topology.metric_space.holder ⟷ Mathlib.Topology.MetricSpace.Holder

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Topology.MetricSpace.Lipschitz
+import Topology.EMetricSpace.Lipschitz
 import Analysis.SpecialFunctions.Pow.Continuity
 
 #align_import topology.metric_space.holder from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Mathbin.Topology.MetricSpace.Lipschitz
-import Mathbin.Analysis.SpecialFunctions.Pow.Continuity
+import Topology.MetricSpace.Lipschitz
+import Analysis.SpecialFunctions.Pow.Continuity
 
 #align_import topology.metric_space.holder from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 

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

@@ -105,7 +105,7 @@ alias ⟨_, LipschitzOnWith.holderOnWith⟩ := holderOnWith_one
 #print holderWith_one /-
 @[simp]
 theorem holderWith_one {C : ℝ≥0} {f : X → Y} : HolderWith C 1 f ↔ LipschitzWith C f :=
-  holderOnWith_univ.symm.trans <| holderOnWith_one.trans lipschitz_on_univ
+  holderOnWith_univ.symm.trans <| holderOnWith_one.trans lipschitzOn_univ
 #align holder_with_one holderWith_one
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -99,7 +99,7 @@ theorem holderOnWith_one {C : ℝ≥0} {f : X → Y} {s : Set X} :
 #align holder_on_with_one holderOnWith_one
 -/
 
-alias holderOnWith_one ↔ _ LipschitzOnWith.holderOnWith
+alias ⟨_, LipschitzOnWith.holderOnWith⟩ := holderOnWith_one
 #align lipschitz_on_with.holder_on_with LipschitzOnWith.holderOnWith
 
 #print holderWith_one /-
@@ -109,7 +109,7 @@ theorem holderWith_one {C : ℝ≥0} {f : X → Y} : HolderWith C 1 f ↔ Lipsch
 #align holder_with_one holderWith_one
 -/
 
-alias holderWith_one ↔ _ LipschitzWith.holderWith
+alias ⟨_, LipschitzWith.holderWith⟩ := holderWith_one
 #align lipschitz_with.holder_with LipschitzWith.holderWith
 
 #print holderWith_id /-

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module topology.metric_space.holder
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.MetricSpace.Lipschitz
 import Mathbin.Analysis.SpecialFunctions.Pow.Continuity
 
+#align_import topology.metric_space.holder from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # Hölder continuous functions
 

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

@@ -68,37 +68,49 @@ def HolderOnWith (C r : ℝ≥0) (f : X → Y) (s : Set X) : Prop :=
 #align holder_on_with HolderOnWith
 -/
 
+#print holderOnWith_empty /-
 @[simp]
 theorem holderOnWith_empty (C r : ℝ≥0) (f : X → Y) : HolderOnWith C r f ∅ := fun x hx => hx.elim
 #align holder_on_with_empty holderOnWith_empty
+-/
 
+#print holderOnWith_singleton /-
 @[simp]
 theorem holderOnWith_singleton (C r : ℝ≥0) (f : X → Y) (x : X) : HolderOnWith C r f {x} := by
   rintro a (rfl : a = x) b (rfl : b = a); rw [edist_self]; exact zero_le _
 #align holder_on_with_singleton holderOnWith_singleton
+-/
 
+#print Set.Subsingleton.holderOnWith /-
 theorem Set.Subsingleton.holderOnWith {s : Set X} (hs : s.Subsingleton) (C r : ℝ≥0) (f : X → Y) :
     HolderOnWith C r f s :=
   hs.inductionOn (holderOnWith_empty C r f) (holderOnWith_singleton C r f)
 #align set.subsingleton.holder_on_with Set.Subsingleton.holderOnWith
+-/
 
+#print holderOnWith_univ /-
 theorem holderOnWith_univ {C r : ℝ≥0} {f : X → Y} : HolderOnWith C r f univ ↔ HolderWith C r f := by
   simp only [HolderOnWith, HolderWith, mem_univ, true_imp_iff]
 #align holder_on_with_univ holderOnWith_univ
+-/
 
+#print holderOnWith_one /-
 @[simp]
 theorem holderOnWith_one {C : ℝ≥0} {f : X → Y} {s : Set X} :
     HolderOnWith C 1 f s ↔ LipschitzOnWith C f s := by
   simp only [HolderOnWith, LipschitzOnWith, NNReal.coe_one, ENNReal.rpow_one]
 #align holder_on_with_one holderOnWith_one
+-/
 
 alias holderOnWith_one ↔ _ LipschitzOnWith.holderOnWith
 #align lipschitz_on_with.holder_on_with LipschitzOnWith.holderOnWith
 
+#print holderWith_one /-
 @[simp]
 theorem holderWith_one {C : ℝ≥0} {f : X → Y} : HolderWith C 1 f ↔ LipschitzWith C f :=
   holderOnWith_univ.symm.trans <| holderOnWith_one.trans lipschitz_on_univ
 #align holder_with_one holderWith_one
+-/
 
 alias holderWith_one ↔ _ LipschitzWith.holderWith
 #align lipschitz_with.holder_with LipschitzWith.holderWith
@@ -109,24 +121,31 @@ theorem holderWith_id : HolderWith 1 1 (id : X → X) :=
 #align holder_with_id holderWith_id
 -/
 
+#print HolderWith.holderOnWith /-
 protected theorem HolderWith.holderOnWith {C r : ℝ≥0} {f : X → Y} (h : HolderWith C r f)
     (s : Set X) : HolderOnWith C r f s := fun x _ y _ => h x y
 #align holder_with.holder_on_with HolderWith.holderOnWith
+-/
 
 namespace HolderOnWith
 
 variable {C r : ℝ≥0} {f : X → Y} {s t : Set X}
 
+#print HolderOnWith.edist_le /-
 theorem edist_le (h : HolderOnWith C r f s) {x y : X} (hx : x ∈ s) (hy : y ∈ s) :
     edist (f x) (f y) ≤ C * edist x y ^ (r : ℝ) :=
   h x hx y hy
 #align holder_on_with.edist_le HolderOnWith.edist_le
+-/
 
+#print HolderOnWith.edist_le_of_le /-
 theorem edist_le_of_le (h : HolderOnWith C r f s) {x y : X} (hx : x ∈ s) (hy : y ∈ s) {d : ℝ≥0∞}
     (hd : edist x y ≤ d) : edist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   (h.edist_le hx hy).trans (mul_le_mul_left' (ENNReal.rpow_le_rpow hd r.coe_nonneg) _)
 #align holder_on_with.edist_le_of_le HolderOnWith.edist_le_of_le
+-/
 
+#print HolderOnWith.comp /-
 theorem comp {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : HolderOnWith Cg rg g t) {Cf rf : ℝ≥0}
     {f : X → Y} (hf : HolderOnWith Cf rf f s) (hst : MapsTo f s t) :
     HolderOnWith (Cg * Cf ^ (rg : ℝ)) (rg * rf) (g ∘ f) s :=
@@ -136,13 +155,17 @@ theorem comp {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : HolderOnWith Cg r
     ENNReal.coe_rpow_of_nonneg _ rg.coe_nonneg, ← ENNReal.mul_rpow_of_nonneg _ _ rg.coe_nonneg]
   exact hg.edist_le_of_le (hst hx) (hst hy) (hf.edist_le hx hy)
 #align holder_on_with.comp HolderOnWith.comp
+-/
 
+#print HolderOnWith.comp_holderWith /-
 theorem comp_holderWith {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : HolderOnWith Cg rg g t)
     {Cf rf : ℝ≥0} {f : X → Y} (hf : HolderWith Cf rf f) (ht : ∀ x, f x ∈ t) :
     HolderWith (Cg * Cf ^ (rg : ℝ)) (rg * rf) (g ∘ f) :=
   holderOnWith_univ.mp <| hg.comp (hf.HolderOnWith univ) fun x _ => ht x
 #align holder_on_with.comp_holder_with HolderOnWith.comp_holderWith
+-/
 
+#print HolderOnWith.uniformContinuousOn /-
 /-- A Hölder continuous function is uniformly continuous -/
 protected theorem uniformContinuousOn (hf : HolderOnWith C r f s) (h0 : 0 < r) :
     UniformContinuousOn f s :=
@@ -153,46 +176,63 @@ protected theorem uniformContinuousOn (hf : HolderOnWith C r f s) (h0 : 0 < r) :
   rcases ennreal.nhds_zero_basis.mem_iff.1 (this (gt_mem_nhds εpos)) with ⟨δ, δ0, H⟩
   exact ⟨δ, δ0, fun x hx y hy h => (hf.edist_le hx hy).trans_lt (H h)⟩
 #align holder_on_with.uniform_continuous_on HolderOnWith.uniformContinuousOn
+-/
 
+#print HolderOnWith.continuousOn /-
 protected theorem continuousOn (hf : HolderOnWith C r f s) (h0 : 0 < r) : ContinuousOn f s :=
   (hf.UniformContinuousOn h0).ContinuousOn
 #align holder_on_with.continuous_on HolderOnWith.continuousOn
+-/
 
+#print HolderOnWith.mono /-
 protected theorem mono (hf : HolderOnWith C r f s) (ht : t ⊆ s) : HolderOnWith C r f t :=
   fun x hx y hy => hf.edist_le (ht hx) (ht hy)
 #align holder_on_with.mono HolderOnWith.mono
+-/
 
+#print HolderOnWith.ediam_image_le_of_le /-
 theorem ediam_image_le_of_le (hf : HolderOnWith C r f s) {d : ℝ≥0∞} (hd : EMetric.diam s ≤ d) :
     EMetric.diam (f '' s) ≤ C * d ^ (r : ℝ) :=
   EMetric.diam_image_le_iff.2 fun x hx y hy =>
     hf.edist_le_of_le hx hy <| (EMetric.edist_le_diam_of_mem hx hy).trans hd
 #align holder_on_with.ediam_image_le_of_le HolderOnWith.ediam_image_le_of_le
+-/
 
+#print HolderOnWith.ediam_image_le /-
 theorem ediam_image_le (hf : HolderOnWith C r f s) :
     EMetric.diam (f '' s) ≤ C * EMetric.diam s ^ (r : ℝ) :=
   hf.ediam_image_le_of_le le_rfl
 #align holder_on_with.ediam_image_le HolderOnWith.ediam_image_le
+-/
 
+#print HolderOnWith.ediam_image_le_of_subset /-
 theorem ediam_image_le_of_subset (hf : HolderOnWith C r f s) (ht : t ⊆ s) :
     EMetric.diam (f '' t) ≤ C * EMetric.diam t ^ (r : ℝ) :=
   (hf.mono ht).ediam_image_le
 #align holder_on_with.ediam_image_le_of_subset HolderOnWith.ediam_image_le_of_subset
+-/
 
+#print HolderOnWith.ediam_image_le_of_subset_of_le /-
 theorem ediam_image_le_of_subset_of_le (hf : HolderOnWith C r f s) (ht : t ⊆ s) {d : ℝ≥0∞}
     (hd : EMetric.diam t ≤ d) : EMetric.diam (f '' t) ≤ C * d ^ (r : ℝ) :=
   (hf.mono ht).ediam_image_le_of_le hd
 #align holder_on_with.ediam_image_le_of_subset_of_le HolderOnWith.ediam_image_le_of_subset_of_le
+-/
 
+#print HolderOnWith.ediam_image_inter_le_of_le /-
 theorem ediam_image_inter_le_of_le (hf : HolderOnWith C r f s) {d : ℝ≥0∞}
     (hd : EMetric.diam t ≤ d) : EMetric.diam (f '' (t ∩ s)) ≤ C * d ^ (r : ℝ) :=
   hf.ediam_image_le_of_subset_of_le (inter_subset_right _ _) <|
     (EMetric.diam_mono <| inter_subset_left _ _).trans hd
 #align holder_on_with.ediam_image_inter_le_of_le HolderOnWith.ediam_image_inter_le_of_le
+-/
 
+#print HolderOnWith.ediam_image_inter_le /-
 theorem ediam_image_inter_le (hf : HolderOnWith C r f s) (t : Set X) :
     EMetric.diam (f '' (t ∩ s)) ≤ C * EMetric.diam t ^ (r : ℝ) :=
   hf.ediam_image_inter_le_of_le le_rfl
 #align holder_on_with.ediam_image_inter_le HolderOnWith.ediam_image_inter_le
+-/
 
 end HolderOnWith
 
@@ -200,40 +240,54 @@ namespace HolderWith
 
 variable {C r : ℝ≥0} {f : X → Y}
 
+#print HolderWith.edist_le /-
 theorem edist_le (h : HolderWith C r f) (x y : X) : edist (f x) (f y) ≤ C * edist x y ^ (r : ℝ) :=
   h x y
 #align holder_with.edist_le HolderWith.edist_le
+-/
 
+#print HolderWith.edist_le_of_le /-
 theorem edist_le_of_le (h : HolderWith C r f) {x y : X} {d : ℝ≥0∞} (hd : edist x y ≤ d) :
     edist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   (h.HolderOnWith univ).edist_le_of_le trivial trivial hd
 #align holder_with.edist_le_of_le HolderWith.edist_le_of_le
+-/
 
