E))) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) y ε)) (LE.le.{0} Real Real.hasLe (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) δ ε) (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {y : E} {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Iff (Disjoint.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} E) (Preorder.toLE.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) y ε)) (LE.le.{0} Real Real.instLEReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) δ ε) (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y)))
+Case conversion may be inaccurate. Consider using '#align disjoint_ball_closed_ball_iff disjoint_ball_closedBall_iffₓ'. -/
 -- This is also true for `ℚ`-normed spaces
 theorem disjoint_ball_closedBall_iff (hδ : 0 < δ) (hε : 0 ≤ ε) :
     Disjoint (ball x δ) (closedBall y ε) ↔ δ + ε ≤ dist x y :=
@@ -187,12 +267,24 @@ theorem disjoint_ball_closedBall_iff (hδ : 0 < δ) (hε : 0 ≤ ε) :
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_ball_closed_ball_iff disjoint_ball_closedBall_iff
 
+/- warning: disjoint_closed_ball_ball_iff -> disjoint_closedBall_ball_iff is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {y : E} {δ : Real} {ε : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Iff (Disjoint.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} E) (Set.booleanAlgebra.{u1} E))) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) y ε)) (LE.le.{0} Real Real.hasLe (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) δ ε) (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {y : E} {δ : Real} {ε : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Iff (Disjoint.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} E) (Preorder.toLE.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) y ε)) (LE.le.{0} Real Real.instLEReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) δ ε) (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y)))
+Case conversion may be inaccurate. Consider using '#align disjoint_closed_ball_ball_iff disjoint_closedBall_ball_iffₓ'. -/
 -- This is also true for `ℚ`-normed spaces
 theorem disjoint_closedBall_ball_iff (hδ : 0 ≤ δ) (hε : 0 < ε) :
     Disjoint (closedBall x δ) (ball y ε) ↔ δ + ε ≤ dist x y := by
   rw [disjoint_comm, disjoint_ball_closedBall_iff hε hδ, add_comm, dist_comm] <;> infer_instance
 #align disjoint_closed_ball_ball_iff disjoint_closedBall_ball_iff
 
+/- warning: disjoint_closed_ball_closed_ball_iff -> disjoint_closedBall_closedBall_iff is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {y : E} {δ : Real} {ε : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Iff (Disjoint.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} E) (Set.booleanAlgebra.{u1} E))) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) y ε)) (LT.lt.{0} Real Real.hasLt (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) δ ε) (Dist.dist.{u1} E (PseudoMetricSpace.toHasDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {x : E} {y : E} {δ : Real} {ε : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Iff (Disjoint.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} E) (Preorder.toLE.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) y ε)) (LT.lt.{0} Real Real.instLTReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) δ ε) (Dist.dist.{u1} E (PseudoMetricSpace.toDist.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x y)))
+Case conversion may be inaccurate. Consider using '#align disjoint_closed_ball_closed_ball_iff disjoint_closedBall_closedBall_iffₓ'. -/
 theorem disjoint_closedBall_closedBall_iff (hδ : 0 ≤ δ) (hε : 0 ≤ ε) :
     Disjoint (closedBall x δ) (closedBall y ε) ↔ δ + ε < dist x y :=
   by
@@ -205,6 +297,12 @@ theorem disjoint_closedBall_closedBall_iff (hδ : 0 ≤ δ) (hε : 0 ≤ ε) :
 
 open Emetric ENNReal
 
+/- warning: inf_edist_thickening -> infEdist_thickening is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (s : Set.{u1} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x s) (ENNReal.ofReal δ)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (s : Set.{u1} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x s) (ENNReal.ofReal δ)))
+Case conversion may be inaccurate. Consider using '#align inf_edist_thickening infEdist_thickeningₓ'. -/
 @[simp]
 theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
     infEdist x (thickening δ s) = infEdist x s - ENNReal.ofReal δ :=
@@ -236,6 +334,12 @@ theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
   exact le_rfl
 #align inf_edist_thickening infEdist_thickening
 
+/- warning: thickening_thickening -> thickening_thickening is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (s : Set.{u1} E), Eq.{succ u1} (Set.{u1} E) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ) s))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (s : Set.{u1} E), Eq.{succ u1} (Set.{u1} E) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ) s))
+Case conversion may be inaccurate. Consider using '#align thickening_thickening thickening_thickeningₓ'. -/
 @[simp]
 theorem thickening_thickening (hε : 0 < ε) (hδ : 0 < δ) (s : Set E) :
     thickening ε (thickening δ s) = thickening (ε + δ) s :=
@@ -248,6 +352,12 @@ theorem thickening_thickening (hε : 0 < ε) (hδ : 0 < δ) (s : Set E) :
     exact ⟨y, ⟨_, hz, hyz⟩, hxy⟩
 #align thickening_thickening thickening_thickening
 
+/- warning: cthickening_thickening -> cthickening_thickening is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (s : Set.{u1} E), Eq.{succ u1} (Set.{u1} E) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ) s))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (s : Set.{u1} E), Eq.{succ u1} (Set.{u1} E) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ) s))
+Case conversion may be inaccurate. Consider using '#align cthickening_thickening cthickening_thickeningₓ'. -/
 @[simp]
 theorem cthickening_thickening (hε : 0 ≤ ε) (hδ : 0 < δ) (s : Set E) :
     cthickening ε (thickening δ s) = cthickening (ε + δ) s :=
@@ -257,6 +367,12 @@ theorem cthickening_thickening (hε : 0 ≤ ε) (hδ : 0 < δ) (s : Set E) :
     exact tsub_le_iff_right.2
 #align cthickening_thickening cthickening_thickening
 
+/- warning: closure_thickening -> closure_thickening is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (s : Set.{u1} E), Eq.{succ u1} (Set.{u1} E) (closure.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2))) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (s : Set.{u1} E), Eq.{succ u1} (Set.{u1} E) (closure.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2))) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s))
+Case conversion may be inaccurate. Consider using '#align closure_thickening closure_thickeningₓ'. -/
 -- Note: `interior (cthickening δ s) ≠ thickening δ s` in general
 @[simp]
 theorem closure_thickening (hδ : 0 < δ) (s : Set E) : closure (thickening δ s) = cthickening δ s :=
@@ -265,6 +381,12 @@ theorem closure_thickening (hδ : 0 < δ) (s : Set E) : closure (thickening δ s
   infer_instance
 #align closure_thickening closure_thickening
 
+/- warning: inf_edist_cthickening -> infEdist_cthickening is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] (δ : Real) (s : Set.{u1} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x s) (ENNReal.ofReal δ))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] (δ : Real) (s : Set.{u1} E) (x : E), Eq.{1} ENNReal (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (EMetric.infEdist.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) x s) (ENNReal.ofReal δ))
+Case conversion may be inaccurate. Consider using '#align inf_edist_cthickening infEdist_cthickeningₓ'. -/
 @[simp]
 theorem infEdist_cthickening (δ : ℝ) (s : Set E) (x : E) :
     infEdist x (cthickening δ s) = infEdist x s - ENNReal.ofReal δ :=
@@ -274,6 +396,12 @@ theorem infEdist_cthickening (δ : ℝ) (s : Set E) (x : E) :
   · rw [← closure_thickening hδ, inf_edist_closure, infEdist_thickening hδ] <;> infer_instance
 #align inf_edist_cthickening infEdist_cthickening
 