+#print HolderWith.comp /-
 theorem comp {Cg rg : ℝ≥0} {g : Y → Z} (hg : HolderWith Cg rg g) {Cf rf : ℝ≥0} {f : X → Y}
     (hf : HolderWith Cf rf f) : HolderWith (Cg * Cf ^ (rg : ℝ)) (rg * rf) (g ∘ f) :=
   (hg.HolderOnWith univ).comp_holderWith hf fun _ => trivial
 #align holder_with.comp HolderWith.comp
+-/
 
+#print HolderWith.comp_holderOnWith /-
 theorem comp_holderOnWith {Cg rg : ℝ≥0} {g : Y → Z} (hg : HolderWith Cg rg g) {Cf rf : ℝ≥0}
     {f : X → Y} {s : Set X} (hf : HolderOnWith Cf rf f s) :
     HolderOnWith (Cg * Cf ^ (rg : ℝ)) (rg * rf) (g ∘ f) s :=
   (hg.HolderOnWith univ).comp hf fun _ _ => trivial
 #align holder_with.comp_holder_on_with HolderWith.comp_holderOnWith
+-/
 
+#print HolderWith.uniformContinuous /-
 /-- A Hölder continuous function is uniformly continuous -/
 protected theorem uniformContinuous (hf : HolderWith C r f) (h0 : 0 < r) : UniformContinuous f :=
   uniformContinuousOn_univ.mp <| (hf.HolderOnWith univ).UniformContinuousOn h0
 #align holder_with.uniform_continuous HolderWith.uniformContinuous
+-/
 
+#print HolderWith.continuous /-
 protected theorem continuous (hf : HolderWith C r f) (h0 : 0 < r) : Continuous f :=
   (hf.UniformContinuous h0).Continuous
 #align holder_with.continuous HolderWith.continuous
+-/
 
+#print HolderWith.ediam_image_le /-
 theorem ediam_image_le (hf : HolderWith C r f) (s : Set X) :
     EMetric.diam (f '' s) ≤ C * EMetric.diam s ^ (r : ℝ) :=
   EMetric.diam_image_le_iff.2 fun x hx y hy =>
     hf.edist_le_of_le <| EMetric.edist_le_diam_of_mem hx hy
 #align holder_with.ediam_image_le HolderWith.ediam_image_le
+-/
 
 end HolderWith
 
@@ -245,6 +299,7 @@ variable [PseudoMetricSpace X] [PseudoMetricSpace Y] {C r : ℝ≥0} {f : X →
 
 namespace HolderWith
 
+#print HolderWith.nndist_le_of_le /-
 theorem nndist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ≥0} (hd : nndist x y ≤ d) :
     nndist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   by
@@ -253,12 +308,16 @@ theorem nndist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ≥0} (hd : nn
   apply hf.edist_le_of_le
   rwa [edist_nndist, ENNReal.coe_le_coe]
 #align holder_with.nndist_le_of_le HolderWith.nndist_le_of_le
+-/
 
+#print HolderWith.nndist_le /-
 theorem nndist_le (hf : HolderWith C r f) (x y : X) :
     nndist (f x) (f y) ≤ C * nndist x y ^ (r : ℝ) :=
   hf.nndist_le_of_le le_rfl
 #align holder_with.nndist_le HolderWith.nndist_le
+-/
 
+#print HolderWith.dist_le_of_le /-
 theorem dist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ} (hd : dist x y ≤ d) :
     dist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   by
@@ -267,10 +326,13 @@ theorem dist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ} (hd : dist x y
   norm_cast at hd ⊢
   exact hf.nndist_le_of_le hd
 #align holder_with.dist_le_of_le HolderWith.dist_le_of_le
+-/
 
+#print HolderWith.dist_le /-
 theorem dist_le (hf : HolderWith C r f) (x y : X) : dist (f x) (f y) ≤ C * dist x y ^ (r : ℝ) :=
   hf.dist_le_of_le le_rfl
 #align holder_with.dist_le HolderWith.dist_le
+-/
 
 end HolderWith
 

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

@@ -264,7 +264,7 @@ theorem dist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ} (hd : dist x y
   by
   lift d to ℝ≥0 using dist_nonneg.trans hd
   rw [dist_nndist] at hd ⊢
-  norm_cast  at hd ⊢
+  norm_cast at hd ⊢
   exact hf.nndist_le_of_le hd
 #align holder_with.dist_le_of_le HolderWith.dist_le_of_le
 

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

@@ -263,8 +263,8 @@ theorem dist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ} (hd : dist x y
     dist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   by
   lift d to ℝ≥0 using dist_nonneg.trans hd
-  rw [dist_nndist] at hd⊢
-  norm_cast  at hd⊢
+  rw [dist_nndist] at hd ⊢
+  norm_cast  at hd ⊢
   exact hf.nndist_le_of_le hd
 #align holder_with.dist_le_of_le HolderWith.dist_le_of_le
 

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

@@ -45,7 +45,7 @@ variable {X Y Z : Type _}
 
 open Filter Set
 
-open NNReal ENNReal Topology
+open scoped NNReal ENNReal Topology
 
 section Emetric
 

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

@@ -68,86 +68,38 @@ def HolderOnWith (C r : ℝ≥0) (f : X → Y) (s : Set X) : Prop :=
 #align holder_on_with HolderOnWith
 -/
 
-/- warning: holder_on_with_empty -> holderOnWith_empty is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] (C : NNReal) (r : NNReal) (f : X -> Y), HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f (EmptyCollection.emptyCollection.{u1} (Set.{u1} X) (Set.hasEmptyc.{u1} X))
-but is expected to have type
-  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] (C : NNReal) (r : NNReal) (f : X -> Y), HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f (EmptyCollection.emptyCollection.{u2} (Set.{u2} X) (Set.instEmptyCollectionSet.{u2} X))
-Case conversion may be inaccurate. Consider using '#align holder_on_with_empty holderOnWith_emptyₓ'. -/
 @[simp]
 theorem holderOnWith_empty (C r : ℝ≥0) (f : X → Y) : HolderOnWith C r f ∅ := fun x hx => hx.elim
 #align holder_on_with_empty holderOnWith_empty
 
-/- warning: holder_on_with_singleton -> holderOnWith_singleton is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] (C : NNReal) (r : NNReal) (f : X -> Y) (x : X), HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f (Singleton.singleton.{u1, u1} X (Set.{u1} X) (Set.hasSingleton.{u1} X) x)
-but is expected to have type
-  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] (C : NNReal) (r : NNReal) (f : X -> Y) (x : X), HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f (Singleton.singleton.{u2, u2} X (Set.{u2} X) (Set.instSingletonSet.{u2} X) x)
-Case conversion may be inaccurate. Consider using '#align holder_on_with_singleton holderOnWith_singletonₓ'. -/
 @[simp]
 theorem holderOnWith_singleton (C r : ℝ≥0) (f : X → Y) (x : X) : HolderOnWith C r f {x} := by
   rintro a (rfl : a = x) b (rfl : b = a); rw [edist_self]; exact zero_le _
 #align holder_on_with_singleton holderOnWith_singleton
 
-/- warning: set.subsingleton.holder_on_with -> Set.Subsingleton.holderOnWith is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {s : Set.{u1} X}, (Set.Subsingleton.{u1} X s) -> (forall (C : NNReal) (r : NNReal) (f : X -> Y), HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s)
-but is expected to have type
-  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {s : Set.{u2} X}, (Set.Subsingleton.{u2} X s) -> (forall (C : NNReal) (r : NNReal) (f : X -> Y), HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s)
-Case conversion may be inaccurate. Consider using '#align set.subsingleton.holder_on_with Set.Subsingleton.holderOnWithₓ'. -/
 theorem Set.Subsingleton.holderOnWith {s : Set X} (hs : s.Subsingleton) (C r : ℝ≥0) (f : X → Y) :
     HolderOnWith C r f s :=
   hs.inductionOn (holderOnWith_empty C r f) (holderOnWith_singleton C r f)
 #align set.subsingleton.holder_on_with Set.Subsingleton.holderOnWith
 
-/- warning: holder_on_with_univ -> holderOnWith_univ is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align holder_on_with_univ holderOnWith_univₓ'. -/
 theorem holderOnWith_univ {C r : ℝ≥0} {f : X → Y} : HolderOnWith C r f univ ↔ HolderWith C r f := by
   simp only [HolderOnWith, HolderWith, mem_univ, true_imp_iff]
 #align holder_on_with_univ holderOnWith_univ
 
-/- warning: holder_on_with_one -> holderOnWith_one is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align holder_on_with_one holderOnWith_oneₓ'. -/
 @[simp]
 theorem holderOnWith_one {C : ℝ≥0} {f : X → Y} {s : Set X} :
     HolderOnWith C 1 f s ↔ LipschitzOnWith C f s := by
   simp only [HolderOnWith, LipschitzOnWith, NNReal.coe_one, ENNReal.rpow_one]
 #align holder_on_with_one holderOnWith_one
 
-/- warning: lipschitz_on_with.holder_on_with -> LipschitzOnWith.holderOnWith is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align lipschitz_on_with.holder_on_with LipschitzOnWith.holderOnWithₓ'. -/
 alias holderOnWith_one ↔ _ LipschitzOnWith.holderOnWith
 #align lipschitz_on_with.holder_on_with LipschitzOnWith.holderOnWith
 
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-Case conversion may be inaccurate. Consider using '#align holder_with_one holderWith_oneₓ'. -/
 @[simp]
 theorem holderWith_one {C : ℝ≥0} {f : X → Y} : HolderWith C 1 f ↔ LipschitzWith C f :=
   holderOnWith_univ.symm.trans <| holderOnWith_one.trans lipschitz_on_univ
 #align holder_with_one holderWith_one
 
-/- warning: lipschitz_with.holder_with -> LipschitzWith.holderWith is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align lipschitz_with.holder_with LipschitzWith.holderWithₓ'. -/
 alias holderWith_one ↔ _ LipschitzWith.holderWith
 #align lipschitz_with.holder_with LipschitzWith.holderWith
 
@@ -157,12 +109,6 @@ theorem holderWith_id : HolderWith 1 1 (id : X → X) :=
 #align holder_with_id holderWith_id
 -/
 
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-Case conversion may be inaccurate. Consider using '#align holder_with.holder_on_with HolderWith.holderOnWithₓ'. -/
 protected theorem HolderWith.holderOnWith {C r : ℝ≥0} {f : X → Y} (h : HolderWith C r f)
     (s : Set X) : HolderOnWith C r f s := fun x _ y _ => h x y
 #align holder_with.holder_on_with HolderWith.holderOnWith
@@ -171,31 +117,16 @@ namespace HolderOnWith
 
 variable {C r : ℝ≥0} {f : X → Y} {s t : Set X}
 
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-Case conversion may be inaccurate. Consider using '#align holder_on_with.edist_le HolderOnWith.edist_leₓ'. -/
 theorem edist_le (h : HolderOnWith C r f s) {x y : X} (hx : x ∈ s) (hy : y ∈ s) :
     edist (f x) (f y) ≤ C * edist x y ^ (r : ℝ) :=
   h x hx y hy
 #align holder_on_with.edist_le HolderOnWith.edist_le
 
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-Case conversion may be inaccurate. Consider using '#align holder_on_with.edist_le_of_le HolderOnWith.edist_le_of_leₓ'. -/
 theorem edist_le_of_le (h : HolderOnWith C r f s) {x y : X} (hx : x ∈ s) (hy : y ∈ s) {d : ℝ≥0∞}
     (hd : edist x y ≤ d) : edist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   (h.edist_le hx hy).trans (mul_le_mul_left' (ENNReal.rpow_le_rpow hd r.coe_nonneg) _)
 #align holder_on_with.edist_le_of_le HolderOnWith.edist_le_of_le
 
-/- warning: holder_on_with.comp -> HolderOnWith.comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align holder_on_with.comp HolderOnWith.compₓ'. -/
 theorem comp {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : HolderOnWith Cg rg g t) {Cf rf : ℝ≥0}
     {f : X → Y} (hf : HolderOnWith Cf rf f s) (hst : MapsTo f s t) :
     HolderOnWith (Cg * Cf ^ (rg : ℝ)) (rg * rf) (g ∘ f) s :=
@@ -206,24 +137,12 @@ theorem comp {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : HolderOnWith Cg r
   exact hg.edist_le_of_le (hst hx) (hst hy) (hf.edist_le hx hy)
 #align holder_on_with.comp HolderOnWith.comp
 
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-Case conversion may be inaccurate. Consider using '#align holder_on_with.comp_holder_with HolderOnWith.comp_holderWithₓ'. -/
 theorem comp_holderWith {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : HolderOnWith Cg rg g t)
     {Cf rf : ℝ≥0} {f : X → Y} (hf : HolderWith Cf rf f) (ht : ∀ x, f x ∈ t) :
     HolderWith (Cg * Cf ^ (rg : ℝ)) (rg * rf) (g ∘ f) :=
   holderOnWith_univ.mp <| hg.comp (hf.HolderOnWith univ) fun x _ => ht x
 #align holder_on_with.comp_holder_with HolderOnWith.comp_holderWith
 