+/- warning: thickening_cthickening -> thickening_cthickening is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (s : Set.{u1} E), Eq.{succ u1} (Set.{u1} E) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ) s))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (s : Set.{u1} E), Eq.{succ u1} (Set.{u1} E) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ) s))
+Case conversion may be inaccurate. Consider using '#align thickening_cthickening thickening_cthickeningₓ'. -/
 @[simp]
 theorem thickening_cthickening (hε : 0 < ε) (hδ : 0 ≤ δ) (s : Set E) :
     thickening ε (cthickening δ s) = thickening (ε + δ) s :=
@@ -283,6 +411,12 @@ theorem thickening_cthickening (hε : 0 < ε) (hδ : 0 ≤ δ) (s : Set E) :
   · rw [← closure_thickening hδ, thickening_closure, thickening_thickening hε hδ] <;> infer_instance
 #align thickening_cthickening thickening_cthickening
 
+/- warning: cthickening_cthickening -> cthickening_cthickening is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (s : Set.{u1} E), Eq.{succ u1} (Set.{u1} E) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ) s))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (s : Set.{u1} E), Eq.{succ u1} (Set.{u1} E) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) δ s)) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ) s))
+Case conversion may be inaccurate. Consider using '#align cthickening_cthickening cthickening_cthickeningₓ'. -/
 @[simp]
 theorem cthickening_cthickening (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (s : Set E) :
     cthickening ε (cthickening δ s) = cthickening (ε + δ) s :=
@@ -292,12 +426,24 @@ theorem cthickening_cthickening (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (s : Set E) :
     exact tsub_le_iff_right.2
 #align cthickening_cthickening cthickening_cthickening
 
+/- warning: thickening_ball -> thickening_ball is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (x : E), Eq.{succ u1} (Set.{u1} E) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ)) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (x : E), Eq.{succ u1} (Set.{u1} E) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ)) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ)))
+Case conversion may be inaccurate. Consider using '#align thickening_ball thickening_ballₓ'. -/
 @[simp]
 theorem thickening_ball (hε : 0 < ε) (hδ : 0 < δ) (x : E) :
     thickening ε (ball x δ) = ball x (ε + δ) := by
   rw [← thickening_singleton, thickening_thickening hε hδ, thickening_singleton] <;> infer_instance
 #align thickening_ball thickening_ball
 
+/- warning: thickening_closed_ball -> thickening_closedBall is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (x : E), Eq.{succ u1} (Set.{u1} E) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ)) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (x : E), Eq.{succ u1} (Set.{u1} E) (Metric.thickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ)) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ)))
+Case conversion may be inaccurate. Consider using '#align thickening_closed_ball thickening_closedBallₓ'. -/
 @[simp]
 theorem thickening_closedBall (hε : 0 < ε) (hδ : 0 ≤ δ) (x : E) :
     thickening ε (closedBall x δ) = ball x (ε + δ) := by
@@ -305,6 +451,12 @@ theorem thickening_closedBall (hε : 0 < ε) (hδ : 0 ≤ δ) (x : E) :
     infer_instance
 #align thickening_closed_ball thickening_closedBall
 
+/- warning: cthickening_ball -> cthickening_ball is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (x : E), Eq.{succ u1} (Set.{u1} E) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ)) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (x : E), Eq.{succ u1} (Set.{u1} E) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ)) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ)))
+Case conversion may be inaccurate. Consider using '#align cthickening_ball cthickening_ballₓ'. -/
 @[simp]
 theorem cthickening_ball (hε : 0 ≤ ε) (hδ : 0 < δ) (x : E) :
     cthickening ε (ball x δ) = closedBall x (ε + δ) := by
@@ -313,6 +465,12 @@ theorem cthickening_ball (hε : 0 ≤ ε) (hδ : 0 < δ) (x : E) :
     infer_instance
 #align cthickening_ball cthickening_ball
 
+/- warning: cthickening_closed_ball -> cthickening_closedBall is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (x : E), Eq.{succ u1} (Set.{u1} E) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ)) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (x : E), Eq.{succ u1} (Set.{u1} E) (Metric.cthickening.{u1} E (PseudoMetricSpace.toPseudoEMetricSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)) ε (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x δ)) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ)))
+Case conversion may be inaccurate. Consider using '#align cthickening_closed_ball cthickening_closedBallₓ'. -/
 @[simp]
 theorem cthickening_closedBall (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (x : E) :
     cthickening ε (closedBall x δ) = closedBall x (ε + δ) := by
@@ -321,42 +479,90 @@ theorem cthickening_closedBall (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (x : E) :
     infer_instance
 #align cthickening_closed_ball cthickening_closedBall
 
+/- warning: ball_add_ball -> ball_add_ball is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (a : E) (b : E), Eq.{succ u1} (Set.{u1} E) (HAdd.hAdd.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHAdd.{u1} (Set.{u1} E) (Set.add.{u1} E (AddZeroClass.toHasAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_2)))))))) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) a ε) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) b δ)) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toHasAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_2))))))) a b) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ball_add_ball ball_add_ballₓ'. -/
 theorem ball_add_ball (hε : 0 < ε) (hδ : 0 < δ) (a b : E) :
     ball a ε + ball b δ = ball (a + b) (ε + δ) := by
   rw [ball_add, thickening_ball hε hδ b, Metric.vadd_ball, vadd_eq_add]
 #align ball_add_ball ball_add_ball
 
+/- warning: ball_sub_ball -> ball_sub_ball is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ball_sub_ball ball_sub_ballₓ'. -/
 theorem ball_sub_ball (hε : 0 < ε) (hδ : 0 < δ) (a b : E) :
     ball a ε - ball b δ = ball (a - b) (ε + δ) := by
   simp_rw [sub_eq_add_neg, neg_ball, ball_add_ball hε hδ]
 #align ball_sub_ball ball_sub_ball
 
+/- warning: ball_add_closed_ball -> ball_add_closedBall is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ball_add_closed_ball ball_add_closedBallₓ'. -/
 theorem ball_add_closedBall (hε : 0 < ε) (hδ : 0 ≤ δ) (a b : E) :
     ball a ε + closedBall b δ = ball (a + b) (ε + δ) := by
   rw [ball_add, thickening_closedBall hε hδ b, Metric.vadd_ball, vadd_eq_add]
 #align ball_add_closed_ball ball_add_closedBall
 
+/- warning: ball_sub_closed_ball -> ball_sub_closedBall is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ball_sub_closed_ball ball_sub_closedBallₓ'. -/
 theorem ball_sub_closedBall (hε : 0 < ε) (hδ : 0 ≤ δ) (a b : E) :
     ball a ε - closedBall b δ = ball (a - b) (ε + δ) := by
   simp_rw [sub_eq_add_neg, neg_closedBall, ball_add_closedBall hε hδ]
 #align ball_sub_closed_ball ball_sub_closedBall
 
+/- warning: closed_ball_add_ball -> closedBall_add_ball is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align closed_ball_add_ball closedBall_add_ballₓ'. -/
 theorem closedBall_add_ball (hε : 0 ≤ ε) (hδ : 0 < δ) (a b : E) :
     closedBall a ε + ball b δ = ball (a + b) (ε + δ) := by
   rw [add_comm, ball_add_closedBall hδ hε b, add_comm, add_comm δ]
 #align closed_ball_add_ball closedBall_add_ball
 
+/- warning: closed_ball_sub_ball -> closedBall_sub_ball is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align closed_ball_sub_ball closedBall_sub_ballₓ'. -/
 theorem closedBall_sub_ball (hε : 0 ≤ ε) (hδ : 0 < δ) (a b : E) :
     closedBall a ε - ball b δ = ball (a - b) (ε + δ) := by
   simp_rw [sub_eq_add_neg, neg_ball, closedBall_add_ball hε hδ]
 #align closed_ball_sub_ball closedBall_sub_ball
 
+/- warning: closed_ball_add_closed_ball -> closedBall_add_closedBall is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real} [_inst_5 : ProperSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)], (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (a : E) (b : E), Eq.{succ u1} (Set.{u1} E) (HAdd.hAdd.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHAdd.{u1} (Set.{u1} E) (Set.add.{u1} E (AddZeroClass.toHasAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_2)))))))) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) a ε) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) b δ)) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toHasAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_2))))))) a b) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real} [_inst_5 : ProperSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)], (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (a : E) (b : E), Eq.{succ u1} (Set.{u1} E) (HAdd.hAdd.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHAdd.{u1} (Set.{u1} E) (Set.add.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_2)))))))) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) a ε) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) b δ)) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_2))))))) a b) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ)))
+Case conversion may be inaccurate. Consider using '#align closed_ball_add_closed_ball closedBall_add_closedBallₓ'. -/
 theorem closedBall_add_closedBall [ProperSpace E] (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (a b : E) :
     closedBall a ε + closedBall b δ = closedBall (a + b) (ε + δ) := by
   rw [(is_compact_closed_ball _ _).add_closedBall hδ b, cthickening_closedBall hδ hε a,
     Metric.vadd_closedBall, vadd_eq_add, add_comm, add_comm δ]
 #align closed_ball_add_closed_ball closedBall_add_closedBall
 
+/- warning: closed_ball_sub_closed_ball -> closedBall_sub_closedBall is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real} [_inst_5 : ProperSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)], (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (forall (a : E) (b : E), Eq.{succ u1} (Set.{u1} E) (HSub.hSub.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHSub.{u1} (Set.{u1} E) (Set.sub.{u1} E (SubNegMonoid.toHasSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_2)))))) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) a ε) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) b δ)) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toHasSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_2))))) a b) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ε δ)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField _inst_2] {δ : Real} {ε : Real} [_inst_5 : ProperSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)], (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (forall (a : E) (b : E), Eq.{succ u1} (Set.{u1} E) (HSub.hSub.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHSub.{u1} (Set.{u1} E) (Set.sub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_2)))))) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) a ε) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) b δ)) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_2))))) a b) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) ε δ)))
+Case conversion may be inaccurate. Consider using '#align closed_ball_sub_closed_ball closedBall_sub_closedBallₓ'. -/
 theorem closedBall_sub_closedBall [ProperSpace E] (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (a b : E) :
     closedBall a ε - closedBall b δ = closedBall (a - b) (ε + δ) := by
   simp_rw [sub_eq_add_neg, neg_closedBall, closedBall_add_closedBall hε hδ]
@@ -368,27 +574,50 @@ section NormedAddCommGroup
 
 variable [NormedAddCommGroup E] [NormedSpace 𝕜 E]
 
+/- warning: smul_closed_ball -> smul_closedBall is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] (c : 𝕜) (x : E) {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Eq.{succ u2} (Set.{u2} E) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3)))))) c (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) x r)) (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3))))) c x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) c) r)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] (c : 𝕜) (x : E) {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Eq.{succ u2} (Set.{u2} E) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3))))))) c (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) x r)) (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3)))))) c x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) c) r)))
+Case conversion may be inaccurate. Consider using '#align smul_closed_ball smul_closedBallₓ'. -/
 theorem smul_closedBall (c : 𝕜) (x : E) {r : ℝ} (hr : 0 ≤ r) :
     c • closedBall x r = closedBall (c • x) (‖c‖ * r) :=
   by
   rcases eq_or_ne c 0 with (rfl | hc)
   · simp [hr, zero_smul_set, Set.singleton_zero, ← nonempty_closed_ball]
-  · exact smul_closed_ball' hc x r
+  · exact smul_closedBall' hc x r
 #align smul_closed_ball smul_closedBall
 
-theorem smul_closed_unit_ball (c : 𝕜) : c • closedBall (0 : E) (1 : ℝ) = closedBall (0 : E) ‖c‖ :=
-  by rw [smul_closedBall _ _ zero_le_one, smul_zero, mul_one]
-#align smul_closed_unit_ball smul_closed_unit_ball
+/- warning: smul_closed_unit_ball -> smul_closedUnitBall is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] (c : 𝕜), Eq.{succ u2} (Set.{u2} E) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3)))))) c (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))))))) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) c))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] (c : 𝕜), Eq.{succ u2} (Set.{u2} E) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3))))))) c (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))))) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) c))
+Case conversion may be inaccurate. Consider using '#align smul_closed_unit_ball smul_closedUnitBallₓ'. -/
+theorem smul_closedUnitBall (c : 𝕜) : c • closedBall (0 : E) (1 : ℝ) = closedBall (0 : E) ‖c‖ := by
+  rw [smul_closedBall _ _ zero_le_one, smul_zero, mul_one]
+#align smul_closed_unit_ball smul_closedUnitBall
 
 variable [NormedSpace ℝ E]
 