-/- warning: holder_on_with.uniform_continuous_on -> HolderOnWith.uniformContinuousOn is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align holder_on_with.uniform_continuous_on HolderOnWith.uniformContinuousOnₓ'. -/
 /-- A Hölder continuous function is uniformly continuous -/
 protected theorem uniformContinuousOn (hf : HolderOnWith C r f s) (h0 : 0 < r) :
     UniformContinuousOn f s :=
@@ -235,89 +154,41 @@ protected theorem uniformContinuousOn (hf : HolderOnWith C r f s) (h0 : 0 < r) :
   exact ⟨δ, δ0, fun x hx y hy h => (hf.edist_le hx hy).trans_lt (H h)⟩
 #align holder_on_with.uniform_continuous_on HolderOnWith.uniformContinuousOn
 
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-Case conversion may be inaccurate. Consider using '#align holder_on_with.continuous_on HolderOnWith.continuousOnₓ'. -/
 protected theorem continuousOn (hf : HolderOnWith C r f s) (h0 : 0 < r) : ContinuousOn f s :=
   (hf.UniformContinuousOn h0).ContinuousOn
 #align holder_on_with.continuous_on HolderOnWith.continuousOn
 
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 protected theorem mono (hf : HolderOnWith C r f s) (ht : t ⊆ s) : HolderOnWith C r f t :=
   fun x hx y hy => hf.edist_le (ht hx) (ht hy)
 #align holder_on_with.mono HolderOnWith.mono
 
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-Case conversion may be inaccurate. Consider using '#align holder_on_with.ediam_image_le_of_le HolderOnWith.ediam_image_le_of_leₓ'. -/
 theorem ediam_image_le_of_le (hf : HolderOnWith C r f s) {d : ℝ≥0∞} (hd : EMetric.diam s ≤ d) :
     EMetric.diam (f '' s) ≤ C * d ^ (r : ℝ) :=
   EMetric.diam_image_le_iff.2 fun x hx y hy =>
     hf.edist_le_of_le hx hy <| (EMetric.edist_le_diam_of_mem hx hy).trans hd
 #align holder_on_with.ediam_image_le_of_le HolderOnWith.ediam_image_le_of_le
 
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 theorem ediam_image_le (hf : HolderOnWith C r f s) :
     EMetric.diam (f '' s) ≤ C * EMetric.diam s ^ (r : ℝ) :=
   hf.ediam_image_le_of_le le_rfl
 #align holder_on_with.ediam_image_le HolderOnWith.ediam_image_le
 
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-Case conversion may be inaccurate. Consider using '#align holder_on_with.ediam_image_le_of_subset HolderOnWith.ediam_image_le_of_subsetₓ'. -/
 theorem ediam_image_le_of_subset (hf : HolderOnWith C r f s) (ht : t ⊆ s) :
     EMetric.diam (f '' t) ≤ C * EMetric.diam t ^ (r : ℝ) :=
   (hf.mono ht).ediam_image_le
 #align holder_on_with.ediam_image_le_of_subset HolderOnWith.ediam_image_le_of_subset
 
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 theorem ediam_image_le_of_subset_of_le (hf : HolderOnWith C r f s) (ht : t ⊆ s) {d : ℝ≥0∞}
     (hd : EMetric.diam t ≤ d) : EMetric.diam (f '' t) ≤ C * d ^ (r : ℝ) :=
   (hf.mono ht).ediam_image_le_of_le hd
 #align holder_on_with.ediam_image_le_of_subset_of_le HolderOnWith.ediam_image_le_of_subset_of_le
 
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-Case conversion may be inaccurate. Consider using '#align holder_on_with.ediam_image_inter_le_of_le HolderOnWith.ediam_image_inter_le_of_leₓ'. -/
 theorem ediam_image_inter_le_of_le (hf : HolderOnWith C r f s) {d : ℝ≥0∞}
     (hd : EMetric.diam t ≤ d) : EMetric.diam (f '' (t ∩ s)) ≤ C * d ^ (r : ℝ) :=
   hf.ediam_image_le_of_subset_of_le (inter_subset_right _ _) <|
     (EMetric.diam_mono <| inter_subset_left _ _).trans hd
 #align holder_on_with.ediam_image_inter_le_of_le HolderOnWith.ediam_image_inter_le_of_le
 
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-Case conversion may be inaccurate. Consider using '#align holder_on_with.ediam_image_inter_le HolderOnWith.ediam_image_inter_leₓ'. -/
 theorem ediam_image_inter_le (hf : HolderOnWith C r f s) (t : Set X) :
     EMetric.diam (f '' (t ∩ s)) ≤ C * EMetric.diam t ^ (r : ℝ) :=
   hf.ediam_image_inter_le_of_le le_rfl
@@ -329,77 +200,35 @@ namespace HolderWith
 
 variable {C r : ℝ≥0} {f : X → Y}
 
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 theorem edist_le (h : HolderWith C r f) (x y : X) : edist (f x) (f y) ≤ C * edist x y ^ (r : ℝ) :=
   h x y
 #align holder_with.edist_le HolderWith.edist_le
 
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-Case conversion may be inaccurate. Consider using '#align holder_with.edist_le_of_le HolderWith.edist_le_of_leₓ'. -/
 theorem edist_le_of_le (h : HolderWith C r f) {x y : X} {d : ℝ≥0∞} (hd : edist x y ≤ d) :
     edist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   (h.HolderOnWith univ).edist_le_of_le trivial trivial hd
 #align holder_with.edist_le_of_le HolderWith.edist_le_of_le
 
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-Case conversion may be inaccurate. Consider using '#align holder_with.comp HolderWith.compₓ'. -/
 theorem comp {Cg rg : ℝ≥0} {g : Y → Z} (hg : HolderWith Cg rg g) {Cf rf : ℝ≥0} {f : X → Y}
     (hf : HolderWith Cf rf f) : HolderWith (Cg * Cf ^ (rg : ℝ)) (rg * rf) (g ∘ f) :=
   (hg.HolderOnWith univ).comp_holderWith hf fun _ => trivial
 #align holder_with.comp HolderWith.comp
 
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-Case conversion may be inaccurate. Consider using '#align holder_with.comp_holder_on_with HolderWith.comp_holderOnWithₓ'. -/
 theorem comp_holderOnWith {Cg rg : ℝ≥0} {g : Y → Z} (hg : HolderWith Cg rg g) {Cf rf : ℝ≥0}
     {f : X → Y} {s : Set X} (hf : HolderOnWith Cf rf f s) :
     HolderOnWith (Cg * Cf ^ (rg : ℝ)) (rg * rf) (g ∘ f) s :=
   (hg.HolderOnWith univ).comp hf fun _ _ => trivial
 #align holder_with.comp_holder_on_with HolderWith.comp_holderOnWith
 
-/- warning: holder_with.uniform_continuous -> HolderWith.uniformContinuous is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align holder_with.uniform_continuous HolderWith.uniformContinuousₓ'. -/
 /-- A Hölder continuous function is uniformly continuous -/
 protected theorem uniformContinuous (hf : HolderWith C r f) (h0 : 0 < r) : UniformContinuous f :=
   uniformContinuousOn_univ.mp <| (hf.HolderOnWith univ).UniformContinuousOn h0
 #align holder_with.uniform_continuous HolderWith.uniformContinuous
 
-/- warning: holder_with.continuous -> HolderWith.continuous is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align holder_with.continuous HolderWith.continuousₓ'. -/
 protected theorem continuous (hf : HolderWith C r f) (h0 : 0 < r) : Continuous f :=
   (hf.UniformContinuous h0).Continuous
 #align holder_with.continuous HolderWith.continuous
 
-/- warning: holder_with.ediam_image_le -> HolderWith.ediam_image_le is a dubious translation:
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-  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y _inst_1 _inst_2 C r f) -> (forall (s : Set.{u2} X), 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.{u1} Y _inst_2 (Set.image.{u2, u1} X Y f s)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (EMetric.diam.{u2} X _inst_1 s) (NNReal.toReal r))))
-Case conversion may be inaccurate. Consider using '#align holder_with.ediam_image_le HolderWith.ediam_image_leₓ'. -/
 theorem ediam_image_le (hf : HolderWith C r f) (s : Set X) :
     EMetric.diam (f '' s) ≤ C * EMetric.diam s ^ (r : ℝ) :=
   EMetric.diam_image_le_iff.2 fun x hx y hy =>
@@ -416,12 +245,6 @@ variable [PseudoMetricSpace X] [PseudoMetricSpace Y] {C r : ℝ≥0} {f : X →
 
 namespace HolderWith
 
-/- warning: holder_with.nndist_le_of_le -> HolderWith.nndist_le_of_le is a dubious translation:
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-  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u2} X] [_inst_2 : PseudoMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y (PseudoMetricSpace.toPseudoEMetricSpace.{u2} X _inst_1) (PseudoMetricSpace.toPseudoEMetricSpace.{u1} Y _inst_2) C r f) -> (forall {x : X} {y : X} {d : NNReal}, (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNDist.nndist.{u2} X (PseudoMetricSpace.toNNDist.{u2} X _inst_1) x y) d) -> (LE.le.{0} Real Real.instLEReal (NNReal.toReal (NNDist.nndist.{u1} Y (PseudoMetricSpace.toNNDist.{u1} Y _inst_2) (f x) (f y))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (NNReal.toReal C) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (NNReal.toReal d) (NNReal.toReal r)))))
-Case conversion may be inaccurate. Consider using '#align holder_with.nndist_le_of_le HolderWith.nndist_le_of_leₓ'. -/
 theorem nndist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ≥0} (hd : nndist x y ≤ d) :
     nndist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   by
@@ -431,23 +254,11 @@ theorem nndist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ≥0} (hd : nn
   rwa [edist_nndist, ENNReal.coe_le_coe]
 #align holder_with.nndist_le_of_le HolderWith.nndist_le_of_le
 
-/- warning: holder_with.nndist_le -> HolderWith.nndist_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align holder_with.nndist_le HolderWith.nndist_leₓ'. -/
 theorem nndist_le (hf : HolderWith C r f) (x y : X) :
     nndist (f x) (f y) ≤ C * nndist x y ^ (r : ℝ) :=
   hf.nndist_le_of_le le_rfl
 #align holder_with.nndist_le HolderWith.nndist_le
 
-/- warning: holder_with.dist_le_of_le -> HolderWith.dist_le_of_le is a dubious translation:
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-  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u2} X] [_inst_2 : PseudoMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y (PseudoMetricSpace.toPseudoEMetricSpace.{u2} X _inst_1) (PseudoMetricSpace.toPseudoEMetricSpace.{u1} Y _inst_2) C r f) -> (forall {x : X} {y : X} {d : Real}, (LE.le.{0} Real Real.instLEReal (Dist.dist.{u2} X (PseudoMetricSpace.toDist.{u2} X _inst_1) x y) d) -> (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} Y (PseudoMetricSpace.toDist.{u1} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (NNReal.toReal C) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) d (NNReal.toReal r)))))
-Case conversion may be inaccurate. Consider using '#align holder_with.dist_le_of_le HolderWith.dist_le_of_leₓ'. -/
 theorem dist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ} (hd : dist x y ≤ d) :
     dist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   by
@@ -457,12 +268,6 @@ theorem dist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ} (hd : dist x y
   exact hf.nndist_le_of_le hd
 #align holder_with.dist_le_of_le HolderWith.dist_le_of_le
 
-/- warning: holder_with.dist_le -> HolderWith.dist_le is a dubious translation:
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-  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u2} X] [_inst_2 : PseudoMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y (PseudoMetricSpace.toPseudoEMetricSpace.{u2} X _inst_1) (PseudoMetricSpace.toPseudoEMetricSpace.{u1} Y _inst_2) C r f) -> (forall (x : X) (y : X), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} Y (PseudoMetricSpace.toDist.{u1} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (NNReal.toReal C) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Dist.dist.{u2} X (PseudoMetricSpace.toDist.{u2} X _inst_1) x y) (NNReal.toReal r))))
-Case conversion may be inaccurate. Consider using '#align holder_with.dist_le HolderWith.dist_leₓ'. -/
 theorem dist_le (hf : HolderWith C r f) (x y : X) : dist (f x) (f y) ≤ C * dist x y ^ (r : ℝ) :=
   hf.dist_le_of_le le_rfl
 #align holder_with.dist_le HolderWith.dist_le

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

@@ -85,11 +85,8 @@ but is expected to have type
   forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] (C : NNReal) (r : NNReal) (f : X -> Y) (x : X), HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f (Singleton.singleton.{u2, u2} X (Set.{u2} X) (Set.instSingletonSet.{u2} X) x)
 Case conversion may be inaccurate. Consider using '#align holder_on_with_singleton holderOnWith_singletonₓ'. -/
 @[simp]
-theorem holderOnWith_singleton (C r : ℝ≥0) (f : X → Y) (x : X) : HolderOnWith C r f {x} :=
-  by
-  rintro a (rfl : a = x) b (rfl : b = a)
-  rw [edist_self]
-  exact zero_le _
+theorem holderOnWith_singleton (C r : ℝ≥0) (f : X → Y) (x : X) : HolderOnWith C r f {x} := by
+  rintro a (rfl : a = x) b (rfl : b = a); rw [edist_self]; exact zero_le _
 #align holder_on_with_singleton holderOnWith_singleton
 
 /- warning: set.subsingleton.holder_on_with -> Set.Subsingleton.holderOnWith is a dubious translation:

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module topology.metric_space.holder
-! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.SpecialFunctions.Pow.Continuity
 /-!
 # Hölder continuous functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define Hölder continuity on a set and on the whole space. We also prove some basic
 properties of Hölder continuous functions.
 
@@ -194,10 +197,7 @@ theorem edist_le_of_le (h : HolderOnWith C r f s) {x y : X} (hx : x ∈ s) (hy :
 #align holder_on_with.edist_le_of_le HolderOnWith.edist_le_of_le
 
 /- warning: holder_on_with.comp -> HolderOnWith.comp is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} {Z : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] [_inst_3 : PseudoEMetricSpace.{u3} Z] {s : Set.{u1} X} {Cg : NNReal} {rg : NNReal} {g : Y -> Z} {t : Set.{u2} Y}, (HolderOnWith.{u2, u3} Y Z _inst_2 _inst_3 Cg rg g t) -> (forall {Cf : NNReal} {rf : NNReal} {f : X -> Y}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 Cf rf f s) -> (Set.MapsTo.{u1, u2} X Y f s t) -> (HolderOnWith.{u1, u3} X Z _inst_1 _inst_3 (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) Cg (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) Cf ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) rg))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) rg rf) (Function.comp.{succ u1, succ u2, succ u3} X Y Z g f) s))
-but is expected to have type
-  forall {X : Type.{u1}} {Y : Type.{u3}} {Z : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u3} Y] [_inst_3 : PseudoEMetricSpace.{u2} Z] {s : Set.{u1} X} {Cg : NNReal} {rg : NNReal} {g : Y -> Z} {t : Set.{u3} Y}, (HolderOnWith.{u3, u2} Y Z _inst_2 _inst_3 Cg rg g t) -> (forall {Cf : NNReal} {rf : NNReal} {f : X -> Y}, (HolderOnWith.{u1, u3} X Y _inst_1 _inst_2 Cf rf f s) -> (Set.MapsTo.{u1, u3} X Y f s t) -> (HolderOnWith.{u1, u2} X Z _inst_1 _inst_3 (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) Cg (NNReal.rpow Cf (NNReal.toReal rg))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) rg rf) (Function.comp.{succ u1, succ u3, succ u2} X Y Z g f) s))
+<too large>
 Case conversion may be inaccurate. Consider using '#align holder_on_with.comp HolderOnWith.compₓ'. -/
 theorem comp {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : HolderOnWith Cg rg g t) {Cf rf : ℝ≥0}
     {f : X → Y} (hf : HolderOnWith Cf rf f s) (hst : MapsTo f s t) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c

@@ -48,23 +48,39 @@ section Emetric
 
 variable [PseudoEMetricSpace X] [PseudoEMetricSpace Y] [PseudoEMetricSpace Z]
 
+#print HolderWith /-
 /-- A function `f : X → Y` between two `pseudo_emetric_space`s is Hölder continuous with constant
 `C : ℝ≥0` and exponent `r : ℝ≥0`, if `edist (f x) (f y) ≤ C * edist x y ^ r` for all `x y : X`. -/
 def HolderWith (C r : ℝ≥0) (f : X → Y) : Prop :=
   ∀ x y, edist (f x) (f y) ≤ C * edist x y ^ (r : ℝ)
 #align holder_with HolderWith
+-/
 
+#print HolderOnWith /-
 /-- A function `f : X → Y` between two `pseudo_emeteric_space`s is Hölder continuous with constant
 `C : ℝ≥0` and exponent `r : ℝ≥0` on a set `s : set X`, if `edist (f x) (f y) ≤ C * edist x y ^ r`
 for all `x y ∈ s`. -/
 def HolderOnWith (C r : ℝ≥0) (f : X → Y) (s : Set X) : Prop :=
   ∀ x ∈ s, ∀ y ∈ s, edist (f x) (f y) ≤ C * edist x y ^ (r : ℝ)
 #align holder_on_with HolderOnWith
+-/
 
+/- warning: holder_on_with_empty -> holderOnWith_empty is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] (C : NNReal) (r : NNReal) (f : X -> Y), HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f (EmptyCollection.emptyCollection.{u1} (Set.{u1} X) (Set.hasEmptyc.{u1} X))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] (C : NNReal) (r : NNReal) (f : X -> Y), HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f (EmptyCollection.emptyCollection.{u2} (Set.{u2} X) (Set.instEmptyCollectionSet.{u2} X))
+Case conversion may be inaccurate. Consider using '#align holder_on_with_empty holderOnWith_emptyₓ'. -/
 @[simp]
 theorem holderOnWith_empty (C r : ℝ≥0) (f : X → Y) : HolderOnWith C r f ∅ := fun x hx => hx.elim
 #align holder_on_with_empty holderOnWith_empty
 
+/- warning: holder_on_with_singleton -> holderOnWith_singleton is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] (C : NNReal) (r : NNReal) (f : X -> Y) (x : X), HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f (Singleton.singleton.{u1, u1} X (Set.{u1} X) (Set.hasSingleton.{u1} X) x)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] (C : NNReal) (r : NNReal) (f : X -> Y) (x : X), HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f (Singleton.singleton.{u2, u2} X (Set.{u2} X) (Set.instSingletonSet.{u2} X) x)
+Case conversion may be inaccurate. Consider using '#align holder_on_with_singleton holderOnWith_singletonₓ'. -/
 @[simp]
 theorem holderOnWith_singleton (C r : ℝ≥0) (f : X → Y) (x : X) : HolderOnWith C r f {x} :=
   by
@@ -73,36 +89,80 @@ theorem holderOnWith_singleton (C r : ℝ≥0) (f : X → Y) (x : X) : HolderOnW
   exact zero_le _
 #align holder_on_with_singleton holderOnWith_singleton
 
+/- warning: set.subsingleton.holder_on_with -> Set.Subsingleton.holderOnWith is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {s : Set.{u1} X}, (Set.Subsingleton.{u1} X s) -> (forall (C : NNReal) (r : NNReal) (f : X -> Y), HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {s : Set.{u2} X}, (Set.Subsingleton.{u2} X s) -> (forall (C : NNReal) (r : NNReal) (f : X -> Y), HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s)
+Case conversion may be inaccurate. Consider using '#align set.subsingleton.holder_on_with Set.Subsingleton.holderOnWithₓ'. -/
 theorem Set.Subsingleton.holderOnWith {s : Set X} (hs : s.Subsingleton) (C r : ℝ≥0) (f : X → Y) :
     HolderOnWith C r f s :=
   hs.inductionOn (holderOnWith_empty C r f) (holderOnWith_singleton C r f)
 #align set.subsingleton.holder_on_with Set.Subsingleton.holderOnWith
 
+/- warning: holder_on_with_univ -> holderOnWith_univ is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, Iff (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f (Set.univ.{u1} X)) (HolderWith.{u1, u2} X Y _inst_1 _inst_2 C r f)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, Iff (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f (Set.univ.{u2} X)) (HolderWith.{u2, u1} X Y _inst_1 _inst_2 C r f)
+Case conversion may be inaccurate. Consider using '#align holder_on_with_univ holderOnWith_univₓ'. -/
 theorem holderOnWith_univ {C r : ℝ≥0} {f : X → Y} : HolderOnWith C r f univ ↔ HolderWith C r f := by
   simp only [HolderOnWith, HolderWith, mem_univ, true_imp_iff]
 #align holder_on_with_univ holderOnWith_univ
 
+/- warning: holder_on_with_one -> holderOnWith_one is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {f : X -> Y} {s : Set.{u1} X}, Iff (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) f s) (LipschitzOnWith.{u1, u2} X Y _inst_1 _inst_2 C f s)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {f : X -> Y} {s : Set.{u2} X}, Iff (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) f s) (LipschitzOnWith.{u2, u1} X Y _inst_1 _inst_2 C f s)
+Case conversion may be inaccurate. Consider using '#align holder_on_with_one holderOnWith_oneₓ'. -/
 @[simp]
 theorem holderOnWith_one {C : ℝ≥0} {f : X → Y} {s : Set X} :
     HolderOnWith C 1 f s ↔ LipschitzOnWith C f s := by
   simp only [HolderOnWith, LipschitzOnWith, NNReal.coe_one, ENNReal.rpow_one]
 #align holder_on_with_one holderOnWith_one
 
+/- warning: lipschitz_on_with.holder_on_with -> LipschitzOnWith.holderOnWith is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {f : X -> Y} {s : Set.{u1} X}, (LipschitzOnWith.{u1, u2} X Y _inst_1 _inst_2 C f s) -> (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) f s)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {f : X -> Y} {s : Set.{u2} X}, (LipschitzOnWith.{u2, u1} X Y _inst_1 _inst_2 C f s) -> (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) f s)
+Case conversion may be inaccurate. Consider using '#align lipschitz_on_with.holder_on_with LipschitzOnWith.holderOnWithₓ'. -/
 alias holderOnWith_one ↔ _ LipschitzOnWith.holderOnWith
 #align lipschitz_on_with.holder_on_with LipschitzOnWith.holderOnWith
 
+/- warning: holder_with_one -> holderWith_one is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {f : X -> Y}, Iff (HolderWith.{u1, u2} X Y _inst_1 _inst_2 C (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) f) (LipschitzWith.{u1, u2} X Y _inst_1 _inst_2 C f)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {f : X -> Y}, Iff (HolderWith.{u2, u1} X Y _inst_1 _inst_2 C (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) f) (LipschitzWith.{u2, u1} X Y _inst_1 _inst_2 C f)
+Case conversion may be inaccurate. Consider using '#align holder_with_one holderWith_oneₓ'. -/
 @[simp]
 theorem holderWith_one {C : ℝ≥0} {f : X → Y} : HolderWith C 1 f ↔ LipschitzWith C f :=
   holderOnWith_univ.symm.trans <| holderOnWith_one.trans lipschitz_on_univ
 #align holder_with_one holderWith_one
 
+/- warning: lipschitz_with.holder_with -> LipschitzWith.holderWith is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {f : X -> Y}, (LipschitzWith.{u1, u2} X Y _inst_1 _inst_2 C f) -> (HolderWith.{u1, u2} X Y _inst_1 _inst_2 C (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) f)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {f : X -> Y}, (LipschitzWith.{u2, u1} X Y _inst_1 _inst_2 C f) -> (HolderWith.{u2, u1} X Y _inst_1 _inst_2 C (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) f)
+Case conversion may be inaccurate. Consider using '#align lipschitz_with.holder_with LipschitzWith.holderWithₓ'. -/
 alias holderWith_one ↔ _ LipschitzWith.holderWith
 #align lipschitz_with.holder_with LipschitzWith.holderWith
 
+#print holderWith_id /-
 theorem holderWith_id : HolderWith 1 1 (id : X → X) :=
   LipschitzWith.id.HolderWith
 #align holder_with_id holderWith_id
+-/
 
+/- warning: holder_with.holder_on_with -> HolderWith.holderOnWith is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u1, u2} X Y _inst_1 _inst_2 C r f) -> (forall (s : Set.{u1} X), HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y _inst_1 _inst_2 C r f) -> (forall (s : Set.{u2} X), HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s)
+Case conversion may be inaccurate. Consider using '#align holder_with.holder_on_with HolderWith.holderOnWithₓ'. -/
 protected theorem HolderWith.holderOnWith {C r : ℝ≥0} {f : X → Y} (h : HolderWith C r f)
     (s : Set X) : HolderOnWith C r f s := fun x _ y _ => h x y
 #align holder_with.holder_on_with HolderWith.holderOnWith
@@ -111,16 +171,34 @@ namespace HolderOnWith
 
 variable {C r : ℝ≥0} {f : X → Y} {s t : Set X}
 
+/- warning: holder_on_with.edist_le -> HolderOnWith.edist_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u1} X}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s) -> (forall {x : X} {y : X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) -> (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) y s) -> (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))))) (EDist.edist.{u2} Y (PseudoEMetricSpace.toHasEdist.{u2} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (EDist.edist.{u1} X (PseudoEMetricSpace.toHasEdist.{u1} X _inst_1) x y) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r)))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u2} X}, (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s) -> (forall {x : X} {y : X}, (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x s) -> (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) y s) -> (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))))) (EDist.edist.{u1} Y (PseudoEMetricSpace.toEDist.{u1} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (EDist.edist.{u2} X (PseudoEMetricSpace.toEDist.{u2} X _inst_1) x y) (NNReal.toReal r)))))
+Case conversion may be inaccurate. Consider using '#align holder_on_with.edist_le HolderOnWith.edist_leₓ'. -/
 theorem edist_le (h : HolderOnWith C r f s) {x y : X} (hx : x ∈ s) (hy : y ∈ s) :
     edist (f x) (f y) ≤ C * edist x y ^ (r : ℝ) :=
   h x hx y hy
 #align holder_on_with.edist_le HolderOnWith.edist_le
 