+/- warning: smul_closed_unit_ball_of_nonneg -> smul_closedUnitBall_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Eq.{succ u1} (Set.{u1} E) (SMul.smul.{0, u1} Real (Set.{u1} E) (Set.smulSet.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{0, u1} Real E (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_4)))))) r (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))))))) r))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Eq.{succ u1} (Set.{u1} E) (HSMul.hSMul.{0, u1, u1} Real (Set.{u1} E) (Set.{u1} E) (instHSMul.{0, u1} Real (Set.{u1} E) (Set.smulSet.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_4))))))) r (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))))) r))
+Case conversion may be inaccurate. Consider using '#align smul_closed_unit_ball_of_nonneg smul_closedUnitBall_of_nonnegₓ'. -/
 /-- In a real normed space, the image of the unit closed ball under multiplication by a nonnegative
 number `r` is the closed ball of radius `r` with center at the origin. -/
-theorem smul_closed_unit_ball_of_nonneg {r : ℝ} (hr : 0 ≤ r) :
-    r • closedBall 0 1 = closedBall (0 : E) r := by
-  rw [smul_closed_unit_ball, Real.norm_of_nonneg hr]
-#align smul_closed_unit_ball_of_nonneg smul_closed_unit_ball_of_nonneg
-
+theorem smul_closedUnitBall_of_nonneg {r : ℝ} (hr : 0 ≤ r) :
+    r • closedBall 0 1 = closedBall (0 : E) r := by rw [smul_closedUnitBall, Real.norm_of_nonneg hr]
+#align smul_closed_unit_ball_of_nonneg smul_closedUnitBall_of_nonneg
+
+/- warning: normed_space.sphere_nonempty -> NormedSpace.sphere_nonempty is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] [_inst_5 : Nontrivial.{u1} E] {x : E} {r : Real}, Iff (Set.Nonempty.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) x r)) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r)
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] [_inst_5 : Nontrivial.{u1} E] {x : E} {r : Real}, Iff (Set.Nonempty.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) x r)) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r)
+Case conversion may be inaccurate. Consider using '#align normed_space.sphere_nonempty NormedSpace.sphere_nonemptyₓ'. -/
 /-- In a nontrivial real normed space, a sphere is nonempty if and only if its radius is
 nonnegative. -/
 @[simp]
@@ -403,6 +632,12 @@ theorem NormedSpace.sphere_nonempty [Nontrivial E] {x : E} {r : ℝ} :
   simp [norm_smul, this, Real.norm_of_nonneg hr]
 #align normed_space.sphere_nonempty NormedSpace.sphere_nonempty
 
+/- warning: smul_sphere -> smul_sphere is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] [_inst_4 : NormedSpace.{0, u2} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] [_inst_5 : Nontrivial.{u2} E] (c : 𝕜) (x : E) {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Eq.{succ u2} (Set.{u2} E) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3)))))) c (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) x r)) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3))))) c x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) c) r)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] [_inst_4 : NormedSpace.{0, u2} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] [_inst_5 : Nontrivial.{u2} E] (c : 𝕜) (x : E) {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Eq.{succ u2} (Set.{u2} E) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3))))))) c (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) x r)) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3)))))) c x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) c) r)))
+Case conversion may be inaccurate. Consider using '#align smul_sphere smul_sphereₓ'. -/
 theorem smul_sphere [Nontrivial E] (c : 𝕜) (x : E) {r : ℝ} (hr : 0 ≤ r) :
     c • sphere x r = sphere (c • x) (‖c‖ * r) :=
   by
@@ -411,17 +646,29 @@ theorem smul_sphere [Nontrivial E] (c : 𝕜) (x : E) {r : ℝ} (hr : 0 ≤ r) :
   · exact smul_sphere' hc x r
 #align smul_sphere smul_sphere
 
+/- warning: affinity_unit_ball -> affinity_unitBall is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (x : E), Eq.{succ u1} (Set.{u1} E) (VAdd.vadd.{u1, u1} E (Set.{u1} E) (Set.vaddSet.{u1, u1} E E (Add.toVAdd.{u1} E (AddZeroClass.toHasAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2)))))))) x (SMul.smul.{0, u1} Real (Set.{u1} E) (Set.smulSet.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{0, u1} Real E (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_4)))))) r (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) x r))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (x : E), Eq.{succ u1} (Set.{u1} E) (HVAdd.hVAdd.{u1, u1, u1} E (Set.{u1} E) (Set.{u1} E) (instHVAdd.{u1, u1} E (Set.{u1} E) (Set.vaddSet.{u1, u1} E E (AddAction.toVAdd.{u1, u1} E E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2)))) (AddTorsor.toAddAction.{u1, u1} E E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2)) (NormedAddTorsor.toAddTorsor.{u1, u1} E E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (SeminormedAddCommGroup.toNormedAddTorsor.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) x (HSMul.hSMul.{0, u1, u1} Real (Set.{u1} E) (Set.{u1} E) (instHSMul.{0, u1} Real (Set.{u1} E) (Set.smulSet.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_4))))))) r (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) x r))
+Case conversion may be inaccurate. Consider using '#align affinity_unit_ball affinity_unitBallₓ'. -/
 /-- Any ball `metric.ball x r`, `0 < r` is the image of the unit ball under `λ y, x + r • y`. -/
-theorem affinity_unit_ball {r : ℝ} (hr : 0 < r) (x : E) : x +ᵥ r • ball 0 1 = ball x r := by
-  rw [smul_unit_ball_of_pos hr, vadd_ball_zero]
-#align affinity_unit_ball affinity_unit_ball
-
+theorem affinity_unitBall {r : ℝ} (hr : 0 < r) (x : E) : x +ᵥ r • ball 0 1 = ball x r := by
+  rw [smul_unitBall_of_pos hr, vadd_ball_zero]
+#align affinity_unit_ball affinity_unitBall
+
+/- warning: affinity_unit_closed_ball -> affinity_unitClosedBall is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (x : E), Eq.{succ u1} (Set.{u1} E) (VAdd.vadd.{u1, u1} E (Set.{u1} E) (Set.vaddSet.{u1, u1} E E (Add.toVAdd.{u1} E (AddZeroClass.toHasAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2)))))))) x (SMul.smul.{0, u1} Real (Set.{u1} E) (Set.smulSet.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{0, u1} Real E (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_4)))))) r (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) x r))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (x : E), Eq.{succ u1} (Set.{u1} E) (HVAdd.hVAdd.{u1, u1, u1} E (Set.{u1} E) (Set.{u1} E) (instHVAdd.{u1, u1} E (Set.{u1} E) (Set.vaddSet.{u1, u1} E E (AddAction.toVAdd.{u1, u1} E E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2)))) (AddTorsor.toAddAction.{u1, u1} E E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2)) (NormedAddTorsor.toAddTorsor.{u1, u1} E E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (SeminormedAddCommGroup.toNormedAddTorsor.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) x (HSMul.hSMul.{0, u1, u1} Real (Set.{u1} E) (Set.{u1} E) (instHSMul.{0, u1} Real (Set.{u1} E) (Set.smulSet.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_4))))))) r (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) x r))
+Case conversion may be inaccurate. Consider using '#align affinity_unit_closed_ball affinity_unitClosedBallₓ'. -/
 /-- Any closed ball `metric.closed_ball x r`, `0 ≤ r` is the image of the unit closed ball under
 `λ y, x + r • y`. -/
-theorem affinity_unit_closedBall {r : ℝ} (hr : 0 ≤ r) (x : E) :
+theorem affinity_unitClosedBall {r : ℝ} (hr : 0 ≤ r) (x : E) :
     x +ᵥ r • closedBall 0 1 = closedBall x r := by
-  rw [smul_closed_unit_ball, Real.norm_of_nonneg hr, vadd_closedBall_zero]
-#align affinity_unit_closed_ball affinity_unit_closedBall
+  rw [smul_closedUnitBall, Real.norm_of_nonneg hr, vadd_closedBall_zero]
+#align affinity_unit_closed_ball affinity_unitClosedBall
 
 end NormedAddCommGroup
 

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

@@ -86,8 +86,8 @@ theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bounded s
     calc
       ‖r • z‖ = ‖r‖ * ‖z‖ := norm_smul _ _
       _ ≤ ε / R * R :=
-        mul_le_mul (mem_closedBall_zero_iff.1 hr) (mem_closedBall_zero_iff.1 (hR zs))
-          (norm_nonneg _) (div_pos εpos Rpos).le
+        (mul_le_mul (mem_closedBall_zero_iff.1 hr) (mem_closedBall_zero_iff.1 (hR zs))
+          (norm_nonneg _) (div_pos εpos Rpos).le)
       _ = ε := by field_simp [Rpos.ne']
       
   have : y = x + r • z := by simp only [hz, add_neg_cancel_left]

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -203,13 +203,13 @@ theorem disjoint_closedBall_closedBall_iff (hδ : 0 ≤ δ) (hε : 0 ≤ ε) :
   exact h.le_bot ⟨hxz, hzy⟩
 #align disjoint_closed_ball_closed_ball_iff disjoint_closedBall_closedBall_iff
 
-open Emetric Ennreal
+open Emetric ENNReal
 
 @[simp]
 theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
-    infEdist x (thickening δ s) = infEdist x s - Ennreal.ofReal δ :=
+    infEdist x (thickening δ s) = infEdist x s - ENNReal.ofReal δ :=
   by
-  obtain hs | hs := lt_or_le (inf_edist x s) (Ennreal.ofReal δ)
+  obtain hs | hs := lt_or_le (inf_edist x s) (ENNReal.ofReal δ)
   · rw [inf_edist_zero_of_mem, tsub_eq_zero_of_le hs.le]
     exact hs
   refine' (tsub_le_iff_right.2 inf_edist_le_inf_edist_thickening_add).antisymm' _
@@ -229,7 +229,7 @@ theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
   rw [some_eq_coe, edist_lt_coe, ← dist_lt_coe, ← add_sub_cancel'_right δ ↑r] at h
   obtain ⟨y, hxy, hyz⟩ := exists_dist_lt_lt hr hδ h
   refine'
-    (Ennreal.add_lt_add_right of_real_ne_top <|
+    (ENNReal.add_lt_add_right of_real_ne_top <|
           inf_edist_lt_iff.2 ⟨_, mem_thickening_iff.2 ⟨_, hz, hyz⟩, edist_lt_ofReal.2 hxy⟩).trans_le
       _
   rw [← of_real_add hr.le hδ.le, sub_add_cancel, of_real_coe_nnreal]
@@ -253,7 +253,7 @@ theorem cthickening_thickening (hε : 0 ≤ ε) (hδ : 0 < δ) (s : Set E) :
     cthickening ε (thickening δ s) = cthickening (ε + δ) s :=
   (cthickening_thickening_subset hε _ _).antisymm fun x =>
     by
-    simp_rw [mem_cthickening_iff, Ennreal.ofReal_add hε hδ.le, infEdist_thickening hδ]
+    simp_rw [mem_cthickening_iff, ENNReal.ofReal_add hε hδ.le, infEdist_thickening hδ]
     exact tsub_le_iff_right.2
 #align cthickening_thickening cthickening_thickening
 
@@ -267,7 +267,7 @@ theorem closure_thickening (hδ : 0 < δ) (s : Set E) : closure (thickening δ s
 
 @[simp]
 theorem infEdist_cthickening (δ : ℝ) (s : Set E) (x : E) :
-    infEdist x (cthickening δ s) = infEdist x s - Ennreal.ofReal δ :=
+    infEdist x (cthickening δ s) = infEdist x s - ENNReal.ofReal δ :=
   by
   obtain hδ | hδ := le_or_lt δ 0
   · rw [cthickening_of_nonpos hδ, inf_edist_closure, of_real_of_nonpos hδ, tsub_zero]
@@ -288,7 +288,7 @@ theorem cthickening_cthickening (hε : 0 ≤ ε) (hδ : 0 ≤ δ) (s : Set E) :
     cthickening ε (cthickening δ s) = cthickening (ε + δ) s :=
   (cthickening_cthickening_subset hε hδ _).antisymm fun x =>
     by
-    simp_rw [mem_cthickening_iff, Ennreal.ofReal_add hε hδ, infEdist_cthickening]
+    simp_rw [mem_cthickening_iff, ENNReal.ofReal_add hε hδ, infEdist_cthickening]
     exact tsub_le_iff_right.2
 #align cthickening_cthickening cthickening_cthickening
 

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

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 | |

@@ -140,7 +140,7 @@ theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bornology
       _ = ε := by field_simp
   have : y = x + r • z := by simp only [hz, add_neg_cancel_left]
   apply hε
-  simpa only [this, dist_eq_norm, add_sub_cancel', mem_closedBall] using I
+  simpa only [this, dist_eq_norm, add_sub_cancel_left, mem_closedBall] using I
 #align eventually_singleton_add_smul_subset eventually_singleton_add_smul_subset
 
 variable [NormedSpace ℝ E] {x y z : E} {δ ε : ℝ}
@@ -267,7 +267,7 @@ theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
     have := hs.trans_lt ((infEdist_le_edist_of_mem hz).trans_lt h)
     rw [ofReal_eq_coe_nnreal hδ.le, some_eq_coe] at this
     exact mod_cast this
-  rw [some_eq_coe, edist_lt_coe, ← dist_lt_coe, ← add_sub_cancel'_right δ ↑r] at h
+  rw [some_eq_coe, edist_lt_coe, ← dist_lt_coe, ← add_sub_cancel δ ↑r] at h
   obtain ⟨y, hxy, hyz⟩ := exists_dist_lt_lt hr hδ h
   refine' (ENNReal.add_lt_add_right ofReal_ne_top <|
     infEdist_lt_iff.2 ⟨_, mem_thickening_iff.2 ⟨_, hz, hyz⟩, edist_lt_ofReal.2 hxy⟩).trans_le _
@@ -427,8 +427,8 @@ theorem NormedSpace.sphere_nonempty [Nontrivial E] {x : E} {r : ℝ} :
   refine' ⟨fun h => nonempty_closedBall.1 (h.mono sphere_subset_closedBall), fun hr =>
     ⟨r • ‖y - x‖⁻¹ • (y - x) + x, _⟩⟩
   have : ‖y - x‖ ≠ 0 := by simpa [sub_eq_zero]
-  simp only [mem_sphere_iff_norm, add_sub_cancel, norm_smul, Real.norm_eq_abs, norm_inv, norm_norm,
-    ne_eq, norm_eq_zero]
+  simp only [mem_sphere_iff_norm, add_sub_cancel_right, norm_smul, Real.norm_eq_abs, norm_inv,
+    norm_norm, ne_eq, norm_eq_zero]
   simp only [abs_norm, ne_eq, norm_eq_zero]
   rw [inv_mul_cancel this, mul_one, abs_eq_self.mpr hr]
 #align normed_space.sphere_nonempty NormedSpace.sphere_nonempty

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)

@@ -26,7 +26,6 @@ variable {𝕜 E : Type*}
 section SMulZeroClass
 
 variable [SeminormedAddCommGroup 𝕜] [SeminormedAddCommGroup E]
-
 variable [SMulZeroClass 𝕜 E] [BoundedSMul 𝕜 E]
 
 theorem ediam_smul_le (c : 𝕜) (s : Set E) : EMetric.diam (c • s) ≤ ‖c‖₊ • EMetric.diam s :=
@@ -38,7 +37,6 @@ end SMulZeroClass
 section DivisionRing
 
 variable [NormedDivisionRing 𝕜] [SeminormedAddCommGroup E]
-
 variable [Module 𝕜 E] [BoundedSMul 𝕜 E]
 
 theorem ediam_smul₀ (c : 𝕜) (s : Set E) : EMetric.diam (c • s) = ‖c‖₊ • EMetric.diam s := by

This way we don't switch between general normed spaces and real normed spaces back and forth throughout the file.