+/- warning: holder_on_with.edist_le_of_le -> HolderOnWith.edist_le_of_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u1} X}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s) -> (forall {x : X} {y : X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) -> (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) y s) -> (forall {d : ENNReal}, (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))))) (EDist.edist.{u1} X (PseudoEMetricSpace.toHasEdist.{u1} X _inst_1) x y) d) -> (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))))) (EDist.edist.{u2} Y (PseudoEMetricSpace.toHasEdist.{u2} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) d ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r))))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u2} X}, (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s) -> (forall {x : X} {y : X}, (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x s) -> (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) y s) -> (forall {d : ENNReal}, (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))))) (EDist.edist.{u2} X (PseudoEMetricSpace.toEDist.{u2} X _inst_1) x y) d) -> (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))))) (EDist.edist.{u1} Y (PseudoEMetricSpace.toEDist.{u1} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) d (NNReal.toReal r))))))
+Case conversion may be inaccurate. Consider using '#align holder_on_with.edist_le_of_le HolderOnWith.edist_le_of_leₓ'. -/
 theorem edist_le_of_le (h : HolderOnWith C r f s) {x y : X} (hx : x ∈ s) (hy : y ∈ s) {d : ℝ≥0∞}
     (hd : edist x y ≤ d) : edist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   (h.edist_le hx hy).trans (mul_le_mul_left' (ENNReal.rpow_le_rpow hd r.coe_nonneg) _)
 #align holder_on_with.edist_le_of_le HolderOnWith.edist_le_of_le
 
+/- warning: holder_on_with.comp -> HolderOnWith.comp is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} {Z : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] [_inst_3 : PseudoEMetricSpace.{u3} Z] {s : Set.{u1} X} {Cg : NNReal} {rg : NNReal} {g : Y -> Z} {t : Set.{u2} Y}, (HolderOnWith.{u2, u3} Y Z _inst_2 _inst_3 Cg rg g t) -> (forall {Cf : NNReal} {rf : NNReal} {f : X -> Y}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 Cf rf f s) -> (Set.MapsTo.{u1, u2} X Y f s t) -> (HolderOnWith.{u1, u3} X Z _inst_1 _inst_3 (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) Cg (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) Cf ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) rg))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) rg rf) (Function.comp.{succ u1, succ u2, succ u3} X Y Z g f) s))
+but is expected to have type
+  forall {X : Type.{u1}} {Y : Type.{u3}} {Z : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u3} Y] [_inst_3 : PseudoEMetricSpace.{u2} Z] {s : Set.{u1} X} {Cg : NNReal} {rg : NNReal} {g : Y -> Z} {t : Set.{u3} Y}, (HolderOnWith.{u3, u2} Y Z _inst_2 _inst_3 Cg rg g t) -> (forall {Cf : NNReal} {rf : NNReal} {f : X -> Y}, (HolderOnWith.{u1, u3} X Y _inst_1 _inst_2 Cf rf f s) -> (Set.MapsTo.{u1, u3} X Y f s t) -> (HolderOnWith.{u1, u2} X Z _inst_1 _inst_3 (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) Cg (NNReal.rpow Cf (NNReal.toReal rg))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) rg rf) (Function.comp.{succ u1, succ u3, succ u2} X Y Z g f) s))
+Case conversion may be inaccurate. Consider using '#align holder_on_with.comp HolderOnWith.compₓ'. -/
 theorem comp {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : HolderOnWith Cg rg g t) {Cf rf : ℝ≥0}
     {f : X → Y} (hf : HolderOnWith Cf rf f s) (hst : MapsTo f s t) :
     HolderOnWith (Cg * Cf ^ (rg : ℝ)) (rg * rf) (g ∘ f) s :=
@@ -131,12 +209,24 @@ theorem comp {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : HolderOnWith Cg r
   exact hg.edist_le_of_le (hst hx) (hst hy) (hf.edist_le hx hy)
 #align holder_on_with.comp HolderOnWith.comp
 
+/- warning: holder_on_with.comp_holder_with -> HolderOnWith.comp_holderWith is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} {Z : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] [_inst_3 : PseudoEMetricSpace.{u3} Z] {Cg : NNReal} {rg : NNReal} {g : Y -> Z} {t : Set.{u2} Y}, (HolderOnWith.{u2, u3} Y Z _inst_2 _inst_3 Cg rg g t) -> (forall {Cf : NNReal} {rf : NNReal} {f : X -> Y}, (HolderWith.{u1, u2} X Y _inst_1 _inst_2 Cf rf f) -> (forall (x : X), Membership.Mem.{u2, u2} Y (Set.{u2} Y) (Set.hasMem.{u2} Y) (f x) t) -> (HolderWith.{u1, u3} X Z _inst_1 _inst_3 (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) Cg (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) Cf ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) rg))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) rg rf) (Function.comp.{succ u1, succ u2, succ u3} X Y Z g f)))
+but is expected to have type
+  forall {X : Type.{u1}} {Y : Type.{u3}} {Z : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u3} Y] [_inst_3 : PseudoEMetricSpace.{u2} Z] {Cg : NNReal} {rg : NNReal} {g : Y -> Z} {t : Set.{u3} Y}, (HolderOnWith.{u3, u2} Y Z _inst_2 _inst_3 Cg rg g t) -> (forall {Cf : NNReal} {rf : NNReal} {f : X -> Y}, (HolderWith.{u1, u3} X Y _inst_1 _inst_2 Cf rf f) -> (forall (x : X), Membership.mem.{u3, u3} Y (Set.{u3} Y) (Set.instMembershipSet.{u3} Y) (f x) t) -> (HolderWith.{u1, u2} X Z _inst_1 _inst_3 (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) Cg (NNReal.rpow Cf (NNReal.toReal rg))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) rg rf) (Function.comp.{succ u1, succ u3, succ u2} X Y Z g f)))
+Case conversion may be inaccurate. Consider using '#align holder_on_with.comp_holder_with HolderOnWith.comp_holderWithₓ'. -/
 theorem comp_holderWith {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : HolderOnWith Cg rg g t)
     {Cf rf : ℝ≥0} {f : X → Y} (hf : HolderWith Cf rf f) (ht : ∀ x, f x ∈ t) :
     HolderWith (Cg * Cf ^ (rg : ℝ)) (rg * rf) (g ∘ f) :=
   holderOnWith_univ.mp <| hg.comp (hf.HolderOnWith univ) fun x _ => ht x
 #align holder_on_with.comp_holder_with HolderOnWith.comp_holderWith
 
+/- warning: holder_on_with.uniform_continuous_on -> HolderOnWith.uniformContinuousOn is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u1} X}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s) -> (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r) -> (UniformContinuousOn.{u1, u2} X Y (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} Y _inst_2) f s)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u2} X}, (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) r) -> (UniformContinuousOn.{u2, u1} X Y (PseudoEMetricSpace.toUniformSpace.{u2} X _inst_1) (PseudoEMetricSpace.toUniformSpace.{u1} Y _inst_2) f s)
+Case conversion may be inaccurate. Consider using '#align holder_on_with.uniform_continuous_on HolderOnWith.uniformContinuousOnₓ'. -/
 /-- A Hölder continuous function is uniformly continuous -/
 protected theorem uniformContinuousOn (hf : HolderOnWith C r f s) (h0 : 0 < r) :
     UniformContinuousOn f s :=
@@ -148,41 +238,89 @@ protected theorem uniformContinuousOn (hf : HolderOnWith C r f s) (h0 : 0 < r) :
   exact ⟨δ, δ0, fun x hx y hy h => (hf.edist_le hx hy).trans_lt (H h)⟩
 #align holder_on_with.uniform_continuous_on HolderOnWith.uniformContinuousOn
 
+/- warning: holder_on_with.continuous_on -> HolderOnWith.continuousOn is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u1} X}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s) -> (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r) -> (ContinuousOn.{u1, u2} X Y (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) (UniformSpace.toTopologicalSpace.{u2} Y (PseudoEMetricSpace.toUniformSpace.{u2} Y _inst_2)) f s)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u2} X}, (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) r) -> (ContinuousOn.{u2, u1} X Y (UniformSpace.toTopologicalSpace.{u2} X (PseudoEMetricSpace.toUniformSpace.{u2} X _inst_1)) (UniformSpace.toTopologicalSpace.{u1} Y (PseudoEMetricSpace.toUniformSpace.{u1} Y _inst_2)) f s)
+Case conversion may be inaccurate. Consider using '#align holder_on_with.continuous_on HolderOnWith.continuousOnₓ'. -/
 protected theorem continuousOn (hf : HolderOnWith C r f s) (h0 : 0 < r) : ContinuousOn f s :=
   (hf.UniformContinuousOn h0).ContinuousOn
 #align holder_on_with.continuous_on HolderOnWith.continuousOn
 
+/- warning: holder_on_with.mono -> HolderOnWith.mono is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u1} X} {t : Set.{u1} X}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s) -> (HasSubset.Subset.{u1} (Set.{u1} X) (Set.hasSubset.{u1} X) t s) -> (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f t)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u2} X} {t : Set.{u2} X}, (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) t s) -> (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f t)
+Case conversion may be inaccurate. Consider using '#align holder_on_with.mono HolderOnWith.monoₓ'. -/
 protected theorem mono (hf : HolderOnWith C r f s) (ht : t ⊆ s) : HolderOnWith C r f t :=
   fun x hx y hy => hf.edist_le (ht hx) (ht hy)
 #align holder_on_with.mono HolderOnWith.mono
 
+/- warning: holder_on_with.ediam_image_le_of_le -> HolderOnWith.ediam_image_le_of_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u1} X}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s) -> (forall {d : ENNReal}, (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.{u1} X _inst_1 s) d) -> (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} Y _inst_2 (Set.image.{u1, u2} X Y f s)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) d ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r)))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u2} X}, (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s) -> (forall {d : ENNReal}, (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} X _inst_1 s) d) -> (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.{u1} Y _inst_2 (Set.image.{u2, u1} X Y f s)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) d (NNReal.toReal r)))))
+Case conversion may be inaccurate. Consider using '#align holder_on_with.ediam_image_le_of_le HolderOnWith.ediam_image_le_of_leₓ'. -/
 theorem ediam_image_le_of_le (hf : HolderOnWith C r f s) {d : ℝ≥0∞} (hd : EMetric.diam s ≤ d) :
     EMetric.diam (f '' s) ≤ C * d ^ (r : ℝ) :=
   EMetric.diam_image_le_iff.2 fun x hx y hy =>
     hf.edist_le_of_le hx hy <| (EMetric.edist_le_diam_of_mem hx hy).trans hd
 #align holder_on_with.ediam_image_le_of_le HolderOnWith.ediam_image_le_of_le
 
+/- warning: holder_on_with.ediam_image_le -> HolderOnWith.ediam_image_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u1} X}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s) -> (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} Y _inst_2 (Set.image.{u1, u2} X Y f s)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (EMetric.diam.{u1} X _inst_1 s) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u2} X}, (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s) -> (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.{u1} Y _inst_2 (Set.image.{u2, u1} X Y f s)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (EMetric.diam.{u2} X _inst_1 s) (NNReal.toReal r))))
+Case conversion may be inaccurate. Consider using '#align holder_on_with.ediam_image_le HolderOnWith.ediam_image_leₓ'. -/
 theorem ediam_image_le (hf : HolderOnWith C r f s) :
     EMetric.diam (f '' s) ≤ C * EMetric.diam s ^ (r : ℝ) :=
   hf.ediam_image_le_of_le le_rfl
 #align holder_on_with.ediam_image_le HolderOnWith.ediam_image_le
 
+/- warning: holder_on_with.ediam_image_le_of_subset -> HolderOnWith.ediam_image_le_of_subset is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u1} X} {t : Set.{u1} X}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s) -> (HasSubset.Subset.{u1} (Set.{u1} X) (Set.hasSubset.{u1} X) t s) -> (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} Y _inst_2 (Set.image.{u1, u2} X Y f t)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (EMetric.diam.{u1} X _inst_1 t) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u2} X} {t : Set.{u2} X}, (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) t s) -> (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.{u1} Y _inst_2 (Set.image.{u2, u1} X Y f t)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (EMetric.diam.{u2} X _inst_1 t) (NNReal.toReal r))))
+Case conversion may be inaccurate. Consider using '#align holder_on_with.ediam_image_le_of_subset HolderOnWith.ediam_image_le_of_subsetₓ'. -/
 theorem ediam_image_le_of_subset (hf : HolderOnWith C r f s) (ht : t ⊆ s) :
     EMetric.diam (f '' t) ≤ C * EMetric.diam t ^ (r : ℝ) :=
   (hf.mono ht).ediam_image_le
 #align holder_on_with.ediam_image_le_of_subset HolderOnWith.ediam_image_le_of_subset
 