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yaël Dillies
 -/
 import Mathlib.Analysis.Normed.Group.Pointwise
-import Mathlib.Analysis.NormedSpace.Basic
+import Mathlib.Analysis.NormedSpace.Real
 
 #align_import analysis.normed_space.pointwise from "leanprover-community/mathlib"@"bc91ed7093bf098d253401e69df601fc33dde156"
 

Remove the duplicates introduced in #8869 by sorting the lemmas in Algebra.Order.SMul into three files:

• Algebra.Order.Module.Defs for the order isomorphism induced by scalar multiplication by a positivity element
• Algebra.Order.Module.Pointwise for the order properties of scalar multiplication of sets. This file is new. I credit myself for https://github.com/leanprover-community/mathlib/pull/9078
• Algebra.Order.Module.OrderedSMul: The material about OrderedSMul per se. Inherits the copyright header from Algebra.Order.SMul. This file should eventually be deleted.

I move each #align to the correct file. On top of that, I delete unused redundant OrderedSMul instances (they were useful in Lean 3, but not anymore) and eq_of_smul_eq_smul_of_pos_of_le/eq_of_smul_eq_smul_of_neg_of_le since those lemmas are weird and unused.

@@ -49,7 +49,7 @@ theorem ediam_smul₀ (c : 𝕜) (s : Set E) : EMetric.diam (c • s) = ‖c‖
     simp [zero_smul_set hs, ← Set.singleton_zero]
   · have := (lipschitzWith_smul c⁻¹).ediam_image_le (c • s)
     rwa [← smul_eq_mul, ← ENNReal.smul_def, Set.image_smul, inv_smul_smul₀ hc s, nnnorm_inv,
-      ENNReal.le_inv_smul_iff (nnnorm_ne_zero_iff.mpr hc)] at this
+      le_inv_smul_iff_of_pos (nnnorm_pos.2 hc)] at this
 #align ediam_smul₀ ediam_smul₀
 
 theorem diam_smul₀ (c : 𝕜) (x : Set E) : diam (c • x) = ‖c‖ * diam x := by

@@ -117,7 +117,7 @@ theorem set_smul_sphere_zero {s : Set 𝕜} (hs : 0 ∉ s) (r : ℝ) :
     _ = (‖·‖) ⁻¹' ((‖·‖ * r) '' s) := by ext; simp [eq_comm]
 
 /-- Image of a bounded set in a normed space under scalar multiplication by a constant is
-bounded. See also `Metric.Bounded.smul` for a similar lemma about an isometric action. -/
+bounded. See also `Bornology.IsBounded.smul` for a similar lemma about an isometric action. -/
 theorem Bornology.IsBounded.smul₀ {s : Set E} (hs : IsBounded s) (c : 𝕜) : IsBounded (c • s) :=
   (lipschitzWith_smul c).isBounded_image hs
 #align metric.bounded.smul Bornology.IsBounded.smul₀

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

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

@@ -268,7 +268,7 @@ theorem infEdist_thickening (hδ : 0 < δ) (s : Set E) (x : E) :
     refine' sub_pos_of_lt _
     have := hs.trans_lt ((infEdist_le_edist_of_mem hz).trans_lt h)
     rw [ofReal_eq_coe_nnreal hδ.le, some_eq_coe] at this
-    exact_mod_cast this
+    exact mod_cast this
   rw [some_eq_coe, edist_lt_coe, ← dist_lt_coe, ← add_sub_cancel'_right δ ↑r] at h
   obtain ⟨y, hxy, hyz⟩ := exists_dist_lt_lt hr hδ h
   refine' (ENNReal.add_lt_add_right ofReal_ne_top <|

@@ -108,6 +108,14 @@ theorem smul_closedBall' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
   simp only [← ball_union_sphere, Set.smul_set_union, _root_.smul_ball hc, smul_sphere' hc]
 #align smul_closed_ball' smul_closedBall'
 
+theorem set_smul_sphere_zero {s : Set 𝕜} (hs : 0 ∉ s) (r : ℝ) :
+    s • sphere (0 : E) r = (‖·‖) ⁻¹' ((‖·‖ * r) '' s) :=
+  calc
+    s • sphere (0 : E) r = ⋃ c ∈ s, c • sphere (0 : E) r := iUnion_smul_left_image.symm
+    _ = ⋃ c ∈ s, sphere (0 : E) (‖c‖ * r) := iUnion₂_congr fun c hc ↦ by
+      rw [smul_sphere' (ne_of_mem_of_not_mem hc hs), smul_zero]
+    _ = (‖·‖) ⁻¹' ((‖·‖ * r) '' s) := by ext; simp [eq_comm]
+
 /-- Image of a bounded set in a normed space under scalar multiplication by a constant is
 bounded. See also `Metric.Bounded.smul` for a similar lemma about an isometric action. -/
 theorem Bornology.IsBounded.smul₀ {s : Set E} (hs : IsBounded s) (c : 𝕜) : IsBounded (c • s) :=
@@ -145,6 +153,13 @@ theorem smul_unitBall_of_pos {r : ℝ} (hr : 0 < r) : r • ball (0 : E) 1 = bal
   rw [smul_unitBall hr.ne', Real.norm_of_nonneg hr.le]
 #align smul_unit_ball_of_pos smul_unitBall_of_pos
 
+lemma Ioo_smul_sphere_zero {a b r : ℝ} (ha : 0 ≤ a) (hr : 0 < r) :
+    Ioo a b • sphere (0 : E) r = ball 0 (b * r) \ closedBall 0 (a * r) := by
+  have : EqOn (‖·‖) id (Ioo a b) := fun x hx ↦ abs_of_pos (ha.trans_lt hx.1)
+  rw [set_smul_sphere_zero (by simp [ha.not_lt]), ← image_image (· * r), this.image_eq, image_id,
+    image_mul_right_Ioo _ _ hr]
+  ext x; simp [and_comm]
+
 -- This is also true for `ℚ`-normed spaces
 theorem exists_dist_eq (x z : E) {a b : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1) :
     ∃ y, dist x y = b * dist x z ∧ dist y z = a * dist x z := by

Removes nonterminal simps on lines looking like simp [...]

@@ -414,7 +414,9 @@ theorem NormedSpace.sphere_nonempty [Nontrivial E] {x : E} {r : ℝ} :
   refine' ⟨fun h => nonempty_closedBall.1 (h.mono sphere_subset_closedBall), fun hr =>
     ⟨r • ‖y - x‖⁻¹ • (y - x) + x, _⟩⟩
   have : ‖y - x‖ ≠ 0 := by simpa [sub_eq_zero]
-  simp [norm_smul, this, Real.norm_of_nonneg hr]
+  simp only [mem_sphere_iff_norm, add_sub_cancel, norm_smul, Real.norm_eq_abs, norm_inv, norm_norm,
+    ne_eq, norm_eq_zero]
+  simp only [abs_norm, ne_eq, norm_eq_zero]
   rw [inv_mul_cancel this, mul_one, abs_eq_self.mpr hr]
 #align normed_space.sphere_nonempty NormedSpace.sphere_nonempty
 

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

@@ -121,7 +121,7 @@ theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bornology
   obtain ⟨ε, εpos, hε⟩ : ∃ ε : ℝ, 0 < ε ∧ closedBall x ε ⊆ u := nhds_basis_closedBall.mem_iff.1 hu
   obtain ⟨R, Rpos, hR⟩ : ∃ R : ℝ, 0 < R ∧ s ⊆ closedBall 0 R := hs.subset_closedBall_lt 0 0
   have : Metric.closedBall (0 : 𝕜) (ε / R) ∈ 𝓝 (0 : 𝕜) := closedBall_mem_nhds _ (div_pos εpos Rpos)
-  filter_upwards [this]with r hr
+  filter_upwards [this] with r hr
   simp only [image_add_left, singleton_add]
   intro y hy
   obtain ⟨z, zs, hz⟩ : ∃ z : E, z ∈ s ∧ r • z = -x + y := by simpa [mem_smul_set] using hy

Use Bornology.IsBounded instead.

@@ -110,16 +110,16 @@ theorem smul_closedBall' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
 
 /-- Image of a bounded set in a normed space under scalar multiplication by a constant is
 bounded. See also `Metric.Bounded.smul` for a similar lemma about an isometric action. -/
-theorem Metric.Bounded.smul₀ {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c • s) :=
-  (lipschitzWith_smul c).bounded_image hs
-#align metric.bounded.smul Metric.Bounded.smul₀
+theorem Bornology.IsBounded.smul₀ {s : Set E} (hs : IsBounded s) (c : 𝕜) : IsBounded (c • s) :=
+  (lipschitzWith_smul c).isBounded_image hs
+#align metric.bounded.smul Bornology.IsBounded.smul₀
 
 /-- If `s` is a bounded set, then for small enough `r`, the set `{x} + r • s` is contained in any
 fixed neighborhood of `x`. -/
-theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bounded s) {u : Set E}
-    (hu : u ∈ 𝓝 x) : ∀ᶠ r in 𝓝 (0 : 𝕜), {x} + r • s ⊆ u := by
+theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bornology.IsBounded s)
+    {u : Set E} (hu : u ∈ 𝓝 x) : ∀ᶠ r in 𝓝 (0 : 𝕜), {x} + r • s ⊆ u := by
   obtain ⟨ε, εpos, hε⟩ : ∃ ε : ℝ, 0 < ε ∧ closedBall x ε ⊆ u := nhds_basis_closedBall.mem_iff.1 hu
-  obtain ⟨R, Rpos, hR⟩ : ∃ R : ℝ, 0 < R ∧ s ⊆ closedBall 0 R := hs.subset_ball_lt 0 0
+  obtain ⟨R, Rpos, hR⟩ : ∃ R : ℝ, 0 < R ∧ s ⊆ closedBall 0 R := hs.subset_closedBall_lt 0 0
   have : Metric.closedBall (0 : 𝕜) (ε / R) ∈ 𝓝 (0 : 𝕜) := closedBall_mem_nhds _ (div_pos εpos Rpos)
   filter_upwards [this]with r hr
   simp only [image_add_left, singleton_add]

The main reasons is that having h : 0 < denom in the context should suffice for field_simp to do its job, without the need to manually pass h.ne or similar.

Quite a few have := … ≠ 0 could be dropped, and some field_simp calls no longer need explicit arguments; this is promising.

This does break some proofs where field_simp was not used as a closing tactic, and it now shuffles terms around a bit different. These were fixed. Using field_simp in the middle of a proof seems rather fragile anyways.

As a drive-by contribution, positivity now knows about π > 0.

fixes: #4835

Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -131,7 +131,7 @@ theorem eventually_singleton_add_smul_subset {x : E} {s : Set E} (hs : Bounded s
       _ ≤ ε / R * R :=
         (mul_le_mul (mem_closedBall_zero_iff.1 hr) (mem_closedBall_zero_iff.1 (hR zs))
           (norm_nonneg _) (div_pos εpos Rpos).le)
-      _ = ε := by field_simp [Rpos.ne']
+      _ = ε := by field_simp
   have : y = x + r • z := by simp only [hz, add_neg_cancel_left]
   apply hε
   simpa only [this, dist_eq_norm, add_sub_cancel', mem_closedBall] using I

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

This has nice performance benefits.

@@ -21,7 +21,7 @@ open Metric Set
 
 open Pointwise Topology
 
-variable {𝕜 E : Type _}
+variable {𝕜 E : Type*}
 
 section SMulZeroClass
 

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yaël Dillies
-
-! This file was ported from Lean 3 source module analysis.normed_space.pointwise
-! leanprover-community/mathlib commit bc91ed7093bf098d253401e69df601fc33dde156
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Normed.Group.Pointwise
 import Mathlib.Analysis.NormedSpace.Basic
 
+#align_import analysis.normed_space.pointwise from "leanprover-community/mathlib"@"bc91ed7093bf098d253401e69df601fc33dde156"
+
 /-!
 # Properties of pointwise scalar multiplication of sets in normed spaces.
 

Add Metric.Bounded.smul and Metric.Bounded.vadd, rename the old smul to smul₀.

@@ -111,14 +111,11 @@ theorem smul_closedBall' {c : 𝕜} (hc : c ≠ 0) (x : E) (r : ℝ) :
   simp only [← ball_union_sphere, Set.smul_set_union, _root_.smul_ball hc, smul_sphere' hc]
 #align smul_closed_ball' smul_closedBall'
 
-theorem Metric.Bounded.smul {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c • s) := by
-  obtain ⟨R, hR⟩ : ∃ R : ℝ, ∀ x ∈ s, ‖x‖ ≤ R := hs.exists_norm_le
-  refine' bounded_iff_forall_norm_le.2 ⟨‖c‖ * R, fun z hz => _⟩
-  obtain ⟨y, ys, rfl⟩ : ∃ y : E, y ∈ s ∧ c • y = z := mem_smul_set.1 hz
-  calc
-    ‖c • y‖ = ‖c‖ * ‖y‖ := norm_smul _ _
-    _ ≤ ‖c‖ * R := mul_le_mul_of_nonneg_left (hR y ys) (norm_nonneg _)
-#align metric.bounded.smul Metric.Bounded.smul
+/-- Image of a bounded set in a normed space under scalar multiplication by a constant is
+bounded. See also `Metric.Bounded.smul` for a similar lemma about an isometric action. -/
+theorem Metric.Bounded.smul₀ {s : Set E} (hs : Bounded s) (c : 𝕜) : Bounded (c • s) :=
+  (lipschitzWith_smul c).bounded_image hs
+#align metric.bounded.smul Metric.Bounded.smul₀
 
 /-- If `s` is a bounded set, then for small enough `r`, the set `{x} + r • s` is contained in any
 fixed neighborhood of `x`. -/

Also adds the version for group actions, and the consequence that if we quotient by a compact subgroup then the quotient map is closed.