+/- warning: holder_on_with.ediam_image_le_of_subset_of_le -> HolderOnWith.ediam_image_le_of_subset_of_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u1} X} {t : Set.{u1} X}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s) -> (HasSubset.Subset.{u1} (Set.{u1} X) (Set.hasSubset.{u1} X) t s) -> (forall {d : ENNReal}, (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.{u1} X _inst_1 t) d) -> (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} Y _inst_2 (Set.image.{u1, u2} X Y f t)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) d ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r)))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u2} X} {t : Set.{u2} X}, (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) t s) -> (forall {d : ENNReal}, (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} X _inst_1 t) d) -> (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.{u1} Y _inst_2 (Set.image.{u2, u1} X Y f t)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) d (NNReal.toReal r)))))
+Case conversion may be inaccurate. Consider using '#align holder_on_with.ediam_image_le_of_subset_of_le HolderOnWith.ediam_image_le_of_subset_of_leₓ'. -/
 theorem ediam_image_le_of_subset_of_le (hf : HolderOnWith C r f s) (ht : t ⊆ s) {d : ℝ≥0∞}
     (hd : EMetric.diam t ≤ d) : EMetric.diam (f '' t) ≤ C * d ^ (r : ℝ) :=
   (hf.mono ht).ediam_image_le_of_le hd
 #align holder_on_with.ediam_image_le_of_subset_of_le HolderOnWith.ediam_image_le_of_subset_of_le
 
+/- warning: holder_on_with.ediam_image_inter_le_of_le -> HolderOnWith.ediam_image_inter_le_of_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u1} X} {t : Set.{u1} X}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s) -> (forall {d : ENNReal}, (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.{u1} X _inst_1 t) d) -> (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} Y _inst_2 (Set.image.{u1, u2} X Y f (Inter.inter.{u1} (Set.{u1} X) (Set.hasInter.{u1} X) t s))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) d ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r)))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u2} X} {t : Set.{u2} X}, (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s) -> (forall {d : ENNReal}, (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} X _inst_1 t) d) -> (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.{u1} Y _inst_2 (Set.image.{u2, u1} X Y f (Inter.inter.{u2} (Set.{u2} X) (Set.instInterSet.{u2} X) t s))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) d (NNReal.toReal r)))))
+Case conversion may be inaccurate. Consider using '#align holder_on_with.ediam_image_inter_le_of_le HolderOnWith.ediam_image_inter_le_of_leₓ'. -/
 theorem ediam_image_inter_le_of_le (hf : HolderOnWith C r f s) {d : ℝ≥0∞}
     (hd : EMetric.diam t ≤ d) : EMetric.diam (f '' (t ∩ s)) ≤ C * d ^ (r : ℝ) :=
   hf.ediam_image_le_of_subset_of_le (inter_subset_right _ _) <|
     (EMetric.diam_mono <| inter_subset_left _ _).trans hd
 #align holder_on_with.ediam_image_inter_le_of_le HolderOnWith.ediam_image_inter_le_of_le
 
+/- warning: holder_on_with.ediam_image_inter_le -> HolderOnWith.ediam_image_inter_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u1} X}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 C r f s) -> (forall (t : Set.{u1} X), 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} Y _inst_2 (Set.image.{u1, u2} X Y f (Inter.inter.{u1} (Set.{u1} X) (Set.hasInter.{u1} X) t s))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (EMetric.diam.{u1} X _inst_1 t) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y} {s : Set.{u2} X}, (HolderOnWith.{u2, u1} X Y _inst_1 _inst_2 C r f s) -> (forall (t : Set.{u2} X), 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.{u1} Y _inst_2 (Set.image.{u2, u1} X Y f (Inter.inter.{u2} (Set.{u2} X) (Set.instInterSet.{u2} X) t s))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (EMetric.diam.{u2} X _inst_1 t) (NNReal.toReal r))))
+Case conversion may be inaccurate. Consider using '#align holder_on_with.ediam_image_inter_le HolderOnWith.ediam_image_inter_leₓ'. -/
 theorem ediam_image_inter_le (hf : HolderOnWith C r f s) (t : Set X) :
     EMetric.diam (f '' (t ∩ s)) ≤ C * EMetric.diam t ^ (r : ℝ) :=
   hf.ediam_image_inter_le_of_le le_rfl
@@ -194,35 +332,77 @@ namespace HolderWith
 
 variable {C r : ℝ≥0} {f : X → Y}
 
+/- warning: holder_with.edist_le -> HolderWith.edist_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u1, u2} X Y _inst_1 _inst_2 C r f) -> (forall (x : X) (y : X), 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))))) (EDist.edist.{u2} Y (PseudoEMetricSpace.toHasEdist.{u2} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (EDist.edist.{u1} X (PseudoEMetricSpace.toHasEdist.{u1} X _inst_1) x y) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y _inst_1 _inst_2 C r f) -> (forall (x : X) (y : X), 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))))) (EDist.edist.{u1} Y (PseudoEMetricSpace.toEDist.{u1} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (EDist.edist.{u2} X (PseudoEMetricSpace.toEDist.{u2} X _inst_1) x y) (NNReal.toReal r))))
+Case conversion may be inaccurate. Consider using '#align holder_with.edist_le HolderWith.edist_leₓ'. -/
 theorem edist_le (h : HolderWith C r f) (x y : X) : edist (f x) (f y) ≤ C * edist x y ^ (r : ℝ) :=
   h x y
 #align holder_with.edist_le HolderWith.edist_le
 
+/- warning: holder_with.edist_le_of_le -> HolderWith.edist_le_of_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u1, u2} X Y _inst_1 _inst_2 C r f) -> (forall {x : X} {y : X} {d : ENNReal}, (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))))) (EDist.edist.{u1} X (PseudoEMetricSpace.toHasEdist.{u1} X _inst_1) x y) d) -> (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))))) (EDist.edist.{u2} Y (PseudoEMetricSpace.toHasEdist.{u2} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) d ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r)))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y _inst_1 _inst_2 C r f) -> (forall {x : X} {y : X} {d : ENNReal}, (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))))) (EDist.edist.{u2} X (PseudoEMetricSpace.toEDist.{u2} X _inst_1) x y) d) -> (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))))) (EDist.edist.{u1} Y (PseudoEMetricSpace.toEDist.{u1} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) d (NNReal.toReal r)))))
+Case conversion may be inaccurate. Consider using '#align holder_with.edist_le_of_le HolderWith.edist_le_of_leₓ'. -/
 theorem edist_le_of_le (h : HolderWith C r f) {x y : X} {d : ℝ≥0∞} (hd : edist x y ≤ d) :
     edist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   (h.HolderOnWith univ).edist_le_of_le trivial trivial hd
 #align holder_with.edist_le_of_le HolderWith.edist_le_of_le
 
+/- warning: holder_with.comp -> HolderWith.comp is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} {Z : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] [_inst_3 : PseudoEMetricSpace.{u3} Z] {Cg : NNReal} {rg : NNReal} {g : Y -> Z}, (HolderWith.{u2, u3} Y Z _inst_2 _inst_3 Cg rg g) -> (forall {Cf : NNReal} {rf : NNReal} {f : X -> Y}, (HolderWith.{u1, u2} X Y _inst_1 _inst_2 Cf rf f) -> (HolderWith.{u1, u3} X Z _inst_1 _inst_3 (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) Cg (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) Cf ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) rg))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) rg rf) (Function.comp.{succ u1, succ u2, succ u3} X Y Z g f)))
+but is expected to have type
+  forall {X : Type.{u1}} {Y : Type.{u3}} {Z : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u3} Y] [_inst_3 : PseudoEMetricSpace.{u2} Z] {Cg : NNReal} {rg : NNReal} {g : Y -> Z}, (HolderWith.{u3, u2} Y Z _inst_2 _inst_3 Cg rg g) -> (forall {Cf : NNReal} {rf : NNReal} {f : X -> Y}, (HolderWith.{u1, u3} X Y _inst_1 _inst_2 Cf rf f) -> (HolderWith.{u1, u2} X Z _inst_1 _inst_3 (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) Cg (NNReal.rpow Cf (NNReal.toReal rg))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) rg rf) (Function.comp.{succ u1, succ u3, succ u2} X Y Z g f)))
+Case conversion may be inaccurate. Consider using '#align holder_with.comp HolderWith.compₓ'. -/
 theorem comp {Cg rg : ℝ≥0} {g : Y → Z} (hg : HolderWith Cg rg g) {Cf rf : ℝ≥0} {f : X → Y}
     (hf : HolderWith Cf rf f) : HolderWith (Cg * Cf ^ (rg : ℝ)) (rg * rf) (g ∘ f) :=
   (hg.HolderOnWith univ).comp_holderWith hf fun _ => trivial
 #align holder_with.comp HolderWith.comp
 
+/- warning: holder_with.comp_holder_on_with -> HolderWith.comp_holderOnWith is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} {Z : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] [_inst_3 : PseudoEMetricSpace.{u3} Z] {Cg : NNReal} {rg : NNReal} {g : Y -> Z}, (HolderWith.{u2, u3} Y Z _inst_2 _inst_3 Cg rg g) -> (forall {Cf : NNReal} {rf : NNReal} {f : X -> Y} {s : Set.{u1} X}, (HolderOnWith.{u1, u2} X Y _inst_1 _inst_2 Cf rf f s) -> (HolderOnWith.{u1, u3} X Z _inst_1 _inst_3 (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) Cg (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) Cf ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) rg))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) rg rf) (Function.comp.{succ u1, succ u2, succ u3} X Y Z g f) s))
+but is expected to have type
+  forall {X : Type.{u1}} {Y : Type.{u3}} {Z : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u3} Y] [_inst_3 : PseudoEMetricSpace.{u2} Z] {Cg : NNReal} {rg : NNReal} {g : Y -> Z}, (HolderWith.{u3, u2} Y Z _inst_2 _inst_3 Cg rg g) -> (forall {Cf : NNReal} {rf : NNReal} {f : X -> Y} {s : Set.{u1} X}, (HolderOnWith.{u1, u3} X Y _inst_1 _inst_2 Cf rf f s) -> (HolderOnWith.{u1, u2} X Z _inst_1 _inst_3 (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) Cg (NNReal.rpow Cf (NNReal.toReal rg))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) rg rf) (Function.comp.{succ u1, succ u3, succ u2} X Y Z g f) s))
+Case conversion may be inaccurate. Consider using '#align holder_with.comp_holder_on_with HolderWith.comp_holderOnWithₓ'. -/
 theorem comp_holderOnWith {Cg rg : ℝ≥0} {g : Y → Z} (hg : HolderWith Cg rg g) {Cf rf : ℝ≥0}
     {f : X → Y} {s : Set X} (hf : HolderOnWith Cf rf f s) :
     HolderOnWith (Cg * Cf ^ (rg : ℝ)) (rg * rf) (g ∘ f) s :=
   (hg.HolderOnWith univ).comp hf fun _ _ => trivial
 #align holder_with.comp_holder_on_with HolderWith.comp_holderOnWith
 
+/- warning: holder_with.uniform_continuous -> HolderWith.uniformContinuous is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u1, u2} X Y _inst_1 _inst_2 C r f) -> (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r) -> (UniformContinuous.{u1, u2} X Y (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} Y _inst_2) f)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y _inst_1 _inst_2 C r f) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) r) -> (UniformContinuous.{u2, u1} X Y (PseudoEMetricSpace.toUniformSpace.{u2} X _inst_1) (PseudoEMetricSpace.toUniformSpace.{u1} Y _inst_2) f)
+Case conversion may be inaccurate. Consider using '#align holder_with.uniform_continuous HolderWith.uniformContinuousₓ'. -/
 /-- A Hölder continuous function is uniformly continuous -/
 protected theorem uniformContinuous (hf : HolderWith C r f) (h0 : 0 < r) : UniformContinuous f :=
   uniformContinuousOn_univ.mp <| (hf.HolderOnWith univ).UniformContinuousOn h0
 #align holder_with.uniform_continuous HolderWith.uniformContinuous
 
+/- warning: holder_with.continuous -> HolderWith.continuous is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u1, u2} X Y _inst_1 _inst_2 C r f) -> (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r) -> (Continuous.{u1, u2} X Y (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) (UniformSpace.toTopologicalSpace.{u2} Y (PseudoEMetricSpace.toUniformSpace.{u2} Y _inst_2)) f)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y _inst_1 _inst_2 C r f) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) r) -> (Continuous.{u2, u1} X Y (UniformSpace.toTopologicalSpace.{u2} X (PseudoEMetricSpace.toUniformSpace.{u2} X _inst_1)) (UniformSpace.toTopologicalSpace.{u1} Y (PseudoEMetricSpace.toUniformSpace.{u1} Y _inst_2)) f)
+Case conversion may be inaccurate. Consider using '#align holder_with.continuous HolderWith.continuousₓ'. -/
 protected theorem continuous (hf : HolderWith C r f) (h0 : 0 < r) : Continuous f :=
   (hf.UniformContinuous h0).Continuous
 #align holder_with.continuous HolderWith.continuous
 
+/- warning: holder_with.ediam_image_le -> HolderWith.ediam_image_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} X] [_inst_2 : PseudoEMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u1, u2} X Y _inst_1 _inst_2 C r f) -> (forall (s : Set.{u1} X), 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} Y _inst_2 (Set.image.{u1, u2} X Y f s)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (EMetric.diam.{u1} X _inst_1 s) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u2} X] [_inst_2 : PseudoEMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y _inst_1 _inst_2 C r f) -> (forall (s : Set.{u2} X), 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.{u1} Y _inst_2 (Set.image.{u2, u1} X Y f s)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (EMetric.diam.{u2} X _inst_1 s) (NNReal.toReal r))))
+Case conversion may be inaccurate. Consider using '#align holder_with.ediam_image_le HolderWith.ediam_image_leₓ'. -/
 theorem ediam_image_le (hf : HolderWith C r f) (s : Set X) :
     EMetric.diam (f '' s) ≤ C * EMetric.diam s ^ (r : ℝ) :=
   EMetric.diam_image_le_iff.2 fun x hx y hy =>
@@ -239,6 +419,12 @@ variable [PseudoMetricSpace X] [PseudoMetricSpace Y] {C r : ℝ≥0} {f : X →
 
 namespace HolderWith
 
+/- warning: holder_with.nndist_le_of_le -> HolderWith.nndist_le_of_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} X] [_inst_2 : PseudoMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u1, u2} X Y (PseudoMetricSpace.toPseudoEMetricSpace.{u1} X _inst_1) (PseudoMetricSpace.toPseudoEMetricSpace.{u2} Y _inst_2) C r f) -> (forall {x : X} {y : X} {d : NNReal}, (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNDist.nndist.{u1} X (PseudoMetricSpace.toNNDist.{u1} X _inst_1) x y) d) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNDist.nndist.{u2} Y (PseudoMetricSpace.toNNDist.{u2} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) C (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) d ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r)))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u2} X] [_inst_2 : PseudoMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y (PseudoMetricSpace.toPseudoEMetricSpace.{u2} X _inst_1) (PseudoMetricSpace.toPseudoEMetricSpace.{u1} Y _inst_2) C r f) -> (forall {x : X} {y : X} {d : NNReal}, (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNDist.nndist.{u2} X (PseudoMetricSpace.toNNDist.{u2} X _inst_1) x y) d) -> (LE.le.{0} Real Real.instLEReal (NNReal.toReal (NNDist.nndist.{u1} Y (PseudoMetricSpace.toNNDist.{u1} Y _inst_2) (f x) (f y))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (NNReal.toReal C) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (NNReal.toReal d) (NNReal.toReal r)))))
+Case conversion may be inaccurate. Consider using '#align holder_with.nndist_le_of_le HolderWith.nndist_le_of_leₓ'. -/
 theorem nndist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ≥0} (hd : nndist x y ≤ d) :
     nndist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   by
@@ -248,11 +434,23 @@ theorem nndist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ≥0} (hd : nn
   rwa [edist_nndist, ENNReal.coe_le_coe]
 #align holder_with.nndist_le_of_le HolderWith.nndist_le_of_le
 
+/- warning: holder_with.nndist_le -> HolderWith.nndist_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} X] [_inst_2 : PseudoMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u1, u2} X Y (PseudoMetricSpace.toPseudoEMetricSpace.{u1} X _inst_1) (PseudoMetricSpace.toPseudoEMetricSpace.{u2} Y _inst_2) C r f) -> (forall (x : X) (y : X), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNDist.nndist.{u2} Y (PseudoMetricSpace.toNNDist.{u2} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) C (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (NNDist.nndist.{u1} X (PseudoMetricSpace.toNNDist.{u1} X _inst_1) x y) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u2} X] [_inst_2 : PseudoMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y (PseudoMetricSpace.toPseudoEMetricSpace.{u2} X _inst_1) (PseudoMetricSpace.toPseudoEMetricSpace.{u1} Y _inst_2) C r f) -> (forall (x : X) (y : X), LE.le.{0} Real Real.instLEReal (NNReal.toReal (NNDist.nndist.{u1} Y (PseudoMetricSpace.toNNDist.{u1} Y _inst_2) (f x) (f y))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (NNReal.toReal C) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (NNReal.toReal (NNDist.nndist.{u2} X (PseudoMetricSpace.toNNDist.{u2} X _inst_1) x y)) (NNReal.toReal r))))
+Case conversion may be inaccurate. Consider using '#align holder_with.nndist_le HolderWith.nndist_leₓ'. -/
 theorem nndist_le (hf : HolderWith C r f) (x y : X) :
     nndist (f x) (f y) ≤ C * nndist x y ^ (r : ℝ) :=
   hf.nndist_le_of_le le_rfl
 #align holder_with.nndist_le HolderWith.nndist_le
 
+/- warning: holder_with.dist_le_of_le -> HolderWith.dist_le_of_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} X] [_inst_2 : PseudoMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u1, u2} X Y (PseudoMetricSpace.toPseudoEMetricSpace.{u1} X _inst_1) (PseudoMetricSpace.toPseudoEMetricSpace.{u2} Y _inst_2) C r f) -> (forall {x : X} {y : X} {d : Real}, (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} X (PseudoMetricSpace.toHasDist.{u1} X _inst_1) x y) d) -> (LE.le.{0} Real Real.hasLe (Dist.dist.{u2} Y (PseudoMetricSpace.toHasDist.{u2} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) C) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) d ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r)))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u2} X] [_inst_2 : PseudoMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y (PseudoMetricSpace.toPseudoEMetricSpace.{u2} X _inst_1) (PseudoMetricSpace.toPseudoEMetricSpace.{u1} Y _inst_2) C r f) -> (forall {x : X} {y : X} {d : Real}, (LE.le.{0} Real Real.instLEReal (Dist.dist.{u2} X (PseudoMetricSpace.toDist.{u2} X _inst_1) x y) d) -> (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} Y (PseudoMetricSpace.toDist.{u1} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (NNReal.toReal C) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) d (NNReal.toReal r)))))
+Case conversion may be inaccurate. Consider using '#align holder_with.dist_le_of_le HolderWith.dist_le_of_leₓ'. -/
 theorem dist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ} (hd : dist x y ≤ d) :
     dist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   by
@@ -262,6 +460,12 @@ theorem dist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ} (hd : dist x y
   exact hf.nndist_le_of_le hd
 #align holder_with.dist_le_of_le HolderWith.dist_le_of_le
 
+/- warning: holder_with.dist_le -> HolderWith.dist_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} X] [_inst_2 : PseudoMetricSpace.{u2} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u1, u2} X Y (PseudoMetricSpace.toPseudoEMetricSpace.{u1} X _inst_1) (PseudoMetricSpace.toPseudoEMetricSpace.{u2} Y _inst_2) C r f) -> (forall (x : X) (y : X), LE.le.{0} Real Real.hasLe (Dist.dist.{u2} Y (PseudoMetricSpace.toHasDist.{u2} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) C) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Dist.dist.{u1} X (PseudoMetricSpace.toHasDist.{u1} X _inst_1) x y) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) r))))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u2} X] [_inst_2 : PseudoMetricSpace.{u1} Y] {C : NNReal} {r : NNReal} {f : X -> Y}, (HolderWith.{u2, u1} X Y (PseudoMetricSpace.toPseudoEMetricSpace.{u2} X _inst_1) (PseudoMetricSpace.toPseudoEMetricSpace.{u1} Y _inst_2) C r f) -> (forall (x : X) (y : X), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} Y (PseudoMetricSpace.toDist.{u1} Y _inst_2) (f x) (f y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (NNReal.toReal C) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Dist.dist.{u2} X (PseudoMetricSpace.toDist.{u2} X _inst_1) x y) (NNReal.toReal r))))
+Case conversion may be inaccurate. Consider using '#align holder_with.dist_le HolderWith.dist_leₓ'. -/
 theorem dist_le (hf : HolderWith C r f) (x y : X) : dist (f x) (f y) ≤ C * dist x y ^ (r : ℝ) :=
   hf.dist_le_of_le le_rfl
 #align holder_with.dist_le HolderWith.dist_le

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

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module topology.metric_space.holder
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Topology.MetricSpace.Lipschitz
-import Mathbin.Analysis.SpecialFunctions.Pow
+import Mathbin.Analysis.SpecialFunctions.Pow.Continuity
 
 /-!
 # Hölder continuous functions

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -46,7 +46,7 @@ open NNReal ENNReal Topology
 
 section Emetric
 
-variable [PseudoEmetricSpace X] [PseudoEmetricSpace Y] [PseudoEmetricSpace Z]
+variable [PseudoEMetricSpace X] [PseudoEMetricSpace Y] [PseudoEMetricSpace Z]
 
 /-- A function `f : X → Y` between two `pseudo_emetric_space`s is Hölder continuous with constant
 `C : ℝ≥0` and exponent `r : ℝ≥0`, if `edist (f x) (f y) ≤ C * edist x y ^ r` for all `x y : X`. -/
@@ -141,7 +141,7 @@ theorem comp_holderWith {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : Holder
 protected theorem uniformContinuousOn (hf : HolderOnWith C r f s) (h0 : 0 < r) :
     UniformContinuousOn f s :=
   by
-  refine' Emetric.uniformContinuousOn_iff.2 fun ε εpos => _
+  refine' EMetric.uniformContinuousOn_iff.2 fun ε εpos => _
   have : tendsto (fun d : ℝ≥0∞ => (C : ℝ≥0∞) * d ^ (r : ℝ)) (𝓝 0) (𝓝 0) :=
     ENNReal.tendsto_const_mul_rpow_nhds_zero_of_pos ENNReal.coe_ne_top h0
   rcases ennreal.nhds_zero_basis.mem_iff.1 (this (gt_mem_nhds εpos)) with ⟨δ, δ0, H⟩
@@ -156,35 +156,35 @@ protected theorem mono (hf : HolderOnWith C r f s) (ht : t ⊆ s) : HolderOnWith
   fun x hx y hy => hf.edist_le (ht hx) (ht hy)
 #align holder_on_with.mono HolderOnWith.mono
 
-theorem ediam_image_le_of_le (hf : HolderOnWith C r f s) {d : ℝ≥0∞} (hd : Emetric.diam s ≤ d) :
-    Emetric.diam (f '' s) ≤ C * d ^ (r : ℝ) :=
-  Emetric.diam_image_le_iff.2 fun x hx y hy =>
-    hf.edist_le_of_le hx hy <| (Emetric.edist_le_diam_of_mem hx hy).trans hd
+theorem ediam_image_le_of_le (hf : HolderOnWith C r f s) {d : ℝ≥0∞} (hd : EMetric.diam s ≤ d) :
+    EMetric.diam (f '' s) ≤ C * d ^ (r : ℝ) :=
+  EMetric.diam_image_le_iff.2 fun x hx y hy =>
+    hf.edist_le_of_le hx hy <| (EMetric.edist_le_diam_of_mem hx hy).trans hd
 #align holder_on_with.ediam_image_le_of_le HolderOnWith.ediam_image_le_of_le
 
 theorem ediam_image_le (hf : HolderOnWith C r f s) :
-    Emetric.diam (f '' s) ≤ C * Emetric.diam s ^ (r : ℝ) :=
+    EMetric.diam (f '' s) ≤ C * EMetric.diam s ^ (r : ℝ) :=
   hf.ediam_image_le_of_le le_rfl
 #align holder_on_with.ediam_image_le HolderOnWith.ediam_image_le
 
 theorem ediam_image_le_of_subset (hf : HolderOnWith C r f s) (ht : t ⊆ s) :
-    Emetric.diam (f '' t) ≤ C * Emetric.diam t ^ (r : ℝ) :=
+    EMetric.diam (f '' t) ≤ C * EMetric.diam t ^ (r : ℝ) :=
   (hf.mono ht).ediam_image_le
 #align holder_on_with.ediam_image_le_of_subset HolderOnWith.ediam_image_le_of_subset
 
 theorem ediam_image_le_of_subset_of_le (hf : HolderOnWith C r f s) (ht : t ⊆ s) {d : ℝ≥0∞}
-    (hd : Emetric.diam t ≤ d) : Emetric.diam (f '' t) ≤ C * d ^ (r : ℝ) :=
+    (hd : EMetric.diam t ≤ d) : EMetric.diam (f '' t) ≤ C * d ^ (r : ℝ) :=
   (hf.mono ht).ediam_image_le_of_le hd
 #align holder_on_with.ediam_image_le_of_subset_of_le HolderOnWith.ediam_image_le_of_subset_of_le
 
 theorem ediam_image_inter_le_of_le (hf : HolderOnWith C r f s) {d : ℝ≥0∞}
-    (hd : Emetric.diam t ≤ d) : Emetric.diam (f '' (t ∩ s)) ≤ C * d ^ (r : ℝ) :=
+    (hd : EMetric.diam t ≤ d) : EMetric.diam (f '' (t ∩ s)) ≤ C * d ^ (r : ℝ) :=
   hf.ediam_image_le_of_subset_of_le (inter_subset_right _ _) <|
-    (Emetric.diam_mono <| inter_subset_left _ _).trans hd
+    (EMetric.diam_mono <| inter_subset_left _ _).trans hd
 #align holder_on_with.ediam_image_inter_le_of_le HolderOnWith.ediam_image_inter_le_of_le
 
 theorem ediam_image_inter_le (hf : HolderOnWith C r f s) (t : Set X) :
-    Emetric.diam (f '' (t ∩ s)) ≤ C * Emetric.diam t ^ (r : ℝ) :=
+    EMetric.diam (f '' (t ∩ s)) ≤ C * EMetric.diam t ^ (r : ℝ) :=
   hf.ediam_image_inter_le_of_le le_rfl
 #align holder_on_with.ediam_image_inter_le HolderOnWith.ediam_image_inter_le
 