I also made some syntax tweaks in some places, mainly making use of our great new implicit functions.

@@ -8,7 +8,6 @@ Authors: Sébastien Gouëzel, Yaël Dillies
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathlib.Analysis.Normed.Group.AddTorsor
 import Mathlib.Analysis.Normed.Group.Pointwise
 import Mathlib.Analysis.NormedSpace.Basic
 

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

@@ -432,13 +432,13 @@ theorem smul_sphere [Nontrivial E] (c : 𝕜) (x : E) {r : ℝ} (hr : 0 ≤ r) :
   · exact smul_sphere' hc x r
 #align smul_sphere smul_sphere
 
-/-- Any ball `Metric.ball x r`, `0 < r` is the image of the unit ball under `λ y, x + r • y`. -/
+/-- Any ball `Metric.ball x r`, `0 < r` is the image of the unit ball under `fun y ↦ x + r • y`. -/
 theorem affinity_unitBall {r : ℝ} (hr : 0 < r) (x : E) : x +ᵥ r • ball (0 : E) 1 = ball x r := by
   rw [smul_unitBall_of_pos hr, vadd_ball_zero]
 #align affinity_unit_ball affinity_unitBall
 
 /-- Any closed ball `Metric.closedBall x r`, `0 ≤ r` is the image of the unit closed ball under
-`λ y, x + r • y`. -/
+`fun y ↦ x + r • y`. -/
 theorem affinity_unitClosedBall {r : ℝ} (hr : 0 ≤ r) (x : E) :
     x +ᵥ r • closedBall (0 : E) 1 = closedBall x r := by
   rw [smul_closedUnitBall, Real.norm_of_nonneg hr, vadd_closedBall_zero]

@@ -65,7 +65,7 @@ theorem infEdist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
   simp_rw [EMetric.infEdist]
   have : Function.Surjective ((c • ·) : E → E) :=
     Function.RightInverse.surjective (smul_inv_smul₀ hc)
-  trans ⨅ (y) (_H : y ∈ s), ‖c‖₊ • edist x y
+  trans ⨅ (y) (_ : y ∈ s), ‖c‖₊ • edist x y
   · refine' (this.iInf_congr _ fun y => _).symm
     simp_rw [smul_mem_smul_set_iff₀ hc, edist_smul₀]
   · have : (‖c‖₊ : ENNReal) ≠ 0 := by simp [hc]

The actual forward-porting was done in #4327 and #4328

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yaël Dillies
 
 ! This file was ported from Lean 3 source module analysis.normed_space.pointwise
-! leanprover-community/mathlib commit 832a8ba8f10f11fea99367c469ff802e69a5b8ec
+! leanprover-community/mathlib commit bc91ed7093bf098d253401e69df601fc33dde156
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

Forward-port of leanprover-community/mathlib#18990

Original title: feat(analysis/normed_space/basic): scaling a set scales its diameter, translating it leaves it unchanged

@@ -25,7 +25,63 @@ open Metric Set
 
 open Pointwise Topology
 
-variable {𝕜 E : Type _} [NormedField 𝕜]
+variable {𝕜 E : Type _}
+
+section SMulZeroClass
+
+variable [SeminormedAddCommGroup 𝕜] [SeminormedAddCommGroup E]
+
+variable [SMulZeroClass 𝕜 E] [BoundedSMul 𝕜 E]
+
+theorem ediam_smul_le (c : 𝕜) (s : Set E) : EMetric.diam (c • s) ≤ ‖c‖₊ • EMetric.diam s :=
+  (lipschitzWith_smul c).ediam_image_le s
+#align ediam_smul_le ediam_smul_le
+
+end SMulZeroClass
+
+section DivisionRing
+
+variable [NormedDivisionRing 𝕜] [SeminormedAddCommGroup E]
+
+variable [Module 𝕜 E] [BoundedSMul 𝕜 E]
+
+theorem ediam_smul₀ (c : 𝕜) (s : Set E) : EMetric.diam (c • s) = ‖c‖₊ • EMetric.diam s := by
+  refine' le_antisymm (ediam_smul_le c s) _
+  obtain rfl | hc := eq_or_ne c 0
+  · obtain rfl | hs := s.eq_empty_or_nonempty
+    · simp
+    simp [zero_smul_set hs, ← Set.singleton_zero]
+  · have := (lipschitzWith_smul c⁻¹).ediam_image_le (c • s)
+    rwa [← smul_eq_mul, ← ENNReal.smul_def, Set.image_smul, inv_smul_smul₀ hc s, nnnorm_inv,
+      ENNReal.le_inv_smul_iff (nnnorm_ne_zero_iff.mpr hc)] at this
+#align ediam_smul₀ ediam_smul₀
+
+theorem diam_smul₀ (c : 𝕜) (x : Set E) : diam (c • x) = ‖c‖ * diam x := by
+  simp_rw [diam, ediam_smul₀, ENNReal.toReal_smul, NNReal.smul_def, coe_nnnorm, smul_eq_mul]
+#align diam_smul₀ diam_smul₀
+
+theorem infEdist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
+    EMetric.infEdist (c • x) (c • s) = ‖c‖₊ • EMetric.infEdist x s := by
+  simp_rw [EMetric.infEdist]
+  have : Function.Surjective ((c • ·) : E → E) :=
+    Function.RightInverse.surjective (smul_inv_smul₀ hc)
+  trans ⨅ (y) (_H : y ∈ s), ‖c‖₊ • edist x y
+  · refine' (this.iInf_congr _ fun y => _).symm
+    simp_rw [smul_mem_smul_set_iff₀ hc, edist_smul₀]
+  · have : (‖c‖₊ : ENNReal) ≠ 0 := by simp [hc]
+    simp_rw [ENNReal.smul_def, smul_eq_mul, ENNReal.mul_iInf_of_ne this ENNReal.coe_ne_top]
+#align inf_edist_smul₀ infEdist_smul₀
+
+theorem infDist_smul₀ {c : 𝕜} (hc : c ≠ 0) (s : Set E) (x : E) :
+    Metric.infDist (c • x) (c • s) = ‖c‖ * Metric.infDist x s := by
+  simp_rw [Metric.infDist, infEdist_smul₀ hc s, ENNReal.toReal_smul, NNReal.smul_def, coe_nnnorm,
+    smul_eq_mul]
+#align inf_dist_smul₀ infDist_smul₀
+
+end DivisionRing
+
+
+variable [NormedField 𝕜]
 
 section SeminormedAddCommGroup