@@ -224,9 +224,9 @@ protected theorem continuous (hf : HolderWith C r f) (h0 : 0 < r) : Continuous f
 #align holder_with.continuous HolderWith.continuous
 
 theorem ediam_image_le (hf : HolderWith C r f) (s : Set X) :
-    Emetric.diam (f '' s) ≤ C * Emetric.diam s ^ (r : ℝ) :=
-  Emetric.diam_image_le_iff.2 fun x hx y hy =>
-    hf.edist_le_of_le <| Emetric.edist_le_diam_of_mem hx hy
+    EMetric.diam (f '' s) ≤ C * EMetric.diam s ^ (r : ℝ) :=
+  EMetric.diam_image_le_iff.2 fun x hx y hy =>
+    hf.edist_le_of_le <| EMetric.edist_le_diam_of_mem hx hy
 #align holder_with.ediam_image_le HolderWith.ediam_image_le
 
 end HolderWith

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

@@ -42,7 +42,7 @@ variable {X Y Z : Type _}
 
 open Filter Set
 
-open NNReal Ennreal Topology
+open NNReal ENNReal Topology
 
 section Emetric
 
@@ -85,7 +85,7 @@ theorem holderOnWith_univ {C r : ℝ≥0} {f : X → Y} : HolderOnWith C r f uni
 @[simp]
 theorem holderOnWith_one {C : ℝ≥0} {f : X → Y} {s : Set X} :
     HolderOnWith C 1 f s ↔ LipschitzOnWith C f s := by
-  simp only [HolderOnWith, LipschitzOnWith, NNReal.coe_one, Ennreal.rpow_one]
+  simp only [HolderOnWith, LipschitzOnWith, NNReal.coe_one, ENNReal.rpow_one]
 #align holder_on_with_one holderOnWith_one
 
 alias holderOnWith_one ↔ _ LipschitzOnWith.holderOnWith
@@ -118,7 +118,7 @@ theorem edist_le (h : HolderOnWith C r f s) {x y : X} (hx : x ∈ s) (hy : y ∈
 
 theorem edist_le_of_le (h : HolderOnWith C r f s) {x y : X} (hx : x ∈ s) (hy : y ∈ s) {d : ℝ≥0∞}
     (hd : edist x y ≤ d) : edist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
-  (h.edist_le hx hy).trans (mul_le_mul_left' (Ennreal.rpow_le_rpow hd r.coe_nonneg) _)
+  (h.edist_le hx hy).trans (mul_le_mul_left' (ENNReal.rpow_le_rpow hd r.coe_nonneg) _)
 #align holder_on_with.edist_le_of_le HolderOnWith.edist_le_of_le
 
 theorem comp {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : HolderOnWith Cg rg g t) {Cf rf : ℝ≥0}
@@ -126,8 +126,8 @@ theorem comp {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : HolderOnWith Cg r
     HolderOnWith (Cg * Cf ^ (rg : ℝ)) (rg * rf) (g ∘ f) s :=
   by
   intro x hx y hy
-  rw [Ennreal.coe_mul, mul_comm rg, NNReal.coe_mul, Ennreal.rpow_mul, mul_assoc, ←
-    Ennreal.coe_rpow_of_nonneg _ rg.coe_nonneg, ← Ennreal.mul_rpow_of_nonneg _ _ rg.coe_nonneg]
+  rw [ENNReal.coe_mul, mul_comm rg, NNReal.coe_mul, ENNReal.rpow_mul, mul_assoc, ←
+    ENNReal.coe_rpow_of_nonneg _ rg.coe_nonneg, ← ENNReal.mul_rpow_of_nonneg _ _ rg.coe_nonneg]
   exact hg.edist_le_of_le (hst hx) (hst hy) (hf.edist_le hx hy)
 #align holder_on_with.comp HolderOnWith.comp
 
@@ -143,7 +143,7 @@ protected theorem uniformContinuousOn (hf : HolderOnWith C r f s) (h0 : 0 < r) :
   by
   refine' Emetric.uniformContinuousOn_iff.2 fun ε εpos => _
   have : tendsto (fun d : ℝ≥0∞ => (C : ℝ≥0∞) * d ^ (r : ℝ)) (𝓝 0) (𝓝 0) :=
-    Ennreal.tendsto_const_mul_rpow_nhds_zero_of_pos Ennreal.coe_ne_top h0
+    ENNReal.tendsto_const_mul_rpow_nhds_zero_of_pos ENNReal.coe_ne_top h0
   rcases ennreal.nhds_zero_basis.mem_iff.1 (this (gt_mem_nhds εpos)) with ⟨δ, δ0, H⟩
   exact ⟨δ, δ0, fun x hx y hy h => (hf.edist_le hx hy).trans_lt (H h)⟩
 #align holder_on_with.uniform_continuous_on HolderOnWith.uniformContinuousOn
@@ -242,10 +242,10 @@ namespace HolderWith
 theorem nndist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ≥0} (hd : nndist x y ≤ d) :
     nndist (f x) (f y) ≤ C * d ^ (r : ℝ) :=
   by
-  rw [← Ennreal.coe_le_coe, ← edist_nndist, Ennreal.coe_mul, ←
-    Ennreal.coe_rpow_of_nonneg _ r.coe_nonneg]
+  rw [← ENNReal.coe_le_coe, ← edist_nndist, ENNReal.coe_mul, ←
+    ENNReal.coe_rpow_of_nonneg _ r.coe_nonneg]
   apply hf.edist_le_of_le
-  rwa [edist_nndist, Ennreal.coe_le_coe]
+  rwa [edist_nndist, ENNReal.coe_le_coe]
 #align holder_with.nndist_le_of_le HolderWith.nndist_le_of_le
 
 theorem nndist_le (hf : HolderWith C r f) (x y : X) :

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

I removed some of the tactics that were not used and are hopefully uncontroversial arising from the linter at #11308.

As the commit messages should convey, the removed tactics are, essentially,

push_cast
norm_cast
congr
norm_num
dsimp
funext
intro
infer_instance

@@ -236,7 +236,6 @@ namespace HolderWith
 
 theorem nndist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ≥0} (hd : nndist x y ≤ d) :
     nndist (f x) (f y) ≤ C * d ^ (r : ℝ) := by
-  norm_cast
   rw [← ENNReal.coe_le_coe, ← edist_nndist, ENNReal.coe_mul, ←
     ENNReal.coe_rpow_of_nonneg _ r.coe_nonneg]
   apply hf.edist_le_of_le

Normalising to naming convention rule number 6.

@@ -52,7 +52,7 @@ def HolderWith (C r : ℝ≥0) (f : X → Y) : Prop :=
 #align holder_with HolderWith
 
 /-- A function `f : X → Y` between two `PseudoEMetricSpace`s is Hölder continuous with constant
-`C : ℝ≥0` and exponent `r : ℝ≥0` on a set `s : set X`, if `edist (f x) (f y) ≤ C * edist x y ^ r`
+`C : ℝ≥0` and exponent `r : ℝ≥0` on a set `s : Set X`, if `edist (f x) (f y) ≤ C * edist x y ^ r`
 for all `x y ∈ s`. -/
 def HolderOnWith (C r : ℝ≥0) (f : X → Y) (s : Set X) : Prop :=
   ∀ x ∈ s, ∀ y ∈ s, edist (f x) (f y) ≤ (C : ℝ≥0∞) * edist x y ^ (r : ℝ)

Following on from previous gcongr golfing PRs #4702 and #4784.

This is a replacement for #7901: this round of golfs, first introduced there, there exposed some performance issues in gcongr, hopefully fixed by #8731, and I am opening a new PR so that the performance can be checked against current master rather than master at the time of #7901.

@@ -114,7 +114,7 @@ theorem edist_le (h : HolderOnWith C r f s) {x y : X} (hx : x ∈ s) (hy : y ∈
 
 theorem edist_le_of_le (h : HolderOnWith C r f s) {x y : X} (hx : x ∈ s) (hy : y ∈ s) {d : ℝ≥0∞}
     (hd : edist x y ≤ d) : edist (f x) (f y) ≤ (C : ℝ≥0∞) * d ^ (r : ℝ) :=
-  (h.edist_le hx hy).trans (mul_le_mul_left' (ENNReal.rpow_le_rpow hd r.coe_nonneg) _)
+  (h.edist_le hx hy).trans <| by gcongr
 #align holder_on_with.edist_le_of_le HolderOnWith.edist_le_of_le
 
 theorem comp {Cg rg : ℝ≥0} {g : Y → Z} {t : Set Y} (hg : HolderOnWith Cg rg g t) {Cf rf : ℝ≥0}

Also rename dimH_image_le_of_locally_lipschitz_on to dimH_image_le_of_locally_lipschitzOn.

@@ -89,7 +89,7 @@ alias ⟨_, LipschitzOnWith.holderOnWith⟩ := holderOnWith_one
 
 @[simp]
 theorem holderWith_one {C : ℝ≥0} {f : X → Y} : HolderWith C 1 f ↔ LipschitzWith C f :=
-  holderOnWith_univ.symm.trans <| holderOnWith_one.trans lipschitz_on_univ
+  holderOnWith_univ.symm.trans <| holderOnWith_one.trans lipschitzOn_univ
 #align holder_with_one holderWith_one
 
 alias ⟨_, LipschitzWith.holderWith⟩ := holderWith_one

@@ -84,7 +84,7 @@ theorem holderOnWith_one {C : ℝ≥0} {f : X → Y} {s : Set X} :
   simp only [HolderOnWith, LipschitzOnWith, NNReal.coe_one, ENNReal.rpow_one]
 #align holder_on_with_one holderOnWith_one
 
-alias holderOnWith_one ↔ _ LipschitzOnWith.holderOnWith
+alias ⟨_, LipschitzOnWith.holderOnWith⟩ := holderOnWith_one
 #align lipschitz_on_with.holder_on_with LipschitzOnWith.holderOnWith
 
 @[simp]
@@ -92,7 +92,7 @@ theorem holderWith_one {C : ℝ≥0} {f : X → Y} : HolderWith C 1 f ↔ Lipsch
   holderOnWith_univ.symm.trans <| holderOnWith_one.trans lipschitz_on_univ
 #align holder_with_one holderWith_one
 
-alias holderWith_one ↔ _ LipschitzWith.holderWith
+alias ⟨_, LipschitzWith.holderWith⟩ := holderWith_one
 #align lipschitz_with.holder_with LipschitzWith.holderWith
 
 theorem holderWith_id : HolderWith 1 1 (id : X → X) :=

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

This has nice performance benefits.

@@ -35,7 +35,7 @@ Hölder continuity, Lipschitz continuity
  -/
 
 
-variable {X Y Z : Type _}
+variable {X Y Z : Type*}
 
 open Filter Set
 

• 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 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module topology.metric_space.holder
-! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.MetricSpace.Lipschitz
 import Mathlib.Analysis.SpecialFunctions.Pow.Continuity
 
+#align_import topology.metric_space.holder from "leanprover-community/mathlib"@"0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8"
+
 /-!
 # Hölder continuous functions
 

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -254,8 +254,8 @@ theorem nndist_le (hf : HolderWith C r f) (x y : X) :
 theorem dist_le_of_le (hf : HolderWith C r f) {x y : X} {d : ℝ} (hd : dist x y ≤ d) :
     dist (f x) (f y) ≤ C * d ^ (r : ℝ) := by
   lift d to ℝ≥0 using dist_nonneg.trans hd
-  rw [dist_nndist] at hd⊢
-  norm_cast  at hd⊢
+  rw [dist_nndist] at hd ⊢
+  norm_cast at hd ⊢
   exact hf.nndist_le_of_le hd
 #align holder_with.dist_le_of_le HolderWith.dist_le_of_